Iggy

no, a point particle is one that takes up no volume in space. It makes a line in space-time. How do you find the height of a rectangle?

how do you find the height of the rectangle? We already agreed that an object (a point object to be specific) makes a surface on a space-time-mass diagram. You find the mass of the object on the diagram the same way you find the height of the rectangle. How do you find the height of a rectangle?

That is correct That isn't what I said. You're not understanding. What point on the width of a rectangle has height? Does "the rectangle" have height, or does "only one single point along the with of the rectangle" have height?

If you ask god to help a brother out and prove his existence (like Elijah did in 1 Kings 18) and god responds then you've successfully tested god. If he doesn't respond then you haven't falsified him. The god of Abraham was tested, or empirically verified. The god of Baal wasn't falsified.

I'll tell the Pope to close his observatory and edit the catechism Could you show me where I said that. No, they've updated that. Let there be light was the big bang after which came the sun and stars

No, mass doesn't increase with time. We don't get a new sun every day adding mass to the old one. Each dot on the diagram is an event -- not an object. Each new event does not imply new mass. Mass is not a property of events. There are two methods for measuring mass. You can apply a force to the object and measure the acceleration. On a space-time diagram this involves dividing a known force applied to the object by the change in the slope of the wolrld-line after the force is applied. You can also measure it with a scale if you know the gravitational acceleration. On a space-time-mass diagram you can just look at the height in the mass dimension. It is not a matter of belief. Imagine a rectangle. It takes two dimensions to show. Do we say that the height changes because the rectangle makes a surface? Each point along the width of the rectangle is not a new and different rectangle adding to its height. Each point along a world-line is not a new and different object adding to its mass.

I mean to say that the god of scripture is amenable to empirical testing, not to say that there is a "way to falsify a religion". Leo expected the 'literal and obvious' meaning of the text... The Catholic Church, in adopting the rule of St. Augustine, teaches “not to depart from the literal and obvious sense, except only where reason makes it untenable or necessity requires Pope Leo XIII, Providentissimus Deus, 15, 1893 only when 'necessity requires' some other interpretation should one be considered. The literal and obvious meaning of "light" in genesis is "light" otherwise it wouldn't be followed up with "And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day." When the interpretation of the Latin and Greek fathers failed, and the literal and obvious meaning of the text failed, Leo was not above considering new interpretations. He established the Pontifical Biblical Commission to look into those cases -- but, always with the presumption of biblical accuracy. That aside, I think it is a mistake to say that a God who isn't completely separate from science doesn't by definition qualify as a God. I believe that is a very recent expectation.

Yes, in classical physics it would be a surface orthogonal to space and time along the world-line. As spyman pointed out, in relativity is warps the space-time around and along the world-line. When do you think particles have mass?

Is there any quotes in he bible at all explaining? It does say god made man in his image. Sorry for the long post on an old point -- it's a fascinating discussion that I just caught up on. On the question of scripture dealing with testability, or empirical verification, there is 1 kings 18, According to the Bible in 1 Kings 18, the challenge was to see which deity could light a sacrifice by fire. After the prophets of Baal had failed to achieve this, Elijah had water poured on his sacrifice several times to saturate the altar, prostrated himself in prayer to God, fire fell from the sky, and immediately consumed the sacrifice and the water, prompting the Israelite witnesses to proclaim, "The Lord, He is God! The Lord, He is God!" Wikipedia - Mount Carmel - Elijah I think there are scriptural roadblocks to the notion that God has to be untestable. As a point of logic, the same people who deny the biblical god's empirical character also grant that he answers prayers and makes covenants and prophecies. Those things seem mutually exclusive to me. A typical retort is that god is all powerful -- he can transcend logic and any other sort of rational trap you try to put him in. A number of, particularly Jewish, scholars have taken a position against that. To give an idea... This logic game tells us that this contradiction is no minor problem. There is a difference between saying God is very powerful and saying God is all-powerful. What is the biblical or rabbinic term for all-powerful? It turns out there is no such term or concept. God has g’vurah, g’dullah, koach—synonyms for might and power—but there is no Hebrew for omnipotence. Rabbi Artson On the Christian side of things, anyone saying that the definition of God separates science and religion as incomparable -- different domains -- would have to sidestep a very well established tradition that... Let them loyally hold that God, the Creator and Ruler of all things, is also the Author of the Scriptures - and that therefore nothing can be proved either by physical science or archaeology which can really contradict the Scriptures... Pope Leo XIII So I don't think this has to be true... not in mainstream Jewish tradition or the largest Christian denomination. This might be a better quote on the latter: Though faith is above reason, there can never be any real discrepancy between faith and reason. Since the same God who reveals mysteries and infuses faith has bestowed the light of reason on the human mind, God cannot deny himself, nor can truth ever contradict truth."37 "Consequently, methodical research in all branches of knowledge, provided it is carried out in a truly scientific manner and does not override moral laws, can never conflict with the faith, because the things of the world and the things of faith derive from the same God. The humble and persevering investigator of the secrets of nature is being led, as it were, by the hand of God in spite of himself, for it is God, the conserver of all things, who made them what they are.38 The Catechism #159

