Mordred

The first answer is correct. Hubbles constant. https://en.m.wikipedia.org/wiki/Hubble%27s_law

You were in that thread but probably focussed on helping others. http://www.scienceforums.net/topic/97871-five-questions-re-sr/?p=939987 The last equation shows the x coordinate change ratio. I would just use the caveat "constant velocity is lost due to direction change which is an acceleration. Re-synchronization is required. As your trying to keep your article short. "2e. From the grounds perspective, the car is just as much length contracted as before because its trajectory has changed but the relative space-time angle is the same. However, this time the car driver notices that his reference system has been messed up: the speed of light doesn't seem the same anymore in both directions. This is because the car has made a turn in Spacetime, changing its trajectory through it. That is an absolute effect; the clocks were synchronized in relation with a different trajectory." Yeah this definetely needs improving... How about the Einstein synchronization is under constant velocity. A change in direction causes rapidity and hyperbolic motion. This causes an assymmetry in the time interval calculations during turnaround unless one includes a hyperbolic synchronization procedure If you include the last equation for x^2 for the hyperbola. That should be enough with the added statement. As we can now tell which twin was the inertial twin. We can now realize that we should have never expected the two twins to be the same age when they meet again. This becomes clear under proper examination

No prob I posted the turnaround resynchronization corrections. Or rather the hyperbola curve correlation earlier on the turnaround previously. Granted the metrics can be simplified somewhat. Oops that was in relativity forum under one of the links you posted. let me dig it up

still applies just a different formula to incorperate relativity. The principle of least action is a key for freefall geodesics in relativity. cross posted with Studiot. If you think about fields and potential energy. You can see that even if the field has zero charge (vector direction) the field still has potential energy until it interacts with the particles being measured. Thats when it equates to a charge towards center of mass.

here is the classical version of the principle of least action. In simplistic form the principle of least action can be expressed as. [latex]Action=S=\int_{t_0}^{t_1}[\frac{1}{2}m (\frac{dx}{dt})^2+-mgx]dt [/latex] Between events t_0 and T_1 there is millions of possible paths. Starting and ending at those points. The correct path is the one where the sum of kinetic energy (LHS of the + sign) and potential energy (rhs of the + sign) is lowest. the lowest action path between potential energy and the objects kinetic energy determines the path

Good ole Pythagoras.

I'll get the formula for you.

The aim is to compare Galilean relativity (3d) to Lorentz (4d). Velocity addition is an excellent tool to do so. Showing how the Lorentz transformation was derived by kinematics would show that our universe is 4D by itself. It will also explain why we use velocity and not acceleration in the equations. Care to make a bet on that? How precisely did Lorentz determine only the x axis was affected. His original transforms all axis was affected. x,y,z and t.

+1 this is the best answer thus far

The last post is almost correct but I note you need some details on what constitutes curvature. Curvature is a relationship between critical density to actual density. Critical density is a calculated value showing when an expanding universe will halt and start contracting. It doesn't require "outside the horizon" If the universe outside the horizon was a different mass density. This would cause a flow that is anistropic. A preferred direction. However we know there is no flow. Isotropic (no preferred direction ). here I wrote this several years back. http://cosmology101.wikidot.com/universe-geometry page 2 with the metrics. http://cosmology101.wikidot.com/geometry-flrw-metric/

You figure the laws of physics between Galilean to Lorentz under velocity addition and refraction a "waste of time" in describing the two models? These are the key aspects behind the two models. It is velocity addition that alone could have been used to develop the Lorentz formulas. Every decent SR textbook covers these details in the beginning lessons. Usually the first few chapters. These same rules determine the required synchronization procedure in the first place....How did you think the synchronization procedure was determined? Philosophical random chance? (What I'm describing is incredibly important, to understanding the Lorentz transformations) It teaches how the Lorentz transformations was developed in the FIRST place. It is far more important than describing the paradoxes. High speed velocity addition ALONE is enough to prove a 4d universe. Without the use of light or any other signal/medium. Its amazing how such a key detail is often overlooked in Block papers lol. Considering if I wanted to I could write a block paper proof of eternalism just using velocity addition. Without using light or an ether. I can just assign any random invariant measuring stick over time. Just replace c in ct. Massless neutrinos would work they don't interact with the electromagnetic field. So the Lorentz ether does not apply to them. Yet the transforms are identical....(assuming of course I have a reliable neutrino detector.) That's the problem I have with block papers. They pick and choose the dynamics that suit their personal view point. Often ignoring cases that contradict their personal philosophical leanings. Peer review doesn't necessarily correct this.

