The Twins Revisited

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The column described how an advanced civilization might construct a stable "wormhole", a trans-spatial shortcut between one region of space and another, and use this shortcut for both faster-than-light travel and time travel. Shortly after the column appeared in Analog , I received an irate letter arrived from a regular reader with a good background in physics.

He complained that one of the points made in my wormhole column was physically incorrect. He demanded that I correct this serious mistake and set the record be set straight with a printed retraction.

This reaction, in itself, isn't unexpected. FTL and time travel are very controversial topics that lie well outside the usual "circle of discourse" of contemporary physics. Even though they are now moving toward this circle of discourse, some objections are to be expected.

However, the complaint was not about FTL or time travel. The reader objected instead to my reference to the twin paradox of special relativity. In the wormhole column, I had stated correctly that if a space ship made a round-trip to a point 0. It was this allusion to the twin paradox which had prompted the letter. The relativistic twin paradox, the slowing of biological clocks by relativistic time dilation and the differences in aging thereby produced are not new in science fiction.

They provide the premise for many excellent SF works: There was no physics goof in the use of the twin paradox in the wormhole column, but the irate letter points up an interesting fact. The twin paradox is still, some 85 years after publication of Einstein's paper on special relativity, not generally understood. Therefore, I've decided to devote this column to an exploration of the twin paradoxes of both special and general relativity.

Physics > Classical Physics

An observer at rest will see three amazing changes in an object moving past him at a velocity v not much less than c: At this velocity, exactly half of the mass-energy of the moving object comes from its mass-energy at rest and the other half is kinetic energy. In other words, acceleration must supply an amount of energy equal to the object's rest mass m 0 , giving it a kinetic energy equal to m 0 c 2.

Much of the confusion surrounding the twin paradox can be traced to two specious arguments: Argument 1 , which might be called the symmetry argument , usually goes like this: But Sam also observes that the stay-at-home observer Ernest travels away from him at speed v and then returns at that speed. Sam is just as good an observer as Ernest, and since each observes the other having the same velocity relative to himself, there can be no difference in the readings of Ernest's clock and Sam's clock when the two clocks are compared at the end of the trip.

But space ships must accelerate and decelerate in their operation. From the equivalence principle of general relativity we know that acceleration is equivalent to the effects of gravity and that gravity must be handled with the elaborate mathematical machinery of general relativity.

Therefore, the twin paradox cannot be analyzed with special relativity alone, and we can't simply use the Lorentz transformations to say what the two clock readings will be after the trip. If there is any difference in the clock readings, it arises strictly from general relativity effects. Let's take the symmetry argument first.

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. 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.

Submission history

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. 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!

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. Gordon revisits and they are open for lunch, Jeff controls the front of house and Jim is in the kitchen. Gordon sits down for lunch with the twins and feels under the tables for gum. Gordon has a surprise for them both, it is a certificate of appreciation for their meatballs from the local Chamber of Commerce. Both the Yelp reviews and Trip Advisor reviews after the show are mostly good with a few bad reviews commenting negatively on some dishes and service.

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In March , they won a poll for the best pizza in Eagle Rock. Capri was aired on May 06 , the episode was filmed in January and is Kitchen Nightmares season 4 episode Click for more Kitchen Nightmares. Posted by Reality TV Revisited. Anonymous 1 February at Anonymous 5 February at John 7 August at Anonymous 22 January at Anonymous 20 May at Anonymous 18 November at Mags 28 January at Anonymous 23 January at Anonymous 8 February at Anonymous 20 April at Anonymous 3 June at Anonymous 5 January at Anonymous 12 June at Tim Rochelle 24 July at Anonymous 10 August at Anonymous 28 September at Anonymous 30 September at Anonymous 11 February at Anonymous 24 May at Tracy Cozzens 29 August at Lisa Little 14 January at InfamousOreob 20 January at

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