with the object Objects have mass. Events are... the 5th dot down -- the indented one: http://fr.wikipedia.org/wiki/%C3%89v%C3%A9nement

It isn't my interpretation. It is how space time works. The definition of "object" coincides with the definition of "world line" in space time. You can't directly observe the Hiroshima atomic blast of 1945. That event is not directly observable at this time. The object, Japan, had mass and existed in 1945. If you keep separate the idea of an event (the dots on the diagram) and the idea of an object (the lines on the diagram) then there should be no issue Except with my car keys, I do generally think conservation laws work and things don't macroscopically pop in and out of existence. past and future events. This has got to be the issue. Objects are not discontinuous in the dime direction in space time. It seems like you've convinced yourself they are, but that won't work.

right ok, but I do hope neither of us runs out of mass before his return

Space and time are the only things depicted. We would need to add a dimension to show mass. Can I ask what you think? Did you have mass on March 9th at 5:00 or at 5:01, or distributed between the two?

Objects, like galaxies, can't be inside or outside a past light cone. Events can. When an object like a galaxy emits light, that is an event. Those events are on our past light cone. The observable universe would include all the mass that we can see. It doesn't refer to all the events we see, it refers to all the things we see. You aren't an event. You persist. He cannot observe distant present *events* A person is not an event. I think this mixing up of events and objects is the source of miscommunication EDITED TO ADD: Point A is an event. You are an object. You could say "For the observer (Spyman) I *was at* point A on March 9th at 5 pm. That would make sense because being at a certain place at a certain time is an event. "point B" is a label. It would mean something like "the event one light-minute away from Spyman on March 9th at 5:01 pm". It is not impossible for you to be one light-minute away from Spyman on March 9th at 5:01 pm. According to the diagram you are there at that time. yes, what Minkowski called your "everlasting career" -- every event that happens at your location at every time in your life -- your world-line. On March 9th at 5:01 pm Spyman can observe Michel only at point A. At 5:02 he can observe you at point B. At 5:01, you *were* in the past at point A and *are* in the present at point B. You are the object at both events. You persist.

*my bold I find it confusing that you switch between events and objects, like how I can't observe distant events in my present, so you are not in my present. If 'you' were an event then that would make sense.

velocity needs to be [math]-\beta / \alpha[/math] My conclusion that Lorentzian and Galilean transformations are the only two options with the postulates of the principle of relativity and the isotropy and homogeneity of space is well published. I gave a link in my last post. It gives a number of references. This one sets it out clearly in the abstract which might help: http://physics.sharif.ir/~sperel/paper1.pdf Wikipedia's derivation does the same thing under group postulates, but they forget to mention that the principle of relativity implies the group postulates. Bottom line, you can derive, [math] \begin{bmatrix} t' \\ z' \end{bmatrix} = \frac{1}{\sqrt{1 + \kappa v^2}} \begin{bmatrix} 1 & \kappa v \\ -v & 1 \end{bmatrix} \begin{bmatrix} t \\ z \end{bmatrix}. [/math] without assuming anything about an invariant speed. Setting [math]\kappa = 0[/math] gives the galilean transforms. [math]\kappa > 0[/math] gives a non-physical result. [math]\kappa < 0[/math] is Lorentzian and you set [math]c \, = \, \frac{1}{\sqrt{- \kappa}} [/math]. Once you have the equation above with kappa in it all you need is one relativistic observation and SR is derived. It wouldn't need to be an invariant speed. edit: at least, I don't think it would. Maybe I'm missing something In a technical sense, either the invariant speed would be finite or infinite. In neither case would it make sense to have some relativistic effects without others.