First off no matter what frame your in. When you measure c it is always invariant. No matter who measures it at whatever speed. It will always measure c. This alone conflicts with Galilean relativity under velocity addition. Under Lorentz velocity addition if Im on a rocket and fire a laser. The laser will still move at c from the perspective of an observer Earth and the rocket. Even if the rocket is moving at 0.9999999999999999999 c. Direct conflict with Galilean relativity which would add the velocity of the rocket and the speed of the laser. for net result 1.99999999999... c Isotropy of light follows from this invarience. Isotropy means no special direction. This means the one way speed in both directions is identical. Otherwise it would not be invariant to all observers. An ether drag is a fluid dynamic with light to try to detect an ether. This is the null result in that led Lorentz to develop the Length contraction. The principle itself follows Snells law of refraction. A static ether with the Earth movement should have caused different refraction indexes. It didn't detect this dynamic. Hence Lorentz offered the length contraction to explain the null result. The statement on action is a correction to the statement "No other explanation is given than that the physical source of length contraction and time dilation is in the geometry of space-time." The formula on potential and kinetic energy relations to action. Is an explanation. which conflicts with the quoted statement. The statement you posted failed to mention "action" which is another explanation other than spacetime geometry. An IF frame in SR is one where our everyday formulas work. In this case geometry... Pythagoras theory is a main one. a^2+b^2=c^2. Within every IF frame this geometry is preserved. This is a rigid frame. All observers in the same frame will observe this geometry within his own frame. When an observer examines another frame this isn't the case. He must use the Lorentz transforms in such a manner to recover Pythagoras. This is your transformation equations. Thats the very basis behind them. I always hate resorting to merely words. Particularly in this case. When I get a chance I will post the kinematics between Galilean relativity (each IF frame, internally follows these relations) to Lorentz. The transformations themself. this is essentially how Lorentz derived the equations in the first place....I believe this will help understand the above comments. I will also include the test for one way vs two way speed of light with regards to Ether. (going to be busy today)

Yes from a philosophical side, with experimental and support. From what I've reviewed on block conjectures. The 3D presentism ontology is incompatible with 4D spacetime. Which includes Lorentz, SR and GR. If you are trying to write a good article for future. An approach is Galilean relativity. - define Rigid inertial frames - describe absolute time. -show velocity addition of vectors. Relativity same sequence as above. - homogeneity and isotropy of spacetime - t-symmetry -homogeneity of space (break the two apart.) - describe proper and coordinate time. then describe twin paradox and the garage car paradox, velocity addition Interject the presentism vs eternalism during the above. (include some basic math examples) Define any key terms. inertial frame, covarient, symmetry, homogeneous and isotropic etc.

no prob already replied there. Anyways time isotropy is essentailly no preferred direction. The laws of physics in each IF is unchanged due to direction of time. It ties into time symmetry. " We may note that temporal homogeneity implies (at least in special relativity) that all methods of time keeping based on repetitive processes are equivalent" Direct quote from the textbook mentioned below. I may have missed a few bold comments are mine. I highly recommend studying the Galilean relativity (strictly 3d ) to 4d. Lorentz ether isn't Galilean relativity. However in each frame it is galilean. The transformations between frames is not. The transformations of Lorentz uses Galilean to define each frame. One of the better coverages is Rindlers "Relativity" in the first 10 pages of his second edition. He keeps the math clasical to a high school student level.

