Mordred

Another question can be : Will planning a route with numerous customers assigned to the route maximize delivery time as opposed to fewer customers on the same route. In essence can better route planning to get as many customers on the same trip decrease average delivery times. Rather than try to prove your boss wrong, it may be more beneficial to seek ways other alternatives to decrease average delivery times. Look into the factors carefully that cause delays, those could even include metro transit systems as buses can slow things down depending on how the bus stops are designed. Also talk to each driver and see if they have recommendations on which routes to take and the problems they face when running those routes. Though to be clear I would imagine some of these factors you may well already be looking into. It is always a better approach to admit an issue, look into what is causing the issue and presenting viable solutions to the issue.

Here this will help on the Universe geometry question. Recall I mentioned parallel transport of light beams above. The curve is the path those light beams follow. They follow this path from another principle in Physics that being the path of least action. Which correlates how potential energy and kinetic energy (defined above) affect the geodesic equations provided on the second page. The first page describes the mass density distribution in how they are used to define the curvature (mass density curves spacetime). The slices seen on page two are simply the manifold with which the light paths follow. That manifold only depends on the beginning and end points of the light path (wold-line). http://cosmology101.wikidot.com/universe-geometry http://cosmology101.wikidot.com/geometry-flrw-metric/ Now onto the time dilation aspects, various fields can cause delays in how fast various signals and processes occur, the term we use to describe this is typically the mass term. This term also represents how strongly a particle couples to a field (binding energy) in a higher gravity potential the binding energy of all particles is stronger so it requires greater energy to go from point a to point b. The same occurs when the particle itself gains energy it also gains greater binding energy. So in each case either the field or the particle has a higher binding energy which slows down the rate f information exchange between particles. As time is treated as a coordinate under spacetime it has a unit of length defined by [latex] ct[/latex]. So due to the binding energy this interval will decrease in length (Lorentz length contraction) due to the mass binding energy. This is time dilation in a nutshell, the length of the time interval in units of length decreases. So the particles take longer to travel the same distance to react with other particles. However keep in mind I am avoiding a lot of the math, and as such having to describe the processes above as simply as possible. When you get into the math and how vector relations transform under spacetime curvature the above becomes far clearer. Here this may help, this article details spacetime diagrams and will also help better understand the animations posted by Janus. There is extremely minimal mathematics in it as it doesn't include the transformation formulas of Lorentz just describes them under graph. https://web.stanford.edu/~oas/SI/SRGR/notes/SRGRLect3_2015.pdf this link explains a bit better the correlation between these diagrams and how they correlate to clock ticks with different observers http://www.slimy.com/~steuard/teaching/classes/spacetime.pdf explanation with the relevant math https://www.farmingdale.edu/faculty/peter-nolan/pdf/relativity/Ch03Rel.pdf

Let me ask you a pertinent question. The field of physics has used Newton's laws long before the development of GR and SR by Einstein. Newton's laws was so strongly believed in that it has lasted the test of time from the 16th century onward. Now if time dilation could be explained away with the use of forces, then why did Einstein ever need to develop SR and GR to account for measurement data that Newton's laws could not accurately predict despite the expertise of all the scientists at the time ? Do you not think they didn't try ? Many of them have far greater math skills than anyone on this forum, you can bet they looked at all possible means of applying Newton's laws to account for time dilation. You might want to consider that

Oh its not foolish at all to listen to someone who has a PH.D in physics over your assertions with no peer reviewed references. So you might try a better approach. Especially since you are now claiming conservation law violations as being viable. I can pretty much guarantee just from reading this thread that you cannot provide any of the relevant mathematics either. So lets start with your first claim that Swansont's first post was wrong that being superposition. Lets see https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_Conceptual_Physics_(Crowell)/11%3A_Electromagnetism/11.2_Magnetic_Fields_by_Superposition http://www.bartol.udel.edu/~seckel/courses/Physics 208/Labs/lab7.pdf https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-007-electromagnetic-energy-from-motors-to-lasers-spring-2011/lecture-notes/MIT6_007S11_lec08.pdf https://www.e-fermat.org/files/articles/153b46caff3555.pdf https://ocw.mit.edu/resources/res-6-001-electromagnetic-fields-and-energy-spring-2008/chapter-8/08.pdf wow what a commonly recognized phenomena that you claim is wrong....

It would not be precisely the same just from this descriptive which cannot account for why different observers will see time running differently when comparing clocks. The local observer in the same reference frame will se time running normally while the distant observer will see the clock of the local observer running different. If the clock rate is strictly determined by the amount of force on the clock then both observers will see the same rate when observing the local clock. Which Eise above is also mentioning...in cross post.

