# Posts tagged with “en”

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## anecdotes(1) - Charlie Watts

Author

Überblick

A famous anecdote relates that during the mid-1980s, an intoxicated Jagger phoned Watts' hotel room in the middle of the night asking "Where's my drummer?". Watts reportedly got up, shaved, dressed in a suit, put on a tie and freshly shined shoes, descended the stairs, and punched Jagger in the face, saying: "Don't ever call me your drummer again. You're my fucking singer!"hahaha!

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## mind. blown. causality paradox in detail explained using a Tachyonic antitelephone

Author

Überblick

mind. blown. (i didn't copy the formular images, for those please see the wiki articel)

As an example, imagine that Alice and Bob are aboard spaceships moving inertially with a relative speed of 0.8c. At some point they pass right next to each other, and Alice defines the position and time of their passing to be at position x = 0, time t = 0 in her frame, while Bob defines it to be at position x' = 0 and time t' = 0 in his frame (note that this is different from the convention used in the previous section, where the origin of the coordinates was the event of Bob receiving a tachyon signal from Alice). In Alice's frame she remains at rest at position x = 0, while Bob is moving in the positive x direction at 0.8c; in Bob's frame he remains at rest at position x' = 0, and Alice is moving in the negative x' direction at 0.8c. Each one also has a tachyon transmitter aboard their ship, which sends out signals that move at 2.4c in the ship's own frame.

When Alice's clock shows that 300 days have elapsed since she passed next to Bob (t = 300 days in her frame), she uses the tachyon transmitter to send a message to Bob, saying "Ugh, I just ate some bad shrimp". At t = 450 days in Alice's frame, she calculates that since the tachyon signal has been traveling away from her at 2.4c for 150 days, it should now be at position x = (2.4)*(150) = 360 light-days in her frame, and since Bob has been traveling away from her at 0.8c for 450 days, he should now be at position x = (0.8)*(450) = 360 light-days in her frame as well, meaning that this is the moment the signal catches up with Bob. So, in her frame Bob receives Alice's message at x = 360, t = 450. Due to the effects of time dilation, in her frame Bob is aging more slowly than she is by a factor of $\backslash frac\{1\}\{\; \backslash gamma\}\; =\; \backslash sqrt\{1\; -\; \{\; (v/c)^2\}\}$, in this case 0.6, so Bob's clock only shows that 0.6*450 = 270 days have elapsed when he receives the message, meaning that in his frame he receives it at x' = 0, t' = 270.

When Bob receives Alice's message, he immediately uses his own tachyon transmitter to send a message back to Alice saying "Don't eat the shrimp!" 135 days later in his frame, at t' = 270 + 135 = 405, he calculates that since the tachyon signal has been traveling away from him at 2.4c in the -x' direction for 135 days, it should now be at position x' = -(2.4)*(135) = -324 light-days in his frame, and since Alice has been traveling at 0.8c in the -x direction for 405 days, she should now be at position x' = -(0.8)*(405) = -324 light-days as well. So, in his frame Alice receives his reply at x' = -324, t' = 405. Time dilation for inertial observers is symmetrical, so in Bob's frame Alice is aging more slowly than he is, by the same factor of 0.6, so Alice's clock should only show that 0.6*405 = 243 days have elapsed when she receives his reply. This means that she receives a message from Bob saying "Don't eat the shrimp!" only 243 days after she passed Bob, while she wasn't supposed to send the message saying "Ugh, I just ate some bad shrimp" until 300 days elapsed since she passed Bob, so Bob's reply constitutes a warning about her own future.

These numbers can be double-checked using the [[Lorentz transformation]]. The Lorentz transformation says that if we know the coordinates x, t of some event in Alice's frame, the same event must have the following x', t' coordinates in Bob's frame:

$\backslash begin\{align\}\; t\text{'}\; \&=\; \backslash gamma\; \backslash left(\; t\; -\; \backslash frac\{vx\}\{c^2\}\; \backslash right)\; \backslash \backslash \; x\text{'}\; \&=\; \backslash gamma\; \backslash left(\; x\; -\; v\; t\; \backslash right)\backslash \backslash \; \backslash end\{align\}$

