Here is a puzzle about Relativity that I am not able to solve; please help:
Imagine that Harry Potter is using his magical powers to test Relativity experimentally. He finds a very small room in a tower in Hogwarts, with two windows in opposing walls. He also finds a broom that is just a bit longer than the distance between the windows.
So, Professor Quirrell stands in the room and watches Harry fly through the room very fast. From Harry’s point of view, the room became shorter. But from Professor Quirrell’s point of view, it’s Harry’s broom that became shorter, and now it seems actually shorter than the distance between the windows.
As an experiment, Harry asks Professor Quirrell to quickly close and than open again both windows simultaneously when Harry is inside the room. From Professor Quirrel’s point of view, it should be possible because the broom is shorter than the room. From Harry’s point of view, it should be impossible because the broom is longer than the room.
What really happens is that “simultaneously” is also relative. This is how Professor Quirrell describes the event: When Harry was inside the room, both windows closed and opened simultaneously, keeping Harry trapped in the room for a short moment. This is how Harry describes it: Before he fully entered the room, the second window was closed and then opened; then he flew across; and then when he already partially left the room, the first window was closed and then opened behind his back. So for both observers the described events make sense.
Is this a correct explanation? (Seems so to me, but I am not sure.)
The problem is, Professor Quirrell, as usually, plays this game one level higher than Harry. Despite their agreement, he decides to close the both windows simultaneously and keep them closed. Let’s suppose the windows and broom are magical, therefore almost indestructible. What exactly happens, microsecond after microsecond, from Professor Quirrell’s point of view? (Until Harry’s broom hits the second window, the situation should be exactly the same, right?) And what exactly happens from Harry’s point of view?
Please post the answer rot13′d so that other people can make their guesses independently. I tried, but I’m giving up. I suspect that my inability to solve the second part means that I also got the first part wrong, but I don’t see how exactly.
Lrf, lbhe rkcynangvba bs gur fgnaqneq fvghngvba vf pbeerpg. Va lbhe fpranevb, Uneel bofreirf gur oebbz fgevxr gur jvaqbj orsber gur erne jvaqbj pybfrf. Vs gur oebbz jvaf gur svtug jvgu gur jvaqbj, Uneel syvrf bhg naq bofreirf gur erne jvaqbj pybfr ba gur erthyne fpurqhyr. Ohg jung vs gur jvaqbj fheivirf naq fgbcf gur oebbz? Jryy, bowrpgf va fcrpvny eryngvivgl pna’g or cresrpgyl evtvq.
N fgnaqneq rknzcyr bs ubj bowrpgf pna’g or evtvq vf jung vs lbh unir gjb evtvq cbyrf zrrgvat ng na natyr naq lbh gel gb punatr gur natyr? Vs gurl jrer evtvq, gur raq bs gur cbyr pbhyq zbir snfgre guna yvtug. Ohg gur gbedhr gnxrf gvzr gb cebcntngr qbja gur cbyr, cebonoyl ng gur fcrrq bs fbhaq. Ng eryngvivfgvp fcrrqf, gur fubpx jnir vf fhcrefbavp.
Fvzvyneyl, gur gnvy bs gur oebbz qbrfa’g srry nal erfvfgnapr hagvy gur vasbezngvba unf cebcntngrq sebz gur pbyyvfvba, ng fybjre guna gur fcrrq bs yvtug. N ernyvfgvp fpranevb vf gung obgu ner qrfgeblrq naq gung gur gnvy bs gur oebbz ragref gur sveronyy abg lrg fybjrq qbja. Dhveery frrf gur pbyyvfvba unccra svefg, gura gnvy syl guebhtu gur jvaqbj, gura gur gnvy ragre gur sveronyy. Uneel frrf vg syl guebhtu jvaqbj, gura gur sebag pbyyvfvba, gura gur gnvy ragre gur sveronyy.
