Mordred

there is also the mass to luminosity formula https://en.m.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation Intensity is the amount of radiation per unit volume as a function of radius to the observer [latex]I=\frac{L}{4\pi r^2}[/latex] Not positive which distance ladder rung they consider the most inaccurate but judging from the questions I would surmise the inverse square law of luminosity. Reason being is that is only locally accurate where expansion has little influence.

I for one cannot think of any biological reason for one to be more advanced than the other. Quite frankly technology development rate deviations is due to cultural environment change. (wars, religion, etc ) not the biological differences.

Ok lets stick with "observer rest frame" [latex]a^2+b^2=c^2 [/latex] time within a reference frame is absolute. Rest frame only... The spacetime geometry is Euclidean flat. There is no spacetime curvature. All the Newtonian physics apply. Optical illusions due to distance change. However the same is true in Observer B's rest frame. Within a rest frame all rules of Pythagoras geometry and trig apply. Time is normalized as 1. These two geometry spacetime conditions are physically Real in every sense.( Geometry relations, don't treat spacetime as a material thing) It isn't until you compare Euclidean geometry A to Geometry B and vise versa do you realize the two do not match. Time and the x axis are distinctly different. So we have to translate the two distinct spacetime Euclidean geometries. This is what relavity allows us to do. Your rest frame geometry compared to my rest frame geometry every observer has his own rest frame Euclidean geometry this is real in every sense. So it isnt that different observers change anothers rest frame geometry. That is false... It is the comparison of my rest frame compared to your rest frame that changes. Not the rest frames itself. Spacetime itself is not absolute. Different observers has his own Euclidean rest frame with different lengths x axis only and time This is real it is also what people have a hard time accepting... An outside observer doesn't change my rest frame. It is the comparison between the two reference rest frames that changes.

There is a distinction people miss. They tend to focus on the object. Lets simplify this. Take a ruler with scale 1:1 now take another ruler B with scale 1:1/2. now observer A uses ruler A. Observer B uses ruler B. Ruler B matches his Euclidean spacetime geometry. Ruler A matches Observer A's Euclidean geometry. They pass the same object to each other from one location to the other. A measures a 1 foot cube. B also measures a one foot cube. How did this happen? did the object change or did spacetime geometry itself change?

Science doesn't consider one set of measurements as being more real than the other set of measurements. They are not saying the object shrinks in actuality due to perception. They are stating the measurement of that object is equally valid according to an observer. However in this case the spacetime is Euclidean flat. No dilation Length contraction and time dilation we have proved to have very real consequences. Different age rates for example. How you measure the different rates depends on the observer. In a sense the spacetime geometry itself has really changed. This is the aspect that confuses people. Particularly time dilation. In those Newtonian examples the deviations on measurements is easily understood as a distance relationship. Follows from Pythagoras theory. When you add length contraction and time dilation you deviate from Pythagoras theory. If you study the math, most of the formulas has a connection to Pythagoras. We have shown two clocks will deviate and this deviation has measurable influence that is quite real. The clock actually slows down. This wouldn't occur in a strictly optical illusion. For example muons falling to Earth don't require observers to set time dilation and length contraction. Even when they are not being observed they are still dilated. How do you pass that off as mere optical illusion?

Lets run a Newton example. Observer A holds an object. Observer B is your distant observer. The far away observer will measure the object as being smaller than observer A's measurement. In an everyday sense people have gotten used to these observer perceptions. So we habitually consider Observer A being more accurate. However this is more due to habit than science. Science wishes to mathematically prove one observer as being more accurate. Yet as it turns out, all efforts to mathematically prove one observer as being more accurate than the other is as far as we can tell impossible. That is what is needed for a preferred observer.

Maybe a simple statement may help. " Every observed measurement is real from the perspective of the observer." without throwing in time dilation or length contraction we can see this when one measures speed or percieved size of an object or even the percieved color (frequency of light) the percieved blackbody temperature will even be affected. Its funny no one has any problem accepting observer perceptions in these cases. Yet the observers in relativity follow precisely the same rules. With or without time dilation. "The key statement is measurement according to an observer" which measurement is more real is impossible to determine. All measurements involve an observer point of view. A preferred frame would be a philosophical choice. There is no mathematical means to prove one observer is more accurate than the other.

+1 on pointing out a key detail. in figure 8 above the turn around hyperbolic curve is detailed below.

