Mordred

No thats not how lightcones work. Every observable event has its own lightcone to an observer. The different regions on the lightcone represent whether the event is spacelike,timelike or lightlike. this statement though close isn't precisely accurate. The lightcones represent only what is possibly causally connected. If there is no possible causal connection you can't define a lightcone as a light signal can never reach an observer.

yes all signals ahead would be extremely blueshifted

covariant and contravariant are directly related to the vector rotation direction in the Einstein field equation tensors. covariant is clockwise rotation. Or other tensors. https://en.m.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors the term invariant means a measurement or equation that is the same measurement or mathematical relation for all observers

Every element has a unique spectral signature. This allows us to measure those elements as well as their distribution. BB nucleosynthesis based on particle physics models and the thermodynamics of said elements allows us to approximate the available material for star formation. This in turn provides a means to estimate the number of Black holes. Every particle can be estimated by the above. Baryonic matter (visible matter and standard model of particles) with measurements only accounts for roughly 3% of the mass of the universe. If the missing mass were in the form of Black holes we wouldnt have any baryonic matter left outside of black holes. In point of detail although the BH itself isn't visible. Its influences upon the thermodynamics of the interstellar and intergalactic material is detectable. see Imaatsfal post. Rather than rely on My and Janus say so... here is an article that details the energy budget. http://arxiv.org/pdf/astro-ph/0406095v2.pdf "The Cosmic energy inventory" these two articles give a good coverage of nucleosynthesis. http://arxiv.org/pdf/hep-th/0503203.pdf "Particle Physics and Inflationary Cosmology" by Andrei Linde http://www.wiese.itp.unibe.ch/lectures/universe.pdf:"Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis

To give an example of the need to get dirty with the math as Markus and I both stress. Lets take an example that relates. Most ppl know that the Schwartzchild metric has an event horizon. However in the Kerr metric you have 4 event horizons. The rotation of the BH has particular observer influences that do not occur in the static BH solution. Simple metrics and verbal descriptions rarely describe every scenario.

Correct These two formulas only hold true when the metric is approximately Euclidean. the line element in this case is [latex]ds^2=dx^2+dy^2+dz^2 [/latex] when the spacetime geometry is best approximated by that line element the first two equations work to good approximation. Those equations won't be accurate in curved spacetime which in spherical polars the line element becomes. [latex]ds^2=dr^2+r^2d\theta^2+r^2sin^2\theta d\phi[/latex] (without expansion or rotation) Which is why I find most claims we see in Speculations of "I solved blah blah in GR but they use nothing more than SR formulas Humorous.

for now Im just answering in the SR limit without adding extra complexities. In order to give Michel a chance to understand the basic relationships the formulas above assume a rest frame and no other influence. Which gets extremely complex in GR as you can have numerous geodesics. Though clarity of which length is being examined will help. (length of object parallel to direction of motion.) or seperation length between two events.?

you can honestly and accurately answer this question yourself. Just look at the two Lorentz formulas. [latex]L=L_o\sqrt{\frac{v^2}{c^2}}=\frac {L_o}{\gamma}[/latex] [latex]T=\frac{T_o}{1-\sqrt {\frac{v^2}{c^2}}}=T_o\gamma [/latex] the longest length measured will be the rest frame. the time interval will be shortest in the rest frame. Which equates to fastest time.

good article I enjoyed that one

That last post doesn't make much sense. When you contract something your changing the volume/density. Yes time is a coordinate in GR but its not a volume related coordinate or a spatial coordinate. (ct,x,y,z)

