md65536

In other words, in theory the simultaneity of events that are not causally related, is inconsequential. In the Wolfram link above, they say "this paradox has stimulated a great deal of controversy, even leading some to doubt the metaphysical underpinnings of the theory of relativity." I think that one would have to attach some extra meaning to the simultaneity of unconnected events, in order to have a metaphysical problem with relativity. There's no accepted theoretical possible consequence to whether for an Earthling it's "now" Tuesday or Wednesday in Andromeda depending on which way you're walking. I don't see how it could be a problem, without consequences. The paradox only exists assuming that standard simultaneity is non-conventional. Related topics: http://en.wikipedia.org/wiki/Einstein_synchronisation http://plato.stanford.edu/entries/spacetime-convensimul/ There would be no paradox if the clocks were set using radar time (source: something I read recently, I could try to dig it up). I see no problem with the "paradox", because regardless of whether remote simultaneity is physically unique, it seems to make no theoretical measurable difference to anyone, if the two Earthlings disagree on what day it is in Andromeda. In other words, it's debatable whether the paradoxical effect is even "real" in any way, but if it is, there's no accepted theoretical effect that says it could matter.

In my uneducated opinion, "profound theological questions" based on theological assumptions (existence of souls and heaven and a set criteria for entrance, etc) are fairly meaningless and can be easily answered with the same type of thinking that leads to the questions. The spirit becomes whole again in death. One side was possessed by demons and the faith of the believing side saves the whole. Something in the bible says that a spouse saves their non-believing partner, so the same thing applies here. Arbitrary rules to answer this sort of question might only bother someone who is skeptical of the arbitrary rules that lead to the question in the first place! Edit: I don't think "meaningless" was the right word to use, however I think the question is profound only due to it being a "complex question" (an informal fallacy).

It sounds like you're talking about the separation rate of photons and their source, as measured in the observer's frame, but that's not "speed of light". I think that round-trip might show an average separation rate relative to a moving object that is a constant and equal to c if the object has a constant velocity. That is: Light from observer takes time t to reach object, and is reflected back and returns in a time of t. At constant v, the closing rate of the signal and object is c - v for time t, and the separation rate of the return signal is c + v for time t, and the average of the two rates is c. Not necessarily so if v varies over the duration of the signal.

I don't think this solves it, but it's something I noticed:

No, the twins' individual clock readings do not depend on any physical connection between them. They age how they age even if they don't even know the other exists, even if they measure nothing from each other.

Wherever the twins are at a place where they can agree on their relative aging, if they've followed a symmetrical path---ie. the twins are interchangeable---they'd have to age the same amount. Symmetry must be broken to have an agreed-upon different aging. Breaking symmetry alone doesn't lead to different aging. You can set it up so that the twins follow very different non-inertial paths configured so that they end up aging the same amount when they reunite. Two ways to think about how the broken symmetry or acceleration makes a difference: 1. It forces different path lengths for the twins. On spacetime diagrams, the inertial twin will be a straight line and the shortest spatial distance, corresponding to the largest proper time (greatest aging) of any path between the events in flat spacetime. 2. The accelerating twin does not use just one inertial reference frame. A naive application of time dilation works for an inertial observer. Switching frames means dealing with relative simultaneity (with standard simultaneity defined with Einstein clock synchronization).

Yep Do you see now your mistake? The observers have the same total acceleration (but split up differently with different timing) with different velocities, and the difference in elapsed time depends only on the velocity and time. If you assume that the difference in timing is a direct effect of acceleration, without considering the actual velocity involved, it's easy to make mistakes like this. Don't worry, remember by your own words there is honor in admitting mistakes. There's no problem using calculations based on acceleration if they correctly account for velocity. As your wikipedia link demonstrates, it is velocity that matters, and when velocity can be expressed as a function of acceleration then time dilation can be expressed as a function of acceleration. That doesn't contradict anyone's statements in this thread. Still, as the relevant quote that I cherry-picked from the source you recommended says, "The acceleration, however, is not the ultimate source of differential aging". That's been demonstrated in several different ways in this thread. Another example, if you still don't see it, is to start the twins off with a relative velocity. Then it is possible for the traveling twin to use the exact same acceleration profile with the exact same timing in each case, but come up with different results depending on the initial velocity, because the "velocity profile" is not the same. I don't understand your explanation of why "The acceleration, however, is not the ultimate source of differential aging". What is accelerating here, if not observers?

