Special Relativity III: Hard Paradoxes

[SsDd]

The lecture video is embedded below.

Additionally, slides used in the lecture are embedded below, or can also be downloaded directly from here.

Questions after the lecture? Please feel free to post them in the same thread.

Click to play embedded YouTube video.

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Lecture Links:-

Twirling Pole Paradox
Superluminal Scissors
Twin Paradox

Play Online Relativistic Games:-

Twin Paradox Applet
Nova Time Traveler

[lhurd]

Been enjoying the lectures. I took way too much math and insufficient physics when I was an undergraduate and I have been enjoying the diversion.

The barn paradox did not have the punchline I was expecting. As I was first taught that one there was the twist that from the point of view of the guy running with the ladder, the barn has contracted and so it is even more absurd to think that the ladder which is now even longer relative to the barn would fit. The explanation I first heard was that we are, of course, in a state of sin by talking about simultaneity. What we mean by "fit" is that the doors are simultaneously shut and of course to one observer this is so and to the other it is patently not.

[jacob90002003@yahoo.ca]

travelling in space at near the speed of light your heart rate slows down a ruler would not measure 12 inches etc. on earth 50 years would pass, but to you only 10 years have passed. if and when you return to earth you would land before you had left. therefore you returned to the past as far as the people on earth are concerned. There is no future time it doesn't exsist only the past and what is happening right now.

[Chris Peterson]

travelling in space at near the speed of light your heart rate slows down a ruler would not measure 12 inches etc.

Yes, but only as seen from a different frame of reference. You wouldn't notice anything odd- indeed, there would be nothing odd.

on earth 50 years would pass, but to you only 10 years have passed. if and when you return to earth you would land before you had left. therefore you returned to the past as far as the people on earth are concerned.

I'm not sure where you are getting this idea. When you return to Earth, you'll be 10 years older but 50 years will have passed on the Earth. You certainly won't arrive before you left; you'll arrive 50 years after you left (in Earth's frame) and 10 years after you left in your own frame.

[neufer]

The barn paradox did not have the punchline I was expecting. As I was first taught that one there was the twist that from the point of view of the guy running with the ladder, the barn has contracted and so it is even more absurd to think that the ladder which is now even longer relative to the barn would fit. The explanation I first heard was that we are, of course, in a state of sin by talking about simultaneity. What we mean by "fit" is that the doors are simultaneously shut and of course to one observer this is so and to the other it is patently not.

Your version is nicer in a way since one need not concern
one's self about the physical properties of the ladder/barn.

A Minkowski diagram of ladder paradox. The garage is shown in light blue, the ladder in light red. The diagram is in the rest frame of the garage, with x and t being the garage space and time axes, respectively. The ladder frame is for a person sitting on the front of the ladder, with x′ and t′ being the ladder space and time axes respectively. The x and x′ axes are each 5 feet long in their respective frames, and the t and t′ axes are each 5 ns in duration.

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Scenario in the garage frame --- Scenario in the ladder frame

[Roger Overcash]

travelling in space at near the speed of light your heart rate slows down a ruler would not measure 12 inches etc.

Yes, but only as seen from a different frame of reference. You wouldn't notice anything odd- indeed, there would be nothing odd.

on earth 50 years would pass, but to you only 10 years have passed. if and when you return to earth you would land before you had left. therefore you returned to the past as far as the people on earth are concerned.

I'm not sure where you are getting this idea. When you return to Earth, you'll be 10 years older but 50 years will have passed on the Earth. You certainly won't arrive before you left; you'll arrive 50 years after you left (in Earth's frame) and 10 years after you left in your own frame.

I feel that most had missed the cause here for the time dilation for the twin paradox. In this case, it has very little to do with special relativity. The earth is also moving away at a high speed relative to the rocket. Someone on the rocket would assume he is stationary and the earth is moving away at a high speed and seeing the people back on earth moving slowly. On the return trip the opposite is true. On a round trip this would mostly cancel out what is gained and what is lost. The time dilation in the twin paradox requires general relativity. The rocket has to be constantly accelerating, throwing more than one G continuously on the traveler. This reference frame of stronger gravity (Gs) has a slower time frame relative to the one G of earth and multiplied over the time of the trip, the time difference occurs.