If you assume the principle of relativity (something you have to do in either case) then your options are only the Galilean or Lorentzian transformations. That was my meaning. In neither case would an invariant length with time dilation be sensible. Looked at another way... if we could for some reason not be able to reach the invariant speed. If light, for some reason, went half the invariant speed and we couldn't accelerate massive objects any faster than light... we still could easily derive the lorentz transforms by making just one time dilation observation. We could even solve what the invariant speed is.

I might look at it a little differently in that time dilation or length contraction are no more a consequence of an invariant speed than the other way around. I mean... I'm not sure having a constant finite speed is any more fundamental than time dilation or any other relativistic observation in deriving the Lorentz transforms. Certainly, the Einstein-like way of doing it, Principle of relativity + finite invariant speed -> Lorentz transforms is more popular. But, I think it would be just as admissible to do... Principle of relativity + time dilation -> Lorentz transforms or any other relativistic effect, because if you derive a general set of equations from just the principle of relativity (and the usually unwritten postulates isotropy and homogeneity) you get an equation with one free parameter, usually written Kappa I think. Then you can either set it positive, negative, or zero and the resulting transforms are either Lorentzian, Galilean, or something that makes no physical sense (wikipedia references section 2.1 here as an example of that approach). Any relativistic observation (time dilation, length contraction, invariant speed, relativity of simultaneity) would serve as an additional postulate allowing one to chose the Lorentz transforms. In othe rwords, I don't think I would say that a constant speed is equivalent to the Lorentz transforms any more than I would say time dilation, for example, is equivalent.

Does anyone know what the elimination half-life is for anthropogenic atmospheric carbon dioxide? In other words, if we suddenly stopped adding CO2 to the atmosphere, how quickly would the levels drop toward pre-industrial levels? I would think somebody has published that and it would be interesting to know. If not, does anyone know what percent of anthropogenic CO2 is sequestered? That would give enough information to estimate in the same way that a drug's terminal elimination half-life can be estimated from knowing how much the kidneys eliminate.

I'd be delighted if you stopped putting quotes around "reference frame" as if it is a phrase that I used in this thread. I didn't. Like I said before, when I say "frame" it is shorthand for coordinate system. I'm talking about coordinate systems because my claim is that acceleration is coordinate dependent. The field equations do not determine the metric uniquely. The components of the metric change with coordinate choice because the field equations leave four degrees of freedom associated with the choice of four coordinates. Simply put, you get one metric if one twin solves saying "I'm at rest" (I'm at rest is a coordinate choice) and you get another if the other does the same. The solution is valid and you get the correct answer either way. I do hope this is clear. I would also be pleased if you stopped repeating things that I said in my last post as if you are teaching me something. I don't want to be insensitive, but it could give the unfortunate impression that you don't read your replies. Agreed. I don't believe that follows. Nah, I'm sure "at rest" can refer to Schwarzschild charts just the same. GR is not so picky as SR. He's not at rest in one coordinate system, and he's not accelerating in another. It's a riddle that only GR can solve

Here is a good link on train wheel and track materials and forces: Modern Tribology Handbook, Volume 1, 34.2 The compressive strength of strong fiberglass, according to wiki, is 350 MPa and from the link train wheels exert pressure in the hundreds of Mpa. It also says the contact point has a temperature of "several hundred degrees Celsius in normal operation"... so I think it would fail or deform before it had a chance to wear out.

ah, thank you. I almost wish my first [-1] would have been for something with a bit more drama At this point I would almost welcome being wrong if I could just get "you are wrong about X because Y proves X wrong". Yep. uh... the global coordinate system doesn't have direct metrical meaning (if it's curved), but that's what the metric is for... unless you mean there is no truly global coordinate system covering the whole cosmos... I can't be sure if this is meant as an objection and if so how. Ok, but my contention is that GR does not prevent us from analyzing the 'paradox' from either twin's perspective -- that the non-inertial twin can consider himself at rest and the other guy accelerating. It's analogous (just an analogy) to analyzing two world-lines in the vicinity of a spherically symmetric mass, first from Schwarzschild coordinates then from free-fall coordinates (or one of several other similar choices). Proper time, the reading on an accelerometer, and other invariant quantities don't depend on the coordinate choice. Whether the observer is "at rest" or "changing velocity" does. Hence, an observer who can model the world around him in a coordinate system where he is stationary while his friend is changing velocity can -- being just as correct -- model the world around him in a coordinate system where he is changing velocity and his friend is stationary. In terms of the twin 'paradox'... The Clock Paradox in a Static Homogeneous Gravitational Field (2006) Differences in proper time being a "coordinate effect, which locally approximates a difference in world lines" is not an objection to this -- it rather relies on it. And the principle of extremal aging establishes that the inertial particle always ages more between events. Why would you think I disagree? No, the metric does indeed depend on the coordinate choice. You wouldn't expect, for example again, Schwarzschild coordinates to have the same metric as Lemaitre coordinates even in the same physical situation. That would be like having the same scale on different style maps (different projections) of the same earth. The length, I agree, must be the same -- all frames must agree on the ages of the reunited twins. I agree also it's more complicated to treat the non-inertial twin at rest than not. No, I don't recall -- I'm quite sure you never did -- show me how to compare arc lengths. Nor would you need to, or how to numerically evaluate line integrals for proper time. I do have a pretty good working knowledge of relativity to solve problems of that sort. Your response, as helpful as you may mean it, doesn't address the issue. You said GR doesn't allow the non-inertial twin to consider himself at rest. This would mean he can't transform to a coordinate system with a line element where he's at rest and compare arc lengths.

no In light of a neg rep, , here are a couple more sources refuting the claim and supporting my position: perhaps they are misguided, but they make such good sense to me that I would very much appreciate being shown why they must be mistaken... yada yada...

frame is shorthand for coordinate system The book that you've twice now told me to read uses the phrase "gravitational field" over 100 times. In section 16.5 "the measurement of the gravitational field" it loosely defines the phrase as the "geometry of spacetime", and that is certainly on point with what I'm saying. When I say that the younger twin experiences a "gravitational field" from his perspective, it is the physical interpretation of the field equations (curved spacetime) to which I'm referring. I don't mean a classical vector field, and it's on point for that reason in fact... Had one tried to explain to Newton the equality of inertial and gravitational mass from the equivalence principle, he would necessarily have had to reply with the following objection: it is indeed true that relative to an accelerated coordinate system bodies experience the same accelerations as they do relative to a gravitating celestial body close to its surface. But where are, in the former case, the masses that produce the accelerations? It is clear that the theory of relativity presupposes the independence of the field concept. -The Meaning of Relativity -- Einstein -- 1922 I don't recall that, but I do recall posting Einstein's GR solution to the twin paradox in post 44. If it is conceptually flawed is the question. I think everyone who has responded to my query has conflated "acceleration relative to geodesic motion" with "acceleration". You did this by saying that an accelerating vehicle must push the occupants back in their seat. You clearly meant a vehicle accelerating relative to geodesic motion, which I could agree, and have, agreed with -- but you are vague and equivocate. golly gee, you don't say! DH said that observers must accelerate by the amount measured by their accelerometer (same conflation). I mentioned the schwarzschild metric because it was the easiest counterexample. I wasn't trying to solve the twin paradox with it, or trying to build you a strawman with it, or anything else like that. Thank you for the literature suggestion. If anyone would like to respond to the proposition, here is another quote from Einstein from a later publication (again, in case I'm communicating it horrifically), This makes such good sense to me that if it is indeed not a valid interpretation of his theory I would very much like to know why that is the case... or how it was determined not to be the case.

"Takes off" relative to what? In what direction? A car that accelerates toward and relative to the center of the earth at 9.8 m/s^2 isn't going to "push you back into the seat". A car that accelerates relative to another car may itself be sitting at rest relative to the road. How fast do you think you're accelerating relative to Halley's comet right now? You're conflating the notion that the road is at rest and the car accelerates with the notion that the road doesn't feel the inertial force that the car does. The latter doesn't imply the former in GR. Either twin can consider himself at rest while the other accelerates and solve the 'paradox' with GR correctly. If you still disagree with that or you don't follow what I mean then please read the link I've given.