Ohg lbh cebonoyl jnag gb xabj nobhg na rynfgvp pbyyvfvba. Obgu bofreiref frr gur oebbz pbzcerff. Dhveery frrf gur oebbz fgneg gb pbzcerff orsber gur gnvy unf tbar guebhtu gur jvaqbj. Ohg ur bayl frrf gur sebag bs gur oebbz pbzcerff. Gur onpx vf fgvyy ng vgf byq qrafvgl. Ol gur gvzr gur jnir bs pbzcerffvba sebz gur gnvy, vg vf vafvqr gur ebbz. Qb lbh pner nobhg pybfvat gur onpx jvaqbj? Va gur vaqrfgehpgvoyr fpranevb, gur oebbz orpbzrf jrqtrq orgjrra gur gjb jvaqbjf, pbzcerffrq gb gur fvmr bs gur ebbz. Haqre na rynfgvp nffhzcgvba, gur raretl unfa’g qvffvcngrq, ohg gur nzbhag bs pbzcerffvba vf n jnir obhapvat onpx naq sbegu orgjrra gur raqf.
Gur svefg cneg vf pbeerpg. Sebz Dhveeryy’f cbvag bs ivrj gur sebag raq bs Uneel’f oebbz uvgf gur sebag jvaqbj nsgre ur’f fuhg gur erne jvaqbj. Nf gur sebag fgbcf vg trgf ybatre, chfuvat onpx ba gur cnegf oruvaq vg, juvpu zhfg rvgure fdhnfu be fanc; gur bayl nafjre V pna tvir gb “gur oebbz vf zntvpnyyl vaqrfgehpgvoyr” vf “gung’f abg culfvpnyyl cbffvoyr”.
Sebz Uneel’f cbvag bs ivrj, gur sebag bs uvf oebbz uvgf gur sebag jvaqbj naq nppryrengrf encvqyl gbjneqf uvz, fuevaxvat nf vg qbrf fb (guvf vf orsber gur erne jvaqbj pybfrf). Vs ur’f fvggvat va gur zvqqyr gura ng fbzr cbvag ur fgbcf naq uvf senzr orpbzrf gur fnzr nf Dhveeryy’f. Vs ur’f fvggvat ng gur irel onpx bs gur oebbz gura ur tbrf guebhtu gur erne jvaqbj nsgre gur sebag bs gur oebbz “fubhyq” unir cnffrq guebhtu gur sebag jvaqbj, ohg ur pna’g lrg frr gung vg unfa’g (orpnhfr bs gur fcrrq bs yvtug). Fb vg’f culfvpnyyl vzcbffvoyr sbe gur oebbz gb or evtvq rabhtu gb fgbc uvz trggvat cnfg gur erne jvaqbj, orpnhfr gung jbhyq zrna genafzvggvat vasbezngvba snfgre guna gur fcrrq bs yvtug. Bar jnl be nabgure, gur oebbz unf gb pbzcerff.
Here is a puzzle about Relativity that I am not able to solve; please help:
Imagine that Harry Potter is using his magical powers to test Relativity experimentally. He finds a very small room in a tower in Hogwarts, with two windows in opposing walls. He also finds a broom that is just a bit longer than the distance between the windows.
So, Professor Quirrell stands in the room and watches Harry fly through the room very fast. From Harry’s point of view, the room became shorter. But from Professor Quirrell’s point of view, it’s Harry’s broom that became shorter, and now it seems actually shorter than the distance between the windows.
As an experiment, Harry asks Professor Quirrell to quickly close and than open again both windows simultaneously when Harry is inside the room. From Professor Quirrel’s point of view, it should be possible because the broom is shorter than the room. From Harry’s point of view, it should be impossible because the broom is longer than the room.
What really happens is that “simultaneously” is also relative. This is how Professor Quirrell describes the event: When Harry was inside the room, both windows closed and opened simultaneously, keeping Harry trapped in the room for a short moment. This is how Harry describes it: Before he fully entered the room, the second window was closed and then opened; then he flew across; and then when he already partially left the room, the first window was closed and then opened behind his back. So for both observers the described events make sense.
Is this a correct explanation? (Seems so to me, but I am not sure.)
The problem is, Professor Quirrell, as usually, plays this game one level higher than Harry. Despite their agreement, he decides to close the both windows simultaneously and keep them closed. Let’s suppose the windows and broom are magical, therefore almost indestructible. What exactly happens, microsecond after microsecond, from Professor Quirrell’s point of view? (Until Harry’s broom hits the second window, the situation should be exactly the same, right?) And what exactly happens from Harry’s point of view?
Please post the answer rot13′d so that other people can make their guesses independently. I tried, but I’m giving up. I suspect that my inability to solve the second part means that I also got the first part wrong, but I don’t see how exactly.