Yes it does, in 3d space, time is absolute. The 3d requires absolute simultaneity. This is essentially a Galilean relativity view. Transform rules x=prime{x}, t=prime{t}. You want illogical both Lorentz ether and SR use coordinate time. There is no 3d Lorentz ether. (that's the spatial component) it does have a time coordinate 4d) The cause of the time dilation merely differ between the two models as to what causes the noted time difference. Lorentz tried to model it according to the absolute frame, in which the aether is completely motionless, and the speed of light in the aether is constant in all directions. IN SR it was shown they are identical in mathematical treatment in equivalence there is no difference between Lorentz ether and SR. (we simply found that due to the symmetry between frames and identical transform rules the Ether isn't needed. The Lorentz Ether is a 4d metric not a 3d. Presentism is 3d in block not 4d. for the reasons above. You kept referring to Lorentz 3d so....( I did hint at that a few times) Even if you compared you absolute frame to an inertial one, there is no difference when comparing two inertial frames. The treatment is identical. You wanted to include block, but block can't distinquish between Lorentz ether or SR. As they are identical mathematically speaking, The only comparison left under block is 3d vs 4d. reversible or not reversible but it can't distinquish between this ether to SR. Identical ratio of time change in both metrics. In Lorentz ether he referred to the coordinate time as local time. But its still a 4d model. You kept wanting block well 3d space is presentism afiak. 4d is eternalism. Particularly with the principle of relativity. Here is another thought. Any measuring stick with invariant velocity in a vacuum could have been used. Never needed to be light we could use any massless particle. +1 for realizing presentism didnt represent Lorentz Ether. I know your goal is to use Block to describe the interconnect 3d space to the transforms of relativity. Block is excellent to compare 3d to 4d ontology. but in block "absolute time" requires no synchronization procedure. The 3d is Galilean relativity. I recommend using the combined approach Galilean relativity to SR/Lorentz transforms with block philosophies. I posted a good book in that thread that details this in the easiest format I could find. (for those math challenged readers) I'll include the same reference here "Relativity Special, General and cosmological second edition." by Wolfgang Rindler All metrics done is shown without the need of tensors. It is probably one of the better approaches for the average reader as it doesn't require high math skills to understand nor answer the questions within the book. Its an amazing book. Quite frankly there is no need for a student to understand tensors to gain a solid understanding of relativity. Unfortunately good books that target the average reader is hard to find.

With the approach your taking, albiet your requests for improvement. By including the different views involved. I see no problem using this technique to help understand relativity. I'll study it in more detail later on lol I noted a request on time reversal symmetry. There is two (at least) valuable lessons in examining your cars. Classical velocity is time reversal. The acceleration is not. This relates to twin paradox. I'll work up a detailed explanation later on. Isotropy of time means time symmetry which equates to reversible processes being modelled.

No today we know there are no rigid bodies. All bodies being comprised of particles. Which at the time of Lorentz. They only had the electron and proton. So there was a natural effort to model gravity by electromagnetic charge dynamics. The neutron was discovered in 1932. So the view of the atom was just Proton-electron. (forgot photon though they were having problems with light. The quantization ie Planck-Einstein) As these were the only two known particles at the time. It made sense to model spacetime with the electromagnetic. On the mathematics side use of symmetry and fields were also developed later.

The link for connected seems off.... A connected element is a tensor. O(1.3) orthogonal group has 4 connected groups (tensors) the two that preserve time. The two that preserve time fall under O+(1,3) the two that preserve space are under SO(1,3) the elements that preserve both space and time are under SO+(1,3). Both SO(1,3) and SO+1,3) have 6 dimensions. The SO(1,3) is doubly covered by SU(2)/Z Anyways number of dimensions isn't the approach, that's just our coordinates under the Lorentz group you have 16 elements, which are constrained such that any transformation can be determined by 6 parameters 3 for rotation and 3 for boosts. The inhomogeneous Lorentz group or Poincare group has 10 parameters, 4 for space-time translation and 6 for homogeneous Lorentz transformation. Under Minkowskii metric the Poincare group is the full group. With the Lorentz group as a subgroup. A field is a function of a space-time point if that point is defined as an event. [latex]x^\mu=(t,\overrightarrow{x})[/latex] This is what I was thinking, but should have clarified. prior to connecting fields to the metric. Essentially a field is a collection of objects. Those objects can be events. where k is the boosts are 4*4 matrices, and L are your 4*4 matrix rotations. these matrix can be defined as [latex](K_i)^j_k=0[/latex], [latex](K_i)^o_\mu=(K_i)^\mu_o=g^i_\mu[/latex] [latex](L_i)^i_k=\epsilon_{ijk}, L^0_\mu=L^\mu_0=0[/latex] where i,j,k=1,2,3 and [latex]\mu=0,1,2,3[/latex] I'm not sure if that helps with your question or adds confusion lol