I once made the mistake of revealing to much personal detail in an older Forum that thankfully no longer exists. Without going into the reasons I was hounded for a good year in PMs of ppl wanting me to validate or cosign their personal models in Cosmology. The right to keep your personal information hidden is highly needed to protect membership. As mentioned the quality of a persons post should be the only judgement required. Even with that protection some of our experts often get PM requests to proof read papers that some people want to get into a peer review publication. In some cases we don't mind doing so. Provided our busy schedules allow for it. For example for the past 2 months I've been proof reading a 1100 page dissertation for a friend of mine. In most cases I ran into the want to be publisher doesn't have anything worth publishing. As it becomes readily apparent the want to be publisher doesn't understand the mainstream models he is competing against. Though on rare occasion I get requests that is worth the effort. Not because the paper is profound but because the author has good knowledge on the topic and is merely looking for ways to improve his paper or is seeking good quality references to support or counter his paper. (yes good quality papers should include counter models) Personally any detailed information I would rather provide on main forums rather than in PM. This way everyone including myself can learn. On another forum a retired astrophysicist revealed too much and was regularly hounded on PMs. He used to get me to help him on subjects he was less familiar with. Unfortunately that forum member passed away a few months back. I will greatly miss his LQC expertise. In both cases neither he nor myself is famous or particularly well known in real life. Simple credentials was enough to get hounded by requests. (thankfully this particular forum is for more relaxed on some of its rules, that members hasva Speculation forum). This has greatly reduced the number of PMs I would have gotten compared to forums that don't support speculative ideas.) Which is one reason I visit here more than other forums. (I don't post personal models in Speculations as I can usually disprove my own models via math).

I recall one happy couple. The wife was deaf and blind. The Husband mute and deaf. They had to communicate via feeling each others sign lanquage with their hands. There are plenty of couples who have severe medical problems. New relations can and do develop despite these limitations.

good example. Using rest frames is essentailly what SR does. However SR doesnt work in every circumstance. Hence we have GR. Sure you can get a good approximation. However no two objects are perfectly in the same frame. (Despite your personal belief) Using primarily rest frames has been tried. It leads to unnecessary difficulties particukarly if both objects aren't at rest. Its not an original thought that the rest frame should be a preferred frame. You can look through the history but this thinking was proven wrong. Well here is one counter argument. "Inertial frames are privileged because they do not have physics whose causes are outside of the system, while non-inertial frames do." this argument states the privelege frame should be the exact opposite.... You can find the paper in the references. https://en.m.wikipedia.org/wiki/Preferred_frame Eather theories also attempted a preferred frame. Then along came GR... "Einstein went on to develop general relativity and the equivalence principle, in which inertial-gravitational frames are no longer privileged,[1]:215223 because their geodesics explain these inertial-gravitational effects without an external cause.[2]"

The more you get away from A not C. A is your closest to reality. A is the source being measured. B is any variation (regardless of cause) between the Source A to measured value.

this is the key point behind the statement. "there is no preferred frame of reference" When you think about it the purpose of relativity is to explain why different observers measure the same event differently. Lets use some basic math to illustrate. Measured frequency of Cows color. Observer a. emitted color frequency= color percieved observer b emitted color frequency+ redshift =color percieved. mathematically formula one is identical to formula two its just redshift =0 for observer a. Both are equally accurate measurements because the RHS specifies color percieved. They both agree that different redshifts will change the color percieved. This is the same on redshift. All observers need to use the same emitter frequency (which is your measured event) but have different reference frames which is the observer events. As each observer is effectively a different distance and has a slightly different time within his own reference frame. They get different results. Does this mean they are wrong? no because they are following the same formula. If they subtract the observer redshift variation from the above equations. They will both conclude the same emitter frequency. Lets look at an official formula you had trouble with on another thread. [latex]v_{recession}=H_oD [/latex]. the galaxies velocity not apparent velocity is dictated by Newtons laws and the conservation of energy/momentum. This part has nothing to do with observers and the above equation. The observers using the above equation are not trying to describe the galaxies momentum due to conservation of momentum and Newtons laws. They are measuring the observer offset due to location and expansion. (personally we would be better off calling recessive velocity, Hubble recession). but were stuck with an inaccurate and misleading terminology for historical reasons. recessive velocity has nothing to do with the laws of inertia or conservation of momentum. Its just an observer offset due to location of the observer. As it doesnt involve the laws of inertia or conservation laws its not a velocity but an apparent or peculiar velocity. (even worse its measuring the change in a commoving volume. The formula above desribes its past location. not its distance today. Commoving vs proper distance) but thats another complexity for another thread.... Lets create a more flexible formula. emitter =A observer variation =B observer measurement=C. [latex]A+B=C [/latex] So you have numerous observers who measure a. Each has his own observer variation B. So each will arrive at a different value for C. Every observer is equally correct accordingly to the above formula for value C at his location. If each observer subtracts B from C they will calculate (not measure ) the same value for A. As long as all observers can calculate the same value for A using the same observer variation metrics in B. We know A is the closest representation to reality. What each observer calculates to be the same after they subtract the observer variation B from Observer measurement C. (no observer will truly have observer variation B=0. There is always some location or gravitational potential offset regardless of how miniscule). But that doesnt matter as long as all observers can calculate the same value for A. Hint B can be any metric provided all observers agree on that metric. (invariant metric). Hint 2 There is no preferred frame as we cannot define any observer reference frame where we can accurately state Observer variation =0. Its nearly impossible to have both events in precisely the same reference frame. (at best its to good approximation) [latex]\colorbox{red}{You have been thinking C equals reality.}[/latex] [latex]\colorbox{red}{But measurements done by an observer never precisely measures reality.}[/latex]