I didn't see your question. I was between windows looking for a good article. I'll let Vand's answer stand. Read the article to answer his questions. Pay attention to the details on the numerous axis... The article gives a good geometric relation summary covering details not included in the above Loedel diagram. (it will also give everyone a common set of reference points (labels) to work from...)

Be careful here Loedel diagrams can be tricky if you miss the axis details. A good summary is here on arxiv "A Graphical Introduction to Special Relativity Based on a Modern Approach to Minkowski Diagrams" https://www.google.ca/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/1508.01968&ved=0ahUKEwjPs4XuoPbOAhVY1mMKHf0cCq0QFghRMA0&usg=AFQjCNGgXcFd5j31T9RqdMZziWfeLeLWGA&sig2=M39ciWw0V6eUwszQDWronw

Thats fine if the graph shows just the changes due to the formula ie time dilation formula. However the spacetime diagram also shows the changes in the spatial seperation between events due to velocity. As well as changes to direction and acceleration/ deceleration. These are aspects that are overlooked by just looking at the graph. Which is what we trying to get you to distinquish.

I think I may have read some of Russel's work. However it was so long ago I can't be certain. Recalling back when I was one of those students. I found the math steps to generate a spacetime diagram was the only way to truly understand them. Ideally I could show several key confusions by posting several different line elements ds^2. Of course ideally It would be best to cover Pythagoras theory deviations in each example. This was the light switch that gave myself my understanding. To this day I apply this lesson when looking at ds^2 line elements. 1) Euclidean (no dilation) 2) SR Newton limit line element. 3) Schwartzchild metric 4) FLRW metric line element. In each of these cases, deviation from Pythagoras theory has different causes. Identifying those causes is an excellent learning aid. (though not specifically SR), the line elements are compatible under SR. It was funny I missed these aspects during my SR course, even though I was doing the math and generating spacetime diagrams. It wasn't until I started comparing those line elements did I clue in. On a side note, there was a poster in Speculations that was trying to prove expansion as time dilation. If that poster ever looks at the differences between the Schwartchild line element and the FLRW metric. He would realize thats impossible. Unfortunately he failed to see this difference when I pointed it out to him so he has wasted the past 1/2 year in the wrong direction (yes he is still trying) Hint keep track of which coordinates are changing. Which changes are due to gamma and which ones simply change the spatial components. [latex](\acute{t},\acute{x},\acute{y},\acute {z})=(t,x,y,z)[/latex] see my previous posted math for clues. Sorry that math was posted in another recent and related thread. http://www.scienceforums.net/topic/97871-five-questions-re-sr/#entry939987

agreed, relying on diagrams for relativity is a poor way to learn relativity. Too often the focus is on the end results. Ignoring the mathematical steps to generate that diagram. Unfortunately too often details are missing by over reliance on the diagrams.

true, but were using the diagrams Michel posted. Your correct that we don't need the extra years on the diagram to show the principle. Still its an excellent point.

Michel pay close attention to the value of gamma to the observed time dilation. This is extremely important. Look at both formulas, time dilation and length contraction. They both contain the same gamma term. One source of confusion on the diagrams on the right is the seperation distance portion. This seperation distance isn't the time dilation though it includes that aspect it doesn't show the details on seperation distance and time dilation into distinctive parts. (the Author probably assumed you would infer that from the equations) The Loedel diagram on the left is a good idea to help show this aspect. as mentioned the confused aspects on lightpath is often confused. Its not uncommon to miss the portion on seperation distance that corresponds to just the spatial 3d components, from the time dilation influence on the seperation distance.

Im glad to see you learned that portion. I admit the math I posted isn't the easiest to understand. A very common mistake, lets hope your wording and example helps. Good idea on the Loedel diagrams.

orbitals are meaningless unless you can prove the electron is a composite particle. The last post doesn't do anything to support that hypothesis. Secondly you need to go through all the related math. Ie calculate the mass of each particle, calculate the spin statistics, parity, color charge, isospin, and electromagnetic charge. You haven't even looked at the particle decay and creation rules in terms of the eightfold way In all honesty this shoe is upon your feet as your ignoring the mentioned conservation rules.

regardless of what you call them. They must follow the same rules. Conservation of spin, parity, charge, lepton number, momentum and color charge. There is a few other conservation rules under the eightfold way,

A fundamental particle is one whos substructure is unknown. You claim that the electron has a substructure comprising of quarks. Yet you haven't shown this. For one thing there are key comservation rules such as conservation of charge. Which will apply

the electron is a fundamental particle. It is not comprised of quarks.

robinpike conceptually you have somewhat an accurate descriptive. However lets use a more accurate terminology. By spacetime route I assume you are referring to the length of the World line. Which is the affine connection between event A and event B (observer/emitter) (ds^2). Am I correct on this? I for one am not sure what your expressing here lol. The first line makes sense on parallel transport to Pythagoras theory correlations. After that you lost me.

