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The Lorentz transformations of special relativity on which the twin paradox is based assume that the set of observations of mass, length, and time is made from one inertial reference frame , one coordinate system that is either at rest or is moving with an unchanging speed in a particular direction.

Clearly, observations do not have to be made from an inertial reference frame, but if they are not, the Lorentz transformations don't directly apply.

[] Langevin's `Twin Paradox' paper revisited

Sam is not in an inertial frame because in mid trip his ship's engines were used to accelerate him and to reverse the direction of his velocity for the return leg of the trip. If one constructs world lines for the two observers by plotting space position against time position on a piece of graph paper, the world line of Ernest is straight, an indication that he is in an inertial frame. The world line of Sam , however, has a kink at the place where the ship's acceleration takes place, an indication Sam is not in an inertial frame.

Therefore, the seeming "symmetry" between systems Ernest and Sam is illusory. Their observations are not equivalent because Ernest observes from an inertial frame while Sam does not. Can we analyze the problem from the point of view of Sam? We can for part of Sam's trip by using the point of view of an observer Albert who goes out with the ship on which Sam travels, but continues to travel on at the same speed in the original direction after Sam's ship turns around and comes back.

Half a year later, after Ernest has traveled. The whole episode takes 4 years according to Albert's clock. However, Ernest's clock runs slow by a factor of 2, so it will register only 2 years. Sam's clock read 0. Catching up with Ernest required 3. Therefore, Sam's clock registered a total elapsed time of 1 year as compared to 2 years on Ernest's clock.

This is the same result as before, even though it was observed from a very different perspective.

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Notice, however, that all the clock readings do not match. But Ernest's clock was at a large distance from Sam when his ship accelerated, so Sam's clock and Ernest's clock cannot be placed side-by-side for comparison. In special relativity separated clocks need not have the same relative readings in all systems. This is the reason that in relativity two separated events can be said to happen at the same time only in reference to a particular reference frame.

Physics > General Physics

The "know-nothing" argument is wrong because its basic premise is incorrect. The formalism of general relativity is not required to deal with acceleration. Special relativity works fine for accelerating objects, as long as the Lorentz transformations are based in a reference frame that is not accelerating. One simply allows object's velocity to change with time. You can think of the process as breaking up the acceleration into little time intervals during which the velocity has a certain average value, and then apply the value of gamma appropriate to that velocity in that time interval.

This may require some calculus, but it doesn't require general relativity, which deals with the effects of gravity fields. However, general relativity does provide us with another way of thinking about the twin paradox. This means that a clock on the surface of the Earth runs slower that an identical clock in gravity free space by a factor of 1 - 6. In one year of running, the earth-based clock would lose 20 milliseconds.

Now consider a thought experiment. Suppose that for a period of one hour, a cosmos-wide g gravitational field switches on over the whole observable universe, and then switches off again.

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Everything in the universe will free-fall in this field, gaining enormous velocity and energy. What are the observable consequences of such a cosmic event? Since all objects in the universe would accelerate together, there would be no observable clues that the gravitational field is even there. It would be as if it had never happened. Because switching on and off such a field has no observable consequences, we can pretend it is happening to deal with acceleration. In the case of Sam and Ernest, suppose that a universe-wide gravitational field switches on, but astronaut Sam, determined to maintain his ship's position, uses it's engines to counteract the force.

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Sam stays at a fixed point. He experiences a force pulling him in the direction of the field, but he remain at rest. After half a year, the force switches on again, this time acting in the opposite direction for twice as long, and Ernest's velocity is reversed, bringing him back to Sam's ship. Sam always uses the engines to hold his fixed spatial position. Finally, the force switches on one last time to bring Ernest to rest with respect to Sam at the same position.

Ernest has never observed any acceleration, since he was always in free fall. Yea me too, some of those fixtures were beautiful, but you just know they were unceremoniously tossed in the trash in favour of those ugly stainless steel mixing bowl things.

Physics > Classical Physics

This was one of my all time favorite episodes and one of his most successful turnarounds too. Not only are they still open and doing well, the Yelp on this restaurant is quite impressive. Infact Jeff is pretty active in responding to the Yelpers not only the positive ones but the negative ones as well, he takes the feedback like a champ. I am definitely planning on visiting this place next time I'm in the greater LA area. Great episode and glad to see two brothers that cared for each other and wanted to turn their lives and business around completely.

I love seeing people open their eyes and willing to change and run with the opportunity when they see it! And people who care!!!! This is a great show and I'm happy to see this one still open!!! Yehhhhh they are still open. They had nothing to fail cause Ramsay show them a path. But these 2 man they have done unexpected and even won a prize of best pizza. Its really true to Cook good food u really need good heart. This is a rare episode that I'm rewatching. I usually don't bother seeing they are still open or closed, but I'm happy to see that they are able to keep open in a sustainable rhythm.

I certainly wish them the best! Having eaten there, I have to say their pizza is really good. Their style of pizza isn't for everyone, however. The crust is thinner than most American pizzas ala real Italian pizza and had a little more salt than normal, but I still liked it. I also had one of their amazing appetizers, I only wish I had the chance to try more.

I managed to speak with them since it was during a slow lunch, and they said they're doing fine, but not great. They want to hold off on that though, because they're worried if they open a second location, they'll totally sink. Best episode of the us version. These are guys you actually want to see succeed because they appeared grateful and took the advice to heart.

This is the bright spot of the series. This episode made me retch. The gum under the tables, the filthy restaurant, the nasty food and kitchen, and the sweaty twins who served garbage. And I do mean I actually gagged whr they were cleaning that gum -- I had to look away. I would never subject myself to that place -- I don't trust the owners not to serve rotten food in dirty conditions. Just watched the revisit since watching the original, very happy to see them doing well i love these guys im from australia i'd go there just to see their cheery faces, i really hope they keep their standards and become the main popular place to eat.

It's not BAD for anyone to cry, at all. But get Jeff together with the crying sister from Yanni's, they'll flood us out!

Kitchen Nightmares US S04E12

It's always nice when a restaurant on Kitchen Nightmares succeeds, but I'm especially happy that Capri is still open! The twins seem like fantastic guys, and I'm glad they took Gordon Ramsay's advice; a lot of people don't do that, which is part of the reason so many restaurants on this show fail.

The twins just needed a boot in the rear to get them going. It also helps that they have very good staff; often times, I've seen bad staff that are just as bad, if not worse than the owner s. After seeing one of the twins tasting food from a pot with his bare fingers, I'd never eat there. The restaurant still looks nasty to me. It's now and I just saw this episode for the first time, I'm on a KN binge.

Love the screaming and dramatics with Ramsey and owners, but not with these guys. I think the twins got to him too. First show that has brought tears to my eyes. Hope they still open!!! Really glad to see this one still open with mostly good reviews. You could tell Gordon genuinely wanted to sort the issues out for these two and who wouldn't..? All comments are moderated, those with swear words and racist language will not be approved.

The staff call them overgrown boys, immature and say that they do as little work as possible. They don't open for lunch and only open 5 nights a week to save on wages. Gordon sits down to try the food, the menu is falling apart and the restaurant was dirty. Gordon tastes a meatball sandwich , Chicken Scarpello and the Colossal Pizza. The waitress confesses to Gordon that the restaurant has not been cleaned as Jim is lazy to do it.

The meatballs are bought in and microwaved, the pizza is falling apart and Kim can't tell him exactly how old the frozen chicken is. Gordon gets the staff to clean up before the next service. Gordon watches a dinner service and finds the kitchen to be dirty, there are rotten vegetables and warm sauce in the fridge. Lots of dishes get returned and there is a lot more sobbing. Gordon discovers that the chicken isn't being safely defrosted, tells Jim to take it off the menu but instead he announces this to the dining room and the diners walk out.

Gordon brands the service lazy and tells Jim and Jeff to clean their kitchen alone. Gordon decides that they need to open for lunch and with help from the staff they open. Jim and Jeff arrive to a full dining room, Gordon had introduced a new simple lunch menu and sits them down to sample it. Gordon takes the twins to a boxing ring to allow them to get out their frustrations about the restaurant. They box each other and promise better communication. Gordon teaches them to make meatballs and Jim goes out to the street to shout about their meatballs.

Overnight the restaurant is transformed and new menus are revealed. On relaunch night the restaurant is packed, Jim is in the kitchen expediting and the food quickly makes its way out the kitchen. Some dishes go out too quickly and are sent out cold. Not long into service that the kitchen starts to fall behind and customers are frustrated. Gordon takes them outside for a pep talk, the kitchen turns it around and the customers love the food.