Let me ask of you Tim. My interpretation doesn't change anything in your car scenario. Reason 1) no preferred frame= no need to use a third absolute frame. Comparison between two frames is sufficient to predict the change in geometry with a value of gamma. Reason 2) Once you use the Lorentz transformations. You are already admitting Minkowskii geometry. Within each group are subgroups. SO(1.3)×SO(2)×U (1). See the group paper on SR I linked. (Ajb pointed this out earlier.) So Compare your absolute frame, which you cannot measure. With the rest frame. in your car example what gamma value do you apply? Ether is a matter field. 1) you don't know the mass/energy density of the absolute frame. 2) You cannot confirm the geometry is [latex]\eta_{\mu\nu}[/latex] You are left making assumed properties of the state of the absolute frame. You have no way to confirm it. Boils down to (measured properties of rest moving) compared to (Measured properties of inertial frame) both compared to a frame with no measurable properties....... We can't even confirm the length of the rod. Makes absolutely no sense lol. Moving to presentism. In block specifically means "Only the present exists". This is a 3d view, time is an illusion. This view also places a restriction (simultaneous events) Yet we know there are events that have no casaul connection between event a and event b. How do you confirm these are simultaneous events.? I posted the criteria prior. So here is a question Which observer "present" is more real ? 1)absolute frame (cannot measure,only assume) 2) rest frame 3) inertial frame. Using any of the above under presentism each of the three observers feels his own frame is more real. Each will view the other frame as inertial. No frame can be confirmed as more "Real" The 3d kinematics of each frame are identical in symmetric relations. All three frames preserve the Pythagoras metric. So what tool do you use to confirm one frame is more real than another? In the 4D the philosophy is no frame is privileged. All observers are correct (his frame is real ) but it admits that another observer will see his frame equally real. There is no way to prove one frame being more real than another. (eternalism) "Eternalism is a philosophical approach to the ontological nature of time, which takes the view that all points in time are equally "real", If you wish to use Block the eternalism view is more real than the presentism view. The presentism view cannot confirm his frame is more real than any other. Eternalism view is compatible with the 4d view. This is the view relativity uses. (a side note, this thread could have been shortened with less confusion. By simply asking opinions on which is more real "Presentism-Lorentz ether. or Eternalim-Minkowskii) under block philosophy. In the GR realm the quantities that all class of observers can agree on (invariant) is proper. This is only achievable by the eternalim view.(under block) "In relativity, proper time along a timelike world line is defined as the time as measured by a clock following that line" Any point on that worldline is equally real. (the above is on the assumption of deterministic aka Block) Quite frankly I don't particularly find Block adequate but Thats another debate. For another time (I tried to keep this restricted to block and Lorentz ether as per your OP)

I hope I didn't inadvertently miss imply (I think I may have oops. good point must have been asleep. Should have been more clear.. I'd like to add a statement. It is one that involves lie groups of SR. https://arxiv.org/abs/physics/0502115 "Belonging of coordinates transformation to a symmetry group indicates that all reference frames defined by the transformation enjoy equal rights in relation to the property admitting this symmetry group. In other words in the bounds of the Lorentz group, i.e. among inertial frames of reference, there is no preferable reference frame" Another feature in group is that SR preserves certain relations. [latex]\Lambda_\eta \Lambda^t=\eta [/latex] which tells us that we preserve the Euclidean/galilean metric with respect to time. On a sphere this can only be done as an infinitesimal approximation.

I do not vote for the presentism argument. Nor the Lorentz ether absolute frame being a privileged observer. Relativity of simultaneity has specific requirements that are not merely "convention" The presentism argument (if I understand it correctly) is a 3d ontology as opposed to a 4d ontology. Presentism follows the logic argument the view that it is only the present "here-now" (the three-dimensional world at the moment `now') that exists. 1) the universe exists only at the constantly changing present moment (past and future do not exist) 2) the universe is three-dimensional It is more real to think of physical reality as a four-dimensional existence, instead of the evolution of a three-dimensional existence First I better define relativity of simultaneity. ( mainly for other readers) 1) homogeneous and isotropic space means that no 3d location is privileged or more convenient. 2) homogeneity of time throughout a homogeneous space has no privileged origin or privileged 3) two events in the same frame of reference are simultaneous if the clocks at two locations is identical 4)Two distant events are simultaneous in a given inertial reference frame if the light signals originating from the points where the events take place arrive simultaneously at the middle point in-between these origin points 5)The two synchronized clocks have the same running time. between frames 1) two light sources generated simultaneous arrive back at origin point 0 at the same time. 2) two light sources emitted at different time arrive back at the origin at the same time. if [latex]t_1=\frac{\sqrt{x_1^2+y_1^2}}{c}[/latex],[latex]t_1=\frac{\sqrt{x_2^2+y_2^2}}{c}[/latex] Presentism regards the event here-now as the most real, It should be stressed that it amounts to a contradiction in terms to say that the world is four-dimensional, but for every observer only the event "here-now" is real. If the world is four-dimensional all its events are equally real otherwise it would not be four-dimensional.This shows that in space time it is impossible to have an event, representing the event "here-now", which is more "real" than the other events. Therefore, objective now of time and objective becoming are impossible in a four-dimensional world, if they imply that there are events which are "more real" than the other space time events. Secondly any view of "time is an illusion" does not reflect reality, because space and time are indissolubly related to each other to form a single whole, the presence of a force field in space must necessarily result in the appearance of physical properties of time caused by the motion of a body in this field. However this does not mean time is a physical property of matter or energy but is dependent upon the state of the space-time system via the force field interactions. As physical also includes the definition "that which is measurable" time is measurable by the duration and rate of change in the system. Volume being a property which is 3d, is a physical property as it can be measured without changing the composition of the system. In a 4d view time and space are inseparable. So the correct ontology is space-time is also a property as it can be made without changing the composition of the system. As time is inseparable from space. Stating that one half of a whole is illusion while the other half is real is a contradiction. (yes I spent some time studying the logic arguments)

Maybe its the physicist side of me. Definetely. When I look at a model. I'm only interested in one key question. "What is its predictive power" Lorentz ether offers nothing by introducing a preferred absolute frame. If the process is symmetric (which block handles without a problem) Then you can use any frame as a reference. "there is no preferred frame" is one of the philosophies of GR. There isn't a single detail that cannot be derived from using any frame conpared to using a rest frame. So Lorentz ether does nothing to improve predictive power. Block vs evolving block must be examined in the same manner. Reversible processes are easy to predict. Irreversible processes not so much. Quantum fluctuations we are restricted to probability. Probability isn't deterministic its statistical. When we look at a waveform we only know that sonewhere on that wave is the particle. We don't know its precise location. So how deterministic is this. Only as deterministic as the probability. Block follows the philosophy "all events must be deterministic." In macro systems ordinarily this works but not in all cases. There are macro processes that are not reversible. Entropy for example isn't reversible. If we start to reverse expansion we should have a decrease in entropy. According to reversible process. However entropy doesn't decrease in this case. It will either remain the same or continue to increase. arrow of time was proposed to be modelled via entropy. So this conflicts with block. (Yes you guys can google the Internet to find counter arguments to the above examples) I know they are there... The problem is the majority of those articles include a detailed math analysis.

You declared you know of two models to help explain the math of SR. You haven't shown how instead you expect us to. See the quote above, sorry I can read.... go ahead try to use Block to explain the math of SR. 1) first convert all metrics to the corresponding Hamiltons and action. 2) then apply the Block universe equation to reduce those to deterministic statistics. Lorentz Ether. The only way to make sense to use this is to call fields ether. Why not just use the fields in the first place. When you teach SR you must be prepared for whatever analysis the questioner asks pertaining to a model. Including the math. Can you perform the math in block? if not don't use it. Can you show where Lorentz ether makes a difference if not don't use it. pretty simple You can't assume that, the purpose is to explain why those equations work if needed, explain how they are derived. Neither Block nor Lorentz ether is needed to explain the Reality involved in SR. You can point to the properties you can determine. Quite frankly if people can't understand perspective due to spatial separation or time dilation. I don't see how block or Lorentz ether will help you. A good course in differential geometry may be better suited lol Anyways in SR one can argue invariant quantites are more real than variant. Invariant naturally are determinant. Variant is potentially but not in all cases. I can easily keep posting processes where it would be extremely difficult to fall under Block. I cannot describe or name any process that can't fit under evolving block. Using Lorentz ether which is questionable if it exists or not to describe reality. Sorry I fail to see the logic in that approach

You asked what are models to describe physical space with spacetime. Where is the hijack ???? All I've seen you do is make declarations and post links that don't describe what your after. Neither Block nor ether is needed to describe the title of this thread. You wish to examine models You obviously have no clue of what is involved in them but you want to use them to teach relativity????? You asked several times to show how EFE describes the time dilation, length contraction aspects. I provided that. In doing so I showed you do not require neither Ether nor block universe to understand relativity. Now it is your turn Prove me wrong. direct quote from the OP....... I provided a third. show your analysis your turn

Why don't you actually study block universe? What is the equation for block universe? It does have one... Maybe you should stop and actually study the model. go ahead challenge me post the math for block with SR.