Learning groups can be daunting. One guide is study each mentioned group. Study how symmetry is established in each group. This article may help it covers the Poincare group with key details into the Lorentz group (SO)1.3 Hint one is time dimension 3 is spatial dimensions... O means orthogonal S is special. This is included in the article. The lorentz group is needed to understand the Poincare group. So study both... Put simply a rotation is the spatial components but doesn't involve time. A boost involves the spacetime translations. The Lorentz group has three rotations and 3 boosts. Each is listed in the article. This article also shows spin statistics aspects of the Poincare group. Representations of the Symmetry Group of Spacetime http://www.google.ca/url?sa=t&source=web&cd=8&ved=0ahUKEwjInbLOke3OAhVDyGMKHeerDUcQFgg0MAc&url=https%3A%2F%2Fapps.carleton.edu%2Fcurricular%2Fmath%2Fassets%2Fsymmetrycompsproject.pdf&usg=AFQjCNGdANQrCLm0y5K2tmUtkbqa0cKOTg&sig2=veTzFam4mg7ARF7VO4hXKw Unfortunately it doesn't cover parity well. PS the wiki Lorentz group page is fairly decent. oh almost forgot you will need to familiarize yourself with Bra-ket notation. The article uses it. group theory often use this notation and others. https://en.m.wikipedia.org/wiki/Bra%E2%80%93ket_notation YdoaPs, Migl, Studiot and wtf have all provided several key details. So study carefully what each is saying. Keep at it. You will be amazed how interconnected particle physics, quantum physics, thermodynamics and GR truly is. All described by geometry under the SO(3)×SO(2)×U(1). standard model particles with no supersymmetric particles. (I don't believe Pati-Salam SO (6) which deals with left and right handedness falls under this but some aspects do.) Particularly in U(1) and SO (2) however Im not positive on Pati-Salam I studied it under the SO (10) MSM and MSSM. lol I'm fairly confident I lost the audience on that last comment... Just thinking to myself as to group representation under SO (1.3) for left/right hand chirality ( Grr thanks Studiot) if I recall correct Pati-Salam SO(4) included SO (3) left and SO (3) right. but not positive lol. Thankfully "Pati-Salam A la SO(10) on arxiv will tell me. For others reading an allowable rotation or boost must fall within a symmetry group. As Studiots comment indicates some rotations or boosts may fall into different groups or sub groups. Adding a rotation, boost or translation not already described under a group, changes to a new group... key note, study symmetry relations in just the spatial components, before tackling the boosts due to time components this is key to understanding the Minkowskii metric, or any other GR metric. aka line element to ds^2 in regards to Pythagoras theory

Pretty decent coverage wtf. +1. Here is a sidenote tidbit. In Minkowskii all observers will see his frame of reference as Euclidean. Define each observer as an event then the transformation is from one event (Euclidean "at rest") to the other event which the previous observer will not see in the Euclidean frame. Even though observer B sees herself in that frame. The ds^2 line element shows the wordline between those two events (separation distance).

I honestly recommend you look at how charge is handled in the Maxwell equations. Charge can be treated as simply a vector. These vectors follow the conservation laws regardless of how infinitesimal you examine. Fields include the sets of all possible values. We already can treat any field in terms of geometry. All particle physics interactions can be described by geometric relations. So I really don't see how the infinitesimal aspects in any way help your model proposal. Geometric charge relations have been well examined and is already being used.

The first thing you need to adress is how you can possibly have a change in motion in the opposite direction as the acceleration. Doesn't matter if you treat particles as point like or waves. Neither treatment will have that characteristic. (opposite to what the laws of physics would predict) The Levi Civita connection is used extensively in GR. It includes the set of infinitesimal and infinite numbers. The SO (1.3) Lorentz group also includes the sets of infinitesimal and infinite numbers. This is the gauge group that handles motion. Newtonian inertia and GR details are contained in this group.