Not even an hour later, a great example of cherry picking quotes.

Sure. From [16], E. Minguzzi (2005) - Differential aging from acceleration: An explicit formula - Am. J. Phys. 73: 876-880 arXiv:physics/0411233 http://arxiv.org/abs/physics/0411233 From the first paragraph: "The old question as to whether acceleration could be consid- ered responsible for differential aging receives a simple answer by noticing that proper and inertial time are re- lated in the time dilation effect; since relative velocity enters there so does acceleration changing the velocity. The acceleration, however, is not the ultimate source of differential aging as the twin paradox in non-trivial space- time topologies can be reformulated without any need of accelerated observers."

I would recommend getting a microcontroller prototyping board like an Arduino, and some parts to play around with. http://www.arduino.cc/ Most of these boards have USB interfaces and can be powered by USB. You download the arduino dev environment, and can run and tinker with example programs right away. There may be other good systems, but I only know about arduino. You can get a complete board off ebay for cheap. Then you could get some robot parts/project kits to go with it, or it should be cheaper to buy some parts to play with. Eg. you can get a bunch of small servos (for RC airplanes) off ebay for cheap (eg. sets of 9-gram servos can go for a few bucks each). There are books on building robots, or web pages... you can find code and designs of other people's arduino projects on the web. https://www.google.ca/search?q=arduino+robots&tbm=isch A good thing to learn about is electronics... resistance and voltage and what individual components do. To control motors, you'll soon need a power supply because USB can't drive much more than a small servo. I guess you'll really need to know about electronics in order to implement your own hardware designs if they're not trivial. A good book will explain the electronics you need to know in the context of the different components (sensors, power, motors, etc), so that you can learn about the electronics as you build more sophisticated devices. That's a quick and cheap way to get started with tinkering, should be possible to do for around $30 with lots of help available on the web.

'Proof by example (also known as inappropriate generalization) is a logical fallacy whereby one or more examples are claimed as "proof" for a more general statement.' [https://en.wikipedia.org/wiki/Proof_by_example] You have done this several times in this and other threads. Finding examples where acceleration plays a key role doesn't contradict cases where it doesn't, such as in post #1.

Iggy's statements are correct. Ignoring them and attacking the thread title instead is attacking a strawman.

In post 206 you asked me to "do the honorable thing and admit that the claim in the title is false", which I did. I explained what I meant by the title and admitted that it was poorly worded and wrong by its literal meaning. What's the point of doing an honorable thing for someone who does not honor it?

Well yes, everyone agrees that acceleration causes different speed which in turn results in time dilation. But why mislead people into thinking that acceleration is the cause of the time dilation, instead of the "differing speed profiles"? It just confuses people who don't understand, because they look at the effects of the acceleration and try to figure out how that has a direct effect on aging or clocks, when the only important effect of acceleration in the typical twin setup is its effect on velocity. It's like saying "Jerk is the root of the twin paradox, because differing jerk profiles -> differing acceleration profiles -> differing speed profiles -> differing total elapsed proper times". And jerk can cause acceleration that changes velocity that can lead to a twin paradox effect, but it's not important because the basic paradox analysis does not have to consider jerk. Nor acceleration... only velocity will suffice. And as I showed in post #1, the different aging still happens in cases where there is no acceleration. You called it "hidden acceleration", which I think is BS, it is hidden because it doesn't physically exist, is hidden from the equations, has a hidden value... I think it's fair to say that no imaginary hidden variables are important in understanding the resolution of the twin paradox.

