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Musings on Random Musings


Kara Zor-El

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Re: Musings on Random Musings

 

Frank and Earnest are in the same inertial frame in the problem you set up, and as long as they remain both in the same frame, the wavelength sent by F and received by E are the same, and the time for the light to go from one to the other is independent of whatever joint motion the two have relative to something else. Each of them will measure the same time interval no matter what.

 

Relativistic effects start happening when you go between frames of reference, not within a single such frame. One of the fundamental assumptions in relativity is that the laws of physics operate the same way in all inertial frames. This assumption isn't due to Einstein; it's one that more or less everyone before and after Einstein requires of anything we call a scientific law. The oddities that everyone associates with relativity come when there are two different reference frames (moving at different constant velocities), and the apparent discrepancies between what one observer sees in the other guy's reference frame and what the other guy measures in his own reference frame.

 

General relativistic effects come about when the observers are in accelerating frames, or equivalently frames in different levels in a gravitational well.

 

("Special" relativity is the special case of constant velocity differences between frames. "General" relativity is the more general case of frames that have non-constant velocity differences, i.e., are accelerating with respect to each other.)

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Re: Musings on Random Musings

 

Also' date=' define stationary. :D[/quote']

 

And 'non-local' :P

 

Space is non-local, right?

 

Both of these are non-trivial questions. Einstein addresses both directly in the early parts of his 1905 paper "One the Electrodynamics of Moving Bodies". I encourage you to read that for yourselves. The heavy math doesn't start until section 3, but every sentence in the early portions of that paper has important and well-considered meaning.

 

Don't be put off by the first paragraph; you probably won't have the physics background to see what's going on. In Maxwell's equations (that describe all of electromagnetism, formulated in the late 19th Century) without the careful attention to relativity (which came 30 - 40 years later) you get a weird situation where if you move a magnet past an electrical conductor you supposedly get one thing, but if you move the conductor past the magnet you get another thing. If that were correct, then you'd have a way to tell absolutely who was moving and who wasn't. There is no equivalent trick in mechanics: when you do the math right, the same thing happens when viewed from two different frames of reference.

 

That fundamental difference between mechanics and electrodynamics was very puzzling to physics. Even more puzzling was the null result when experiments were made to try to detect the absolute motion of the Earth. We know that the Earth moves in approximately a circle at about 30 km/second around the Sun, so its motion at one time of the year is 60 km/s different from its motion six months later. But a measurement that should have detected the consequences of these differences in Earth's velocity failed, and failed spectacularly, finding no such difference.

 

The contradictions are resolved when you abandon the idea of absolute time and instead assume the speed of light is a constant in all frames of reference independent of the motion of the body that emits the light, AND define what you mean by "time" and "distance" precisely, AND work out the consequences of those assumptions and definitions.

 

If you don't work them through, and cling to the intuition you've developed from an existence spent at low velocities and small accelerations and the seductive and intuitive idea of absolute time, then you won't understand and you will persist in thinking that there is a "correct" physical frame of reference in any particular problem, and you'll flunk out of a lot of physics courses at the sophomore level or higher. And if life were fair, any GPS-based device would stop functioning in your presence (and you'll be killed in your next plane trip), because if you don't include the relativistic terms in the GPS system you get errors in position of hundreds of meters (and some of those errors are vertical, not just horizontal).

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Re: Musings on Random Musings

 

Both of these are non-trivial questions. Einstein addresses both directly in the early parts of his 1905 paper "One the Electrodynamics of Moving Bodies". I encourage you to read that for yourselves. The heavy math doesn't start until section 3, but every sentence in the early portions of that paper has important and well-considered meaning.

 

Don't be put off by the first paragraph; you probably won't have the physics background to see what's going on. In Maxwell's equations (that describe all of electromagnetism, formulated in the late 19th Century) without the careful attention to relativity (which came 30 - 40 years later) you get a weird situation where if you move a magnet past an electrical conductor you supposedly get one thing, but if you move the conductor past the magnet you get another thing. If that were correct, then you'd have a way to tell absolutely who was moving and who wasn't. There is no equivalent trick in mechanics: when you do the math right, the same thing happens when viewed from two different frames of reference.

 

That fundamental difference between mechanics and electrodynamics was very puzzling to physics. Even more puzzling was the null result when experiments were made to try to detect the absolute motion of the Earth. We know that the Earth moves in approximately a circle at about 30 km/second around the Sun, so its motion at one time of the year is 60 km/s different from its motion six months later. But a measurement that should have detected the consequences of these differences in Earth's velocity failed, and failed spectacularly, finding no such difference.

 

The contradictions are resolved when you abandon the idea of absolute time and instead assume the speed of light is a constant in all frames of reference independent of the motion of the body that emits the light, AND define what you mean by "time" and "distance" precisely, AND work out the consequences of those assumptions and definitions.

 

If you don't work them through, and cling to the intuition you've developed from an existence spent at low velocities and small accelerations and the seductive and intuitive idea of absolute time, then you won't understand and you will persist in thinking that there is a "correct" physical frame of reference in any particular problem, and you'll flunk out of a lot of physics courses at the sophomore level or higher. And if life were fair, any GPS-based device would stop functioning in your presence (and you'll be killed in your next plane trip), because if you don't include the relativistic terms in the GPS system you get errors in position of hundreds of meters (and some of those errors are vertical, not just horizontal).

 

Ah, the Michaelson-Morley experiment. I've heard it described as one of the most important "null result" experiments in modern science. And there are some (imo nutjobs) on Youtube that deny the results.

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Re: Musings on Random Musings

 

The actual experiment:

http://en.wikipedia.org/wiki/Bell_test_experiments#Aspect.2C_1981-2

 

Stated more simply' date=' the experiment provides strong evidence that a quantum event at one location can affect an event at another location without any obvious mechanism for communication between the two locations. This has been called "spooky action at a distance" by Einstein (who doubted the physical reality of this effect). However, these experiments do not allow faster-than-light communication, as the events themselves appear to be inherently random.[/quote']
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Re: Musings on Random Musings

 

Chromosome 2 in humans is a result of an end-to-end fusion of two ancestral chromosomes, leaving telomeres in the 'middle', and a second (inactive) centromere.

As far as we know, is this arrangement unique to humans, or has this occurred to any other animal (or plant) on Earth as well?

This is very common, I'd think. The number of chromosomes vary between species, and this would be one last step in the process of speciesation.

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Re: Musings on Random Musings

 

Game Seven of what?

 

jg

 

 

Actually, Game 7 of the first round of the National Hockey League championships between the Chicago Blackhawks and Vancouver Canucks, won last night in the fifth minute of overtime by the Canucks, on a goal from Alexandre Burrow at about 10:20 local, or four hours after my usual bedtime.* The city was under an all-enveloping cloud of gloom and silence for much of the last week as the Canucks gave up a 3 game advantage over the Blackhawks, a team that has emerged as its post-season nemesis over the last 3 years. It's lifted now, and the Canucks go on to play the Nashville Predators in the next round. I imagine Hermit will chime in soon about how excited Nashville is about spring hockey.

 

 

*(I work early! And I'm totally not defensive about my lifestyle!)

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