Where v is Bob's speed along the x-axis in Alice's frame, c is the speed of light (we are using units of days for time and light-days for distance, so in these units c = 1), and $\backslash gamma\; =\; \backslash frac\{1\}\{\; \backslash sqrt\{1\; -\; \{\; (v/c)^2\}\}\}$ is the [[Lorentz factor]]. In this case v=0.8c, and $\backslash gamma\; =\; \backslash frac\{1\}\{0.6\}$. In Alice's frame, the event of Alice sending the message happens at x = 0, t = 300, and the event of Bob receiving Alice's message happens at x = 360, t = 450. Using the Lorentz transformation, we find that in Bob's frame the event of Alice sending the message happens at position x' = (1/0.6)*(0 - 0.8*300) = -400 light-days, and time t' = (1/0.6)*(300 - 0.8*0) = 500 days. Likewise, in Bob's frame the event of Bob receiving Alice's message happens at position x' = (1/0.6)*(360 - 0.8*450) = 0 light-days, and time t' = (1/0.6)*(450 - 0.8*360) = 270 days, which are the same coordinates for Bob's frame that were found in the earlier paragraph.

Comparing the coordinates in each frame, we see that in Alice's frame her tachyon signal moves forwards in time (she sent it at an earlier time than Bob received it), and between being sent and received we have (difference in position)/(difference in time) = 360/150 = 2.4c. In Bob's frame, Alice's signal moves back in time (he received it at t' = 270, but it was sent at t' = 500), and it has a (difference in position)/(difference in time) of 400/230, about 1.739c. The fact that the two frames disagree about the order of the events of the signal being sent and received is an example of the [[relativity of simultaneity]], a feature of relativity which has no analogue in classical physics, and which is key to understanding why in relativity FTL communication must necessarily lead to causality violation.

Bob is assumed to have sent his reply almost instantaneously after receiving Alice's message, so the coordinates of his sending the reply can be assumed to be the same: x = 360, t = 450 in Alice's frame, and x' = 0, t' = 270 in Bob's frame. If the event of Alice receiving Bob's reply happens at x = 0, t = 243 in her frame (as in the earlier paragraph), then according to the Lorentz transformation, in Bob's frame Alice receives his reply at position x' = (1/0.6)*(0 - 0.8*243) = -324 light-days, and at time t' = (1/0.6)*(243 - 0.8*0) = 405 days. So evidently Bob's reply does move forward in time in his own frame, since the time it was sent was t' = 270 and the time it was received was t' = 405. And in his frame (difference in position)/(difference in time) for his signal is 324/135 = 2.4c, exactly the same as the speed of Alice's original signal in her own frame. Likewise, in Alice's frame Bob's signal moves backwards in time (she received it before he sent it), and it has a (difference in position)/(difference in time) of 360/207, about 1.739c.

Thus the times of sending and receiving in each frame, as calculated using the Lorentz transformation, match up with the times given in earlier paragraphs, before we made explicit use of the Lorentz transformation. And by using the Lorentz transformation we can see that the two tachyon signals behave symmetrically in each observer's frame: the observer who sends a given signal measures it to move forward in time at 2.4c, the observer who receives it measures it to move back in time at 1.739c. This sort of possibility for symmetric tachyon signals is necessary if tachyons are to respect the first of the two [[postulates of special relativity]], which says that all laws of physics must work exactly the same in all inertial frames. This implies that if it's possible to send a signal at 2.4c in one frame, it must be possible in any other frame as well, and likewise if one frame can observe a signal that moves backwards in time, any other frame must be able to observe such a phenomenon as well. This is another key idea in understanding why FTL communication leads to causality violation in relativity; if tachyons were allowed to have a "preferred frame" in violation of the first postulate of relativity, in that case it could theoretically be possible to avoid causality violations.

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## Troll level: Ted Bundy

Author

Überblick

Ted Bundy was an American serial killer, kidnapper, rapist, and necrophile who killed at least 30 people. So much for that, but he is considered one of the most intelligent serial killers ever. As such, he was a master troll (not to mention his escape):

During the penalty phase of the trial, Bundy took advantage of an obscure Florida law providing that a marriage declaration in court, in the presence of a judge, constituted a legal marriage. As he was questioning former Washington State DES coworker Carole Ann Boone—who had moved to Florida to be near Bundy, had testified on his behalf during both trials, and was again testifying on his behalf as a character witness—he asked her to marry him. She accepted, and Bundy declared to the court that they were legally married.

Imagine you stand trial for murder and you use some obscure law to legally and instantly marry a wittness, while you are both in court and she is being questioned about you and your murder doing.

Troll level: Grandmaster