Now one twin experiences constant proper acceleration in each of its acceleration phases, and the other experiences increasing proper acceleration. There was nothing to fix, your modifications---all of them in this thread---are detrimental to understanding.

Have you read any of the rest of that wiki page? Quotes: 'Eventually, Lord Halsbury and others removed any acceleration by introducing the "three-brother" approach. The traveling twin transfers his clock reading to a third one, traveling in the opposite direction.' and 'Transfer of clock reading in a twin paradox trip An "out and back" twin paradox adventure may incorporate the transfer of clock reading from an "outgoing" astronaut to an "incoming" astronaut, thus entirely eliminating the effect of acceleration. Acceleration is not involved in any kinematical effects of special relativity. The time differential between two reunited clocks is deduced through purely uniform linear motion considerations, as seen in Einstein's original paper on the subject,[9] as well as in all subsequent derivations of the Lorentz transformations.'

Why would the rotation be accelerated? Wouldn't that produce increasing proper acceleration? No one else is talking about that case.

How do you figure that? Variable r is the distance from the center of the carousel, and [math]\omega[/math] is the angular velocity, right? Both are constant here. How does [math]r \omega[/math] increase with time?

Oh I see now. So the pacing twin spends the same total time accelerating in each direction as the traveling twin does, but the acceleration is split up alternating back-and-forth so the pacing twin never reaches significant speed relative to a truly inertial (stationary) twin, aging essentially the same as a truly inertial twin. Edit: Ehh, I may have ruined your example by comparing a constantly accelerating twin with an inertial twin and not using GR. Yes xyzt, a slow pacing twin would still age less than an inertial twin, but the relative speed could be kept low even with high acceleration, so that the difference in aging could be made negligible. If you calculate it in terms of acceleration only, you should find that the acceleration in one direction counteracts the acceleration in the other direction? Edit: I'll just take all that back because I don't actually know how this case is properly handled.

I think that when dealing with interpretations, it is best to consider the most general cases. As soon as you start specifying details in a way that makes it more complex, without it *needing* to be complex (ie. where you can prove that there can be no other way but the complex one), then you're going down the wrong path. With an interpretation you're basically filling in the missing details, and there's no point in deciding on things that can't be proven. In this case, the "worlds" of a MWI might simply be the superposition of all possible states of the universe, and each world is simply a consistent instance or observation of that. There's no need to assume they're persistent, or that there's a certain number of them, or that anything physical happens in order for one to be defined. I don't know much about it either, or what can be derived from assuming a MWI, but if you speculate on ways that it's confusing or impossible, consider whether there are other possibilities that make it simple.

Is that a requirement, or just an interpretation (or sub-interpretation)? Aren't there MWIs that have all possible worlds "already existing", like a block multiverse? There must be interpretations that don't require any information communication at all. Each possibility could exist independently, regardless of what happens in other worlds, and when. Not that I think there's any meaning to this... I feel like I'm discussing the rules of a make-believe world.

I think so. If they're each convergent, there should be no harm in extra iterations, right? Why would you stop if one of the values is close enough but not the other?

Most complex games like GTA have a graphics and game "engine", and use a scripting language to implement much of the game story/encounters or whatever. Most console and PC games are written in C++. Some have a custom scripting language built into the game or engine (usually implemented in the same language) like UnrealEngine3 has UnrealScript + Kismet, or quake3 has quakeC. Lua is a popular scripting language... it's implemented in C. You'd typically use or build a graphics engine, which provides features and game structures, which would in turn use a graphics library like OpenGL, rather than programming the game to use OpenGL directly. Apparently modern GTA games use Rockstar's RAGE engine. GTA3/VC/SA used RenderWare.

Oh, I see. Well, what does it mean if one is < TOL? What would it mean if the other was > TOL?

Assuming it's like C, || means "or", meaning the condition is true if either of those things is true. && would mean "and", requiring both to be true.