tag:blogger.com,1999:blog-5592542.post7155823987961939626..comments2020-01-08T18:54:45.879-08:00Comments on Rondam Ramblings: We interrupt this blog to bring you a little eureka momentRonhttp://www.blogger.com/profile/11752242624438232184noreply@blogger.comBlogger12125tag:blogger.com,1999:blog-5592542.post-10542413463854737922019-04-08T08:32:14.308-07:002019-04-08T08:32:14.308-07:00@Peter:
> if two clocks do in fact meet twice,...@Peter:<br /><br />> if two clocks do in fact meet twice, at least one has to accelerate somewhere<br /><br />That's true. But it's possible to tweak the scenario so that both clocks undergo the same accelerations (not at the same time of course) and still reunite with different ages. Figuring out how makes a good exercise.<br />Ronhttps://www.blogger.com/profile/11752242624438232184noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-32181872186732707602019-04-07T20:30:26.817-07:002019-04-07T20:30:26.817-07:00the triangle inequality (which I mentioned to Ron)...<i>the triangle inequality (which I mentioned to Ron), which in the spacetime version says that the sum of the lengths of any two sides of this triangle must be *less* than the length of the third</i><br /><br />Actually, I misstated this. The correct statement is that the sum of two sides that are placed so that the future endpoint of one is the past endpoint of the other, must be less than the Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-73314451867390620772019-04-07T20:11:52.335-07:002019-04-07T20:11:52.335-07:00Thanks for the interesting comments, Peter!Thanks for the interesting comments, Peter!Don Geddishttps://www.blogger.com/profile/04214642122689048677noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-26835472148593174182019-04-07T19:24:16.176-07:002019-04-07T19:24:16.176-07:00Instead, it is an intuitive "explanation"...<i>Instead, it is an intuitive "explanation" that matches the mathematics.</i><br /><br />Actually, it doesn't. This is a pet peeve of mine so I'll elaborate a bit. :-)<br /><br />Timelike worldlines, like yours and mine, have a thing called "4-velocity" at any point, which is the unit vector pointing into the future that is tangent to the worldline at that point. Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-2713702300448332822019-04-07T19:10:30.830-07:002019-04-07T19:10:30.830-07:00If you point your single speed in the direction of...<i>If you point your single speed in the direction of space, like a photon, then you get none left over to go through time. At the other extreme, if you sit still in one place so that you don't go through space at all, then you will find time passing at the maximum rate. Or, you can choose something in the middle, where some of your (one and only) velocity will allow you to travel through Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-47279838276127819922019-04-07T18:58:37.137-07:002019-04-07T18:58:37.137-07:00I'll admit that I haven't worked out the m...<i>I'll admit that I haven't worked out the math yet.</i><br /><br />Spoiler alert: it does work out. :-)<br /><br /><i>The math must work out, that there is never enough time (or distance) for C's clock -- which starts behind but is ticking faster -- to catch up to B's clock, which starts ahead but is ticking slower. Regardless of the relative speeds of A and B, as they head Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-26064726882459745472019-04-07T18:38:39.838-07:002019-04-07T18:38:39.838-07:00Everything in this "explanation" is wron...<i>Everything in this "explanation" is wrong.</i><br /><br />I think this is a bit extreme. A better statement would be "this explanation does not generalize". Or, expanding somewhat: whenever you have two people who separate, then later come back together, and they find that their elapsed times are different, there must be some difference between them. So the general form of Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-42609827471810810002019-04-07T15:20:15.856-07:002019-04-07T15:20:15.856-07:00BTW: I haven't read Maudlin's book (yet). ...BTW: I haven't read Maudlin's book (yet). But I once came across Lewis Carroll Epstein's <a href="https://www.amazon.com/Relativity-Visualized-Lewis-Carroll-Epstein/dp/093521805X" rel="nofollow">Relativity Visualized</a> (1985). From what you describe of Maudlin's book, they seem to have similar goals: explain relativity without math. Epstein even directly tackles the Don Geddishttps://www.blogger.com/profile/04214642122689048677noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-43947347277422924882019-04-07T15:03:47.727-07:002019-04-07T15:03:47.727-07:00"earth doesn't move with respect to the m..."<i>earth doesn't move with respect to the medium ... the speed of light is the same in all frames ... [is] not the only possibility.</i>"<br /><br />Yes, yes! Absolutely. Fair enough. But that's why I would say that making that assumption, and then exploring the consequences, <i>does</i> make the "constant speed of light" the "foundational principle" of (Don Geddishttps://www.blogger.com/profile/04214642122689048677noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-62871627775433343502019-04-07T14:53:39.074-07:002019-04-07T14:53:39.074-07:00> it was the experimental evidence of the const...> it was the experimental evidence of the constant ("measurement of the") speed of light, that required the development of relativity<br /><br />Well, kinda sorta. The Michaelson-Morley experiment didn't really prove that light has the same speed in all reference frames, it only showed that earth doesn't move with respect to the medium through which light travels (the Ronhttps://www.blogger.com/profile/11752242624438232184noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-88655921884715025712019-04-07T14:29:17.243-07:002019-04-07T14:29:17.243-07:00"the speed of light is not constant ... measu..."<i>the speed of light is not constant ... measuring the "speed" of light will give you the same result no matter what reference frame you're in ... It is not, as is often taught, the foundational principle of relativity. Einstein himself got this wrong.</i>"<br /><br />I'm not sure that I fully appreciate this philosophical point. To be fair to Einstein, the Don Geddishttps://www.blogger.com/profile/04214642122689048677noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-52376170779502145382019-04-07T14:19:12.687-07:002019-04-07T14:19:12.687-07:00In your 3 clocks example, I'm trying to think ...In your 3 clocks example, I'm trying to think through the C perspective. You've described it from the perspective of B, which is clear. And of course only one thing can happen, so the math surely must work out.<br /><br />But from C's perspective: it is stationary. It notices A & B meet, and synchronize their clocks. Then it sees A moving very fast towards it, and B moving Don Geddishttps://www.blogger.com/profile/04214642122689048677noreply@blogger.com