The problem is Strawman you don't understand Swansorts question in the first place. Instead of trying to understand it. You assume you do then insult our members instead of posting a scientific discussion. We don't mind members disagreeing however we do require that they defend their viewpoints with a scientific discussion. I have yet to see that on your posts this thread. Quite frankly if you cannot discuss things scientifically or follow the forum rules... Take yourself elsewhere. We dont need members who cannot follow rules or cannot contribute to a discussion without resorting to insult. You haven't offered a single scientific post this entire thread. Instead you post mere attempts to insult rather childish. We dont need your garbage here. edit just noticed you are already banned

Why not? You have two or more observers of the same event. Both observers accurately measure that event according to his reference frame. GR explains why both observers get slightly different measurements. It is no different than having different observers seeing an object as visually appearing as different size according to his distance. You have no problem understanding why different observers will see a different size of an object. Ie someone on a plane. Relativity is essentially the same.

But the cow doesn't have any misconceptions... Might be easier to teach relativity 👌 I agree great explanation Marcus

This seems to be a common problem for learning the complexities of physics. People tend to think "what is real" so they look one observer view that is more "real" than another observer viewpoint. Relativity teaches us that all viewpoints are equally accurate to the observer viewpoint. You get the same problem with "artifacts of coordinate systems". People tend to think a scenario in say the Schwartzchild metric is accurate though in other metrics such as turtle coordinates that scenario has a different result. One might believe "real is what you see" but therein lies the problem not everyone sees the same thing. To each observer "real is what they see and measure". This is certainly accurate from the viewpoint of each observer, provided one recognizes that their descriptions of reality is an observer viewpoint. For example "describe a table". We often view this table as being solid. To us the table certainly feels solid. Yet if you are an observer who is tiny enough to see the atoms of the table. That table may very well look extremely full of empty space and probably wouldn't even be recognizable as a table. You have two completely different viewpoints of reality. Which one is correct. the answer is both of them. On a side note on the last bit. Another common misunderstanding is the ideal gas laws. One might think these laws are only usable on a gas. Yet if you consider the main difference between a gas and solid is mainly density. Then one realizes that the ideal gas laws can be applied to any solid. Even the pebble in your shoe. This last bit if you follow it will help better understand relativity.

Ive never seen it before in Canada. I will definetely look into it. My wife will probably enjoy it as well.

roflmao I often feel like the instructor on that video 😞 Just a side note there is a humorous story behind "cows are blue". I used to work as an automation tech at a Pork slaughterhouse years ago. My knowledge of automation far exceeeded anyone else I worked with. The "cows are blue" expression used to be my favourite to describe how reliant that plant was on my descriptions of a breakdown. I could literally tell the managers anything and they had no choice but to accept it. "cows are blue" described that. At university in my career change I decided to mathematically show cows are blue via redshift. It was one of my report assignments (got an A on the report lol)

I certainly wasn't expecting the cow example to cause extra complications. I would have thought it would have been as obvious as observers comparing size. ie To a distant observer an object appearing smaller. It certainly doesnt mean the object is smaller. I suppose whats obvious to one person isn't to another.

You need to think of what is meant by synchronized and clock rate. The clock will no longer be synchronized. However both length and clock rate will return to match the original conditions. Albiet the clock wont be synchronized.

What do you think? The answer should be obvious. Have you never driven towards mountains? Perhaps another question is have you ever seen a mountain with its trees suddenly turn blue because someone else farther away looked at it. Or a cow

He probably would. I would also imagine understanding his location influence is extremely important when he is calibrating atomic clocks.