Do you have anything further ie a reference of some kind ? Considering this directly applies to color conservation

No the problem is that you are confusing the measuring tool to time. Time is simply an assignment to a property called rate of change. The tools we use to measure rates simply have regular intervals. They simply provide a scale of reference to the rate of change. They do not define the term time all this effort of clock comparisons has been absolutely pointless in defining time. The tools used to measure a quantity never defines the quantity being measured. for example a thermometer does not define what a temperature is or what causes temperature. Clocks do not define time nor does a ruler define the property of length. If a color changes at a given rate we could use that as a clock.... not all change requires motion, decay rates of particles for example which has been mentioned. ie muon decay... of course it would actually be nice to see the mathematics that can describe what we observe as time dilation under your model and see where it truly deviates from GR. Quite frankly no verbal argument no matter how accurate will overturn a predictive model (which requires mathematics). One requires the ability to test any model via its mathematics and then compares them to observation. Simply because your model cannot account for muons does not mean muons isn't a piece of evidence that time doesn't require mechanical components as a basis against your mechanical components of your clock analogies to motion. Arbitrarily ignoring other pieces of evidence that a theory may be wrong isn't going to fly. (though without the mathematics you don't even have a theory but nothing more than a hypothesis ) Not all clocks require a relation to motion to operate. For example the decay rates of atomic clocks. Another piece of evidence that time dilation occurs outside of clocks, is gravitational redshift...

Good point and example thanks.

Lets say you have some event that results in two entangled electrons. Now with electrons you only have two possible polarization states. Spin up and spin down. Furthermore you must also comply with conservation of spin. Prior to measurement the superposition which as Studiot mentioned is also in classical theory however isn't restricted to physics either. It is a statistics term so can be used in any statistical analysis. The superposition in the above case is that prior to measurement of a given particle it can be either spin up or down. However once you measure the particle the other must be the opposite for the reasons above. Now what causes entanglement? Well this is far trickier to answer. However I will take a reasonable stab at it. Entanglement can occur whenever you have some viable means to establish some degree of correlation function between any two objects. Once you have a correlation you gain a means to make a reasonable prediction of the other object via a measurement of the first object. The processes to establish a correlation function can vary and do not necessarily involve an interaction between the two objects

Handy videos and a good work up Janus No worries Sinnie take your time to absorb the material.

mental image of being an observer near c. Suddenly yelling "Geez its bright in here, turn off the lights ! '. Suddenly followed by mental image of a spacecraft travelling at those speeds vs oncoming space debris lol you can visualize the rest...

Anyways that should provide a good direction of approach. I've watched your other thread though I have to catch up to where your at with it when I get time lol to know how serious you approach a topic and have a measure of your skills in that topic. Quite frankly its fun to study with all the relevancy to the topic. Hope this helps... note to above yes graviton as a gauge boson would likely be massless. One still need to correlate the possibility under group. One also sees the [latex]D_\mu[/latex] above this is the Differential matrix , and it correlates the difference between the covariant and contravariant terms. It will change in values as per the application applied in particular in different field treatments.

Yes the four momentum is instrinsic in GR however it requires the use of indices that follow the Einstein summation for covariant and contravariant terms. see here to see how this can apply in the above https://en.wikipedia.org/wiki/Four-momentum the remainder of the equation that you are trying to fill in the relativity section is in the 4 momentum, 4 force and 3 velocity format. This way you have the same coordinate relations throughout the equation. Though it is assumed direction of motion would be in the [latex] x^1 [/latex] direction this isn't always the case. Now I am going to ask a related question :How much affect does gravity play on the path integral relations that the first equation describes in its particle to particle scattering ? (side note the other portions are already Lorentz invariant). https://en.wikipedia.org/wiki/Lorentz_covariance https://gdenittis.files.wordpress.com/2016/04/ayudantiavi.pdf see here for further details on the Lorentz group and Lorentz invariance with ( you will see that the RHS of the [latex]\underbrace{\mathbb{R}}_{relativity}[/latex] is already Lorentz invariant in the terms. (side note QFT does this via the Klein Gordon equation as opposed to the Schrodinger ) Which brings to mind another question one can ask. Why was the [latex]\underbrace{\mathbb{R}}_{relativity}[/latex] left unfilled ? personally my feelings on this is that we haven't got a working quantum theory of gravity that doesn't suffer the renormalization problem sufficient to extrapolate the hypothetical graviton interactions (the graviton isn't yet part of the standard model of particles). Although if such a graviton could be possible with the spin 2 being the more likely (under research) spin 0 is also plausible. This in turn affects the degrees of freedom required to determine the gauge group representations. One must account for all effective degrees of freedom. see here for an example equation 36 for an example of the QCD Langrangian. https://cds.cern.ch/record/935622/files/p27.pdf This articles has pertinent details to understand a large portion of the equation in the OP. (the last article should provide a sufficient answer to the question of whether your Langrangian attempts suffice). Keep in mind the line from the introductory, the remainder of the article should hone in on how complex it really is.... In final note an effective Langrangian for the relativity portion should correlate to all the effective degrees of freedom that define the spin 2 statistics. A source of observational evidence is the graviton waves (quadrupolar ). So I would start here. [latex] g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}[/latex] if you research these groups you will find much of the work in terms of the Langrenians is already done. see this example on massive spin 2. gives other spin examples also https://arxiv.org/pdf/hep-th/0609170.pdf equation 21. Which reflects that the [latex]\underbrace{\mathbb{R}}_{relativity}[/latex] will correspond to something similar to this. [latex]\underbrace{|D_{\mu} D_{\nu}|\upsilon_{\alpha}}_{relativity}[/latex] ROUGH EXAMPLE ONLY>>>>one lack being massless particles...