Lrf, lbhe rkcynangvba bs gur fgnaqneq fvghngvba vf pbeerpg. Va lbhe fpranevb, Uneel bofreirf gur oebbz fgevxr gur jvaqbj orsber gur erne jvaqbj pybfrf. Vs gur oebbz jvaf gur svtug jvgu gur jvaqbj, Uneel syvrf bhg naq bofreirf gur erne jvaqbj pybfr ba gur erthyne fpurqhyr. Ohg jung vs gur jvaqbj fheivirf naq fgbcf gur oebbz? Jryy, bowrpgf va fcrpvny eryngvivgl pna’g or cresrpgyl evtvq.
N fgnaqneq rknzcyr bs ubj bowrpgf pna’g or evtvq vf jung vs lbh unir gjb evtvq cbyrf zrrgvat ng na natyr naq lbh gel gb punatr gur natyr? Vs gurl jrer evtvq, gur raq bs gur cbyr pbhyq zbir snfgre guna yvtug. Ohg gur gbedhr gnxrf gvzr gb cebcntngr qbja gur cbyr, cebonoyl ng gur fcrrq bs fbhaq. Ng eryngvivfgvp fcrrqf, gur fubpx jnir vf fhcrefbavp.
Fvzvyneyl, gur gnvy bs gur oebbz qbrfa’g srry nal erfvfgnapr hagvy gur vasbezngvba unf cebcntngrq sebz gur pbyyvfvba, ng fybjre guna gur fcrrq bs yvtug. N ernyvfgvp fpranevb vf gung obgu ner qrfgeblrq naq gung gur gnvy bs gur oebbz ragref gur sveronyy abg lrg fybjrq qbja. Dhveery frrf gur pbyyvfvba unccra svefg, gura gnvy syl guebhtu gur jvaqbj, gura gur gnvy ragre gur sveronyy. Uneel frrf vg syl guebhtu jvaqbj, gura gur sebag pbyyvfvba, gura gur gnvy ragre gur sveronyy.
Ohg lbh cebonoyl jnag gb xabj nobhg na rynfgvp pbyyvfvba. Obgu bofreiref frr gur oebbz pbzcerff. Dhveery frrf gur oebbz fgneg gb pbzcerff orsber gur gnvy unf tbar guebhtu gur jvaqbj. Ohg ur bayl frrf gur sebag bs gur oebbz pbzcerff. Gur onpx vf fgvyy ng vgf byq qrafvgl. Ol gur gvzr gur jnir bs pbzcerffvba sebz gur gnvy, vg vf vafvqr gur ebbz. Qb lbh pner nobhg pybfvat gur onpx jvaqbj? Va gur vaqrfgehpgvoyr fpranevb, gur oebbz orpbzrf jrqtrq orgjrra gur gjb jvaqbjf, pbzcerffrq gb gur fvmr bs gur ebbz. Haqre na rynfgvp nffhzcgvba, gur raretl unfa’g qvffvcngrq, ohg gur nzbhag bs pbzcerffvba vf n jnir obhapvat onpx naq sbegu orgjrra gur raqf.
Gur svefg cneg vf pbeerpg. Sebz Dhveeryy’f cbvag bs ivrj gur sebag raq bs Uneel’f oebbz uvgf gur sebag jvaqbj nsgre ur’f fuhg gur erne jvaqbj. Nf gur sebag fgbcf vg trgf ybatre, chfuvat onpx ba gur cnegf oruvaq vg, juvpu zhfg rvgure fdhnfu be fanc; gur bayl nafjre V pna tvir gb “gur oebbz vf zntvpnyyl vaqrfgehpgvoyr” vf “gung’f abg culfvpnyyl cbffvoyr”.
Sebz Uneel’f cbvag bs ivrj, gur sebag bs uvf oebbz uvgf gur sebag jvaqbj naq nppryrengrf encvqyl gbjneqf uvz, fuevaxvat nf vg qbrf fb (guvf vf orsber gur erne jvaqbj pybfrf). Vs ur’f fvggvat va gur zvqqyr gura ng fbzr cbvag ur fgbcf naq uvf senzr orpbzrf gur fnzr nf Dhveeryy’f. Vs ur’f fvggvat ng gur irel onpx bs gur oebbz gura ur tbrf guebhtu gur erne jvaqbj nsgre gur sebag bs gur oebbz “fubhyq” unir cnffrq guebhtu gur sebag jvