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And what exactly do think I was doing in post #6? You ignored that post because you are trolling. Say it mathematically, please. Otherwise all you are doing is waving your hands. Besides, this is not answering Jill's question. More utter nonsense. Do you have the foggiest idea what the expansion of space means? It is space itself that is expanding, not the material that occupies space. Besides, you have been told that the expansion of space at the scale of a balloon is immeasurably small. You need to address this fact. Seconded.

In other words, because you can't do math you need to belittle it. Sorry, that doesn't cut it. You are not doing science.

The reason I wrote that post is because that is how science, and particularly so physics, works. I am not picking on your conjecture per se. This is exactly how physicists pick on each other. Now I will pick on you: Your words are, to all appearances, utter nonsense. It is up to you to demonstrate that they are not nonsense. Because all that you have done is done is wave your hands. These is literally nothing to see here until you make your ideas a bit more concrete. There is nothing here to put to the labs. It is not up to us to take your half-baked ideas from the realm of philosophical nonsense to the realm of physical reality. That burden falls upon you, the proponent of this new idea. No. No.

You are still not making sense. You appear to be thinking that the traveling twin suddenly gets younger upon returning to Earth. That simply does not happen. If the traveling twin loses his hand at some time during the trip, the hand will still be missing when the trip ends. It appears you think there is some God's eye frame in which one can absolutely compare events in two frames separated by some non-zero distance and moving with respect to one another. Such a frame doesn't exist. Simultaneity is relative.

This doesn't make a bit of sense. Please elaborate.

You haven't done any math, how can you call this anything but hand waving? My challenge to you: Specify the axioms of your model. No hand waving, please. Mathematics is the language of physics. You need to use math. Explain the phenomenon we call gravity using on these axioms. Once again, no waving. Please describe this phenomenon mathematically. Now some questions: What is the motivation for these axioms? How would you test them? What experiment would falsify your model?

Wall O' Nonsense. In fact, multiple walls of nonsense.

This is a science forum, not a forum for naval gazers who have no idea how things work. And you do? The expansion of space is immeasurably small at distances observable by our eyes. The expansion of the universe has nothing to do with why distant objects appear smaller. On human scales, the universe is locally cartesian and flat. Neveos, this is a science forum, not a naval gazer's forum. The burden is upon you to provide justify your claims. With mathematics. Moderators: I strongly recommend that this thread be put into put up or shut up mode. Merged post follows: Consecutive posts merged Yes, it is. Space is locally cartesian.

No magic at all. Read up on the science of optics. Classical and quantum physics explain this quite well. I too wonder why this thread was put into speculations. You have a nonsensical explanation of a well-understood phenomenon. It should have been put in the Trashbin. swansont was apparently answering the side disagreement between Sayonora and JillSwift. His answer had nothing to do with your particular nonsense.

You were right the first time around. VY CM is nonsense, which is why google returns nonsense for this designation. If on the other hand he had asked where VY CMa is you would have been answer quickly.

I tried to give a detailed explanation in post #9, Janus added some more info in post #11. Space-time diagrams (see post #12) help a lot. I think the problem is that you have some misconceptions about relativity. A couple common ones that get in the way of understanding: There is no absolute reference frame. There is no way to tell who is moving and who isn't. Time dilation and length contraction don't happen to you. Suppose you are traveling at a relativistic speed with respect to someone else. Time dilation and length contraction are something you see happening elsewhere. That other party will appear to you to be subject to time dilation and length contraction. The why is because, as Janus mentioned, the traveling twin accelerated to turn around. While velocity is relative, acceleration is not. Acceleration remains absolute in both special and general relativity.

Some reference material for you: http://math.ucr.edu/home/baez/crackpot.html http://en.wikipedia.org/wiki/Illusory_superiority http://www.apa.org/journals/features/psp7761121.pdf

This is a very important point. Understanding it is crucial to understanding relativity in general. BTW, the same goes for length contraction. It too is something you measure as happening to someone else. Not true. See post #9. Here's a space-time diagram of a trip to and from a point 3 light years away at 3/5 c. Source: http://www.csupomona.edu/~ajm/materials/twinparadox.html In this case, the Earthbound twin sees his brother aging slower for the first eight years of the trip and then aging faster for the final two years.

All frames are equally valid, and they all yield the same answer. Here is a situation that yields the numbers that asprung hinted at in the original post. Suppose the traveling twin has a magical spacecraft that can instantaneous accelerate to any speed less than the speed of light and not have the occupants turn into a blob of protoplasm at the rear end of the spacecraft. At age 20, the traveling twin sets off for a star 14.79 light years away at a 98.6% of the speed of light. (The actual numbers: The star is [math]5\sqrt{35}/2[/math] light years distant, and the space craft velocity is [math]\sqrt{35}/6\, c[/math]). To the traveling twin, that 14.79 light year distance to the star contracts by a factor of 6. The spacecraft clock indicates that the outbound journey takes 2.5 years. This is exactly how much the traveling twin ages during the outbound journey. The same thing happens on the return trip. Total elapsed time for the trip from the perspective of the traveling twin is 5 years. As far as the traveling twin is concerned, she is 25 years old when she returns -- and she has a clock and a youthful smile to prove it. From the perspective of the Earthbound twin, the outbound trip takes 15 years, and so does the return trip. As far as the Earthbound twin is concerned, he is 50 years old when his twin returns -- and he has a clock and some gray hairs to prove it. Both are right, and both agree that the other is also right. Suppose during this trip the two twins remain in constant communication with one another, with a timing signal embedded in the communication stream. This timing signal is in the form of a counter that increments once per second, with seconds measured in the frame of the transmitter. During the outbound trip, both twins will see the same thing. The signal sent by the other twin is incrementing slower than once per second: once every [math]6+\sqrt{35} \approx 11.92[/math] seconds. Each twin sees the other as aging slower than they themselves are aging. Both twins will see the same thing just before the traveling twin finally returns. In this case, each twin sees the other as aging faster than they themselves are aging. The factor is the inverse of the slowing on the outbound trip. The timing signal from the other twin increments 11.92 times every second. So, if both twins see the same thing, how can the traveling twin come home having aged only 5 years while her twin has aged 30 years? This is the crux of the twin paradox. The answer is that the point in time at which the signal transitions from slow to fast is not the same for the two twins. In the case of the traveling twin, this occurs when the traveling twin turns around. In the case of the Earthbound twin, this occurs shortly before the traveling twin returns. Merged post follows: Consecutive posts mergedI had stuff to do in real life, so I left that last post a bit unfinished. To finish it off, what does each of the twins see on their own clock and in the signal sent by the other twin? From the traveling twin's perspective, it takes here 2.5 years to travel to the other star. When she arrives, the signal from her twin will show that the Earthbound twin has aged by all of 76.63 days ([math]2.5\,\text{years}/(6+\surd 35)[/math]). After she turns around, the relativistic Doppler works exactly the other way. The time counter from her Earthbound twin advances 11.92 times per seconds. Her Earthbound twin appears to age 29.79 years during the 2.5 year return trip. On her return, the count sent from Earth will show that thirty years have passed on the Earth. The Earthbound twin calculates that it will take the traveling twin fifteen years to reach the star. However, that is not when the Earthbound twin sees the traveling twins signal switch from slow to fast. It takes an additional 14.79 years for the turnaround signal to reach Earth. In terms of signals, the Earthbound twin sees the traveling twin aging slowly (1 second per 11.92 seconds) for 29.79 years. The traveling twin appears to have aged only 2.5 years during this 29.79 year interval During the next 76.63 days the Earthbound twin will "see" the traveling twin as aging 11.92 times faster than he is aging. 76.63 day * 11.92 = 2.5 years. Total trip time from the perspective of the Earthbound twin is 30 years. Total aging of the traveling twin is five years. Bottom line: Both the traveling twin and Earthbound twin arrive at the same answers for the how much each of the twins aged during the trip. The traveling twin ages five years, and the Earthbound twin ages thirty years.

Now why would you assume that? He is 25 in his own frame.

What lost hand? That won't happen for another 25 years, in some future trip taken by the space twin.

nec209, these guys are making fun of you because this is some rather old news.

Just because something happens in multiple steps does not mean that there is a "goal". It takes many steps for water that falls on a mountainside before it reaches the ocean. Does this mean water has a goal to run downhill? Of course not. Its just dumb physics. The problem here is that using the term "goal" connotes intelligence. Here are a few synonyms for "goal": aim, ambition, aspiration, design, destination, intent, objective, plan, purpose, thought, will This mistaken connotation with intelligence is what led to this thread. Sorry to be a broken record, but Evolution does not have a goal. Don't anthropomorphize. Double doh. Piling on to iNow's facepalm, if "survival is evolution's goal", evolution has done one heck of a lousy job! It has a 0.1% success rate by this metric. 99.9% of the species that have ever lived are now extinct. No. The CO2 that came out of Lake Nyos had no intent. It did not "run after people". That, too, implies intent. While anthropomorphizing can help in gaining an understanding of a process ("water seeks to run downhill", "a forest fire greedily consumes everything combustible", "the goal of evolution is survival of the fittest"), one should always be aware that they are anthropomorphizing. Flowing water, raging forest fires, and evolution do not have goals. They are mindless processes.

Exactly. He is using the word "goal" and then claiming evolution is "intelligent". Well, duh. Goal implies intent. Think of it this way, Mr. Skeptic. Water placed in a freezer has a goal of turning to ice. Lightning striking a dead tree has a goal of starting an inferno. CO2 escaping from Lake Nyos had a goal of suffocating people and animals. There is no goal here. Just effect.

That is not a preset goal. What constitutes "fitness" is very dynamic. There is no intelligence behind it. In fact, "fitness" can be downright unintelligent. Witness all the different sexual dimorphisms in animal world. Male deer waste a lot of energy in growing and shedding antlers. Antlers are downright tame compared to some of the oddities in the insect world. If there is an intelligent designer behind evolution it is a dang cruel one. Evolutionary algorithms, like evolution, do not have a goal. In the case of EAs the goal is in the hands of the intelligent designer who uses evolutionary algorithms. In the case of evolution there is no goal, period. Why? An intelligent designer can do whatever it wants. An intelligent designer would just extract a rib and make it morph into some other form. Why use something slow and suboptimal like evolution? When it comes to designing things in the human world, using EAs (and machine learning in general) is often the last resort. Those techniques rarely escape the toy AI world because, like evolution, they are slow and often suboptimal.

Whoa there! First off, evolutionary algorithms are considered AI because the underlying concepts were developed by the AI community. Just because someone in the AI community developed some technique does not mean the technique itself is "intelligent". There is a huge difference between evolutionary algorithms and biological evolution. You cannot just pick up an evolutionary algorithm off the shelf and tell it "go solve this problem". You have to numerically define the goal, you have to come up with a scoring algorithm that assesses the distance between a tentative solution and this goal, and you have to specify various parameters that control the evolution. Evolutionary algorithms in and of themselves are not intelligent. They are just math. There is always an intelligent designer, a person, behind EAs when EAs are used to solve a problem. As has been discussed right here in this forum far too many times, biological evolution does not need an intelligent designer to function.

I knew from your first post, James, that you had a hidden, and most likely crackpot, agenda. Nonsense moved to Speculations.

I did say "informally". Formally, improper integrals such as [math]\int_{-\infty}^{\infty}\exp(-x^2)\,dx[/math] are better treated as a limit of a proper integral [math]\lim_{L\to\infty}\int_{-L}^{L}\exp(-x^2)\,dx[/math] Now add a complex offset to the integration interval: [math]\lim_{L\to\infty}\int_{-L+ib}^{L+ib}\exp(-z^2)\,dz[/math] Informally, this becomes [math]\int_{-\infty+ib}^{\infty+ib}\exp(-z^2)\,dz[/math] Not that that helps much because ... You're doing Fourier analysis and you haven't taken complex analysis? Shudder. Where can you learn it? As far as a cogent presentation goes, a book. Online stuff is too haphazard. I have Carrier, Krook, and Pearson, functions of a complex variable: theory and technique and Rudin, Real and Complex Analysis. Carrier is aimed at undergrads. Rudin is a lower level graduate text. Both are old, although Rudin is still apparently the gold standard. I hear ya. I'm a physicist by training but an aerospace engineer by profession. Sometimes the engineers I work with day in and day out can drive me nuts -- and these are aerospace engineers, one of the hardest of engineering disciplines. Merged post follows: Consecutive posts mergedThis page shows how to compute a Gaussian integral with a complex offset: http://ccrma.stanford.edu/~jos/sasp/Gaussian_Integral_Complex_Offset.html

Nope. It is not valid. When you are using a u-substitution in a definite integral you have to apply the substitution to the integration limits as well as to the integrand. The u-substitution works for a real offset because, informally, infinity plus some finite real offset is still just infinity. Infinity plus some finite imaginary offset is not just infinity. There are many definite integrals where pretending the complex offset isn't going to affect the answer will get you in loads of trouble. In this case ignoring that the offset is complex turns out to yield the correct answer. The reason is because (a) exp(-z^2) tends to zero as Re(z) tends to plus or minus infinity, and (b) exp(-z^2) is analytic on the complex plane.

Really. Look in your text. That's correct, but you have To make the above less messy, call it [math]\int _{-\infty}^{\infty} \exp\left(-(at+ib)^2\right)\,dt[/math] It is easy to go from the Gaussian integral [math]\int _{-\infty}^{\infty} \exp\left(-t^2\right)\,dt = \sqrt{\pi}[/math] to [math]\int _{-\infty}^{\infty} \exp\left(-at^2\right)\,dt = \sqrt{\frac{\pi} a}[/math] and even to [math]\int _{-\infty}^{\infty} \exp\left(-(at+b)^2\right)\,dt = \sqrt{\frac{\pi} a}[/math] All you need is a change of variables. Showing that [math]\int _{-\infty}^{\infty} \exp\left(-(at+ib)^2\right)\,dt = \sqrt{\frac{\pi} a}[/math] is going to take a bit more work. The change of variables technique is not valid here. If this is for a physics class you can probably get away with it. If it is for a math class, you can't. Showing that the same result pertains with a complex offset requires the use of Cauchy's integral formula.