Measurements are a representation of what we can measure, so those representations are a means to describe what dynamics we interact with. Time is a representative term for a property we define as a rate... in so far as to rate of change. Those changes do not necessarily require movement, they more than often do however one must have two states to compare to get an interval. So as a property of everyday objects changing and time representing the rate of that change then time is definitely real. It is however not something that can exist on its own. It is a property of the rate of change in any physical process.

This is one of the trickier questions that is asked by everyone (literally that takes the time to understand relativity). What is the physics behind time dilation ie What causes time dilation ? This may be expressed in numerous ways and some rather unusual methods, however it is one of the more difficult concepts to grasp. So I will endeavour to supply a Heuristic explanation. As you know in Newton's laws of inertia we have a key set of relations, the 3 laws of inertia. Now many new to relativity posters commonly think these laws have been superseded by relativity which is incorrect. In truth those laws are fundamental to understanding time dilation and how time dilation works. Now I am often heard stressing the importance of paying attention to the definitions. This situation is one of the main reasons I do so. You've probably know that mass is involved with regards to time dilation. The two types of mass we are interested in is inertial mass and gravitational mass. However the common mistake is forgetting that mass in physics is defined as " Resistance to inertia change " as per those three laws I mentioned earlier. Another key definition often missed is that energy is "ability to perform work " Now if you think about those two definitions this will give you a more accurate picture of the equation [latex] E=mc^2[/latex] put into a direct English translation. "The ability to perform work is directly proportional to the objects resistance to inertia change multiplied by the square of constant c." Now we have two types of mass that you described above. You have the observer on earth and the observer in a spacecraft. Each has a different type of mass. Gravitational mass and inertial mass. Each form of mass is a measure of resistance to inertia change however the causes is different in so far as which type of energy supplies the work to supply the resistance. ( for this I will apply the term potential energy to the gravitational mass terms and kinetic energy to inertial mass terms ). Now we need to examine another key term " Spacetime ". This is distinct from our 3d Galilean view of volume, in so far as we add a variable time dimension. so now our familiar 3d universe is now a 4d universe. [latex]{x,y,z}\rightarrow {ct,x,y,z}[/latex] where the ct coordinate gives us a unit of vector length. This places it on the same playing field as the vectors commonly learn in classical trigonometry. However another feature of importance is in defining an interval. Spacetime curvature I will get into later. Now here is where we get into the term inertial frames, in SR the primary transformations involve inertial reference frames. Now lets carefully define what is an inertial frame. As per the above it is a frame where the events are at constant velocity ie freefall. There is no acceleration in either magnitude or direction. As per the laws of inertia above. It is also a frame where our vector mathematics work as per the Galilean transforms. If you have acceleration we must account for this in other ways in gauge symmetry terms a rotation called rapidity, suffice it to say additional calculations. Ok so far ? lets hope so and push on to why I stressed the above. we can simplify the above by another key relation under relativity "the equivalence principle" [latex] m_g=m_i [/latex] gravitational mass is equivalent to the inertial mass. So now we can put all this together. In the case of gravitational mass the location (potential energy In physics, is the energy held by an object because of its position relative to other objects". ) in this case the observer on Earth compared to the location of the spaceship. However what does this energy describe in this case ? well it describes the ability to perform work in terms of the binding energy at that location. The mass term at that location describes the locations ability to resist inertia change. If were are describing multiple locations in roughly the same potential we can define this under spacetime coordinates. (spacetime field). When conditions are similar enough that Newtons laws apply without significant time dilation we can use our everyday vector addition we grew up with ie Pythagoras theory without adding any additional terms or ratios of change. The resistance due to mass directly affects the time coordinate in terms of the interval {ct} recall I mentioned vectors ? I also mentioned Newtons laws of inertia. key formula being applied [latex] f=ma[/latex] or any equivalent formula such as the coupling strength of a field. They are in essence the same except the fields involved. It takes more energy to achieve the same distance covered, the mass term is higher so 1 Newton of force will move the object less in a higher potential. This applies to all processes in the same potential conditions, it affects the rate at which all particles in the immediate locale interact. (hence the twin aging, different clock rates, rates of decay etc.) You should be able to formulate how inertial mass relates to the mass in terms of its binding energy to the time interval used in coordinate form. It should also help understand why the Lorentz transforms apply to both the time axis and the x axis where the object is described as moving away from or towards the observer. see here for the transforms. Each transform describes the interval length (defined as a vector ) change between reference frames due to the mass terms influence. recall as an object gains inertia it gains inertia mass... Now spacetime curvature as promised. Think of this as a coordinate map with axis [latex] ct,x,y,z[/latex] when you have no curvature terms then Pythagous theory applies in the triangle identities. Angles on triangles will add up to 180 degrees. Our regular everyday vector commutation rules apply. We also have no appreciable time dilation so our coordinate axis are all identical and 90 degrees from one another. When you get time dilation affects however this no longer applies, the angles no longer add up to 180 degrees, this is due to the length contraction and time interval contraction. It is now skewed to the original symmetry (skew symmetric}. the amount of skew depends on those transforms in that link above. Now spacetime under GR describes the freefall condition (constant inertia). This freefall condition has a further detail that of parallel transport. Instead of having 1 object drop , drop two or more. In the case of the Earth the centre of mass is at the centre of the Earth (roughly). So these dropped objects no longer fall parallel to each other they converge upon one another as they approach the centre of mass. Now depending on arbitrary choice we can say this is positive or negative curvature but that's really an arbitrary choice. The position the two dropped objects will diverge in the opposite case. granted the above is largely a simplification however all the essential principles are there. The last example is an example of tidal force under GR. One of the things to remember is that under GR objects follow the shortest spacetime path, that path is mathematically defined from the above under a freefall symmetry basis. The curvature terms apply to the particle path or its worldline. Usually denoted by the separation distance [latex] ds^2[/latex] this will contain the details on how those coordinate axis transform in regard to one another in describing the freefall world line of a particle. The convergence and divergence of said curvature will affect the parallel transport of multiple particles. An everyday analogy of the above, think of time dilation in much the same way as signal propagation delay in electronic circuits. Where the signal can be delayed as it passes by an EM field in the right alignment. The physics behind the two is very similar. the constant c isn't simply the speed of light it is also the restriction of all information exchanges between any two points or particles.

! Moderator Note This thread has some excellent questions that while they are essential in cosmology, those questions are better suited for the Relativity forum. I will move the thread there, though I may also participate.

As this is related to how one describes a particle and StingyJunkie's wavecicle reference I will just post a link to another thread where I had posted the details below. https://www.scienceforums.net/topic/118004-hypothetically-can-empty-space-“slice”-through-a-solid-object/?do=findComment&comment=1092620 As Swansont mentioned thinking of particles as little corpuscular balls is the wrong descriptive of a particle. See the link for further details

HUP doesn't depend on measurement to be a cause, it is a fundamental constraint that is present even without the object being measured.

going straight from Newton to a relativistic Langrangian by simply adding gamma isn't sufficient by itself. You must also preserve Lorentz invariance which will require the use of proper time given as [latex]\tau [/latex]. Recall different observers will measure the variant quantities differently this includes time. Even then its not complete, as you will need to include the 4 momentum and 4 velocity. See here, it mentions some of the issues I didn't https://en.wikipedia.org/wiki/Relativistic_Lagrangian_mechanics Another related reference here http://fma.if.usp.br/~amsilva/Livros/Zwiebach/chapter5.pdf A primary goal is to ascertain from the Euler-Langrangian the geodesic equation. http://people.uncw.edu/hermanr/GRcosmo/euler-equation-geodesics.pdf This wiki link has a good breakdown of how to employ the Euler Langrangian to derive the geodesic https://en.wikipedia.org/wiki/Geodesics_in_general_relativity

A simple layman way to think of the equation of state is as an energy density to pressure term ratio, via the [latex]w=\frac{\rho}{p}[/latex]. The proofs of each is a good course of study and a good cosmology textbook will include those proofs with the corresponding wavelengths (particularly in the case of radiation). If you like I can check my database for some decent articles on the topic as it is fundamental to understanding the FLRW fluid equation and the deceleration equation. I'm aware your GR isn't strong so in terms of the stress tensor I will try to find a more Newtonian approximation

use latex not just tex as the command this forum requires it fully. Hence on the cosmocalc you need to change tex to latex. Yes the matter density is both as per the methodology of the FRW metric, for individual particle contributions you need to step into the statistics I mentioned earlier. Recall under the FRW metric its based on the effective equation of states for matter w=0 which encompasses all on relativistic species. Neutrinos has the radiation equation of state however as it is relativistic along with photons. PS your FRW skills have greatly improved since I first helped you when you first joined well done and keep it up I've granted a +2 for the considerable improvement

here is the formula [latex]H = H_0 \left(\Omega_\Lambda + (1-\Omega) (z+1)^2 + \Omega_m (z+1)^3 + \Omega_r (z+1)^4\right)^{0.5}[/latex] other relevant formulas see here https://www.physicsforums.com/insights/lightcone7-tutorial-part-iii-things-computed/ at least those used in the calculator

kk good email has been sent as I am curious myself if he's going to update this version. It is possible to latex the results here if you look through the small tex output and change tex to latex where required at begin and end or the array commands. Demo [latex]{\small\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline z&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&V_{gen}/c&H(t)&rho, kg/m^3 \\ \hline 1090.000&0.000372&0.000627&45.340&0.042&0.0567&21.121&1.561e+6&5.028e-18\\ \hline 339.033&0.002490&0.003948&44.193&0.130&0.1786&10.753&2.477e+5&1.266e-19\\ \hline 104.978&0.015284&0.023444&42.024&0.397&0.5527&5.811&4.172e+4&3.591e-21\\ \hline 32.030&0.090052&0.136169&38.065&1.152&1.6534&3.210&7.182e+3&1.065e-22\\ \hline 9.295&0.521890&0.784445&30.935&3.005&4.6122&1.788&1.247e+3&3.208e-24\\ \hline 2.209&2.976146&4.372203&18.268&5.694&10.8504&1.029&2.237e+2&1.033e-25\\ \hline 0.000&13.799968&14.437487&0.000&0.000&16.5313&1.000&6.774e+1&9.470e-27\\ \hline -0.688&32.967504&17.251750&11.156&35.795&17.2927&2.685&5.669e+1&6.632e-27\\ \hline -0.868&47.865307&17.359119&14.270&108.178&17.3591&6.305&5.634e+1&6.551e-27\\ \hline -0.944&62.796207&17.367429&15.591&279.265&17.3674&14.891&5.631e+1&6.544e-27\\ \hline -0.976&77.729642&17.368136&16.150&683.511&17.3681&35.182&5.631e+1&6.544e-27\\ \hline -0.990&92.663443&17.368093&16.387&1638.657&17.3681&83.127&5.631e+1&6.544e-27\\ \hline \end{array}}[/latex]

I don't think we can at least not without deriving the S-eq matter radiation equality value. I can however see if I can ask Jorrie and Cobert if they are working on the 2018 results for programming the calculator. The primary programmer being Cobert myself and Marcus helped in so far as writing the manuals and adding suggestions and methodologies to make it easier for others to understand. Primary example using Gyrs instead of Mpc. Marcus found people better understood distances in light-years as opposed to parsecs. Found his latest version for the 2015 Planck results I will adjust my signature to reflect the newer version, sent an email to see if Jorrie is working on the 2018 http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7-2017-1/LightCone_Ho7.html lol newer version will take me a bit to get used to lmao

I wouldn't place too much faith on this paper in and of itself, while its findings are interesting I personally feel it isn't conclusive enough by itself to overturn the constant of Lambda. It is noteworthy but it will most likely take further studies to test its robustness. Over the years I have seen numerous papers suggesting findings of an evolving Lambda but they are in essence insufficient in the face of the evidence for the constancy of Lambda. grr there was something I should be remembering at roughly Z=4.5 to 5.5, I'll have to see if I can remember what it was but if I recall it had to do with apparent luminosity. Anyways that's just my inside voice typing... Found a related in regards to my inside voice an older study of the QLF quasar luminosity function at z>5, this papers discusses some of the corrections that need to apply in some of the findings they had. In essence trying to solve why two different findings of the same quasars had two different results in the Lyman alpha forest findings. https://iopscience.iop.org/article/10.1088/0004-637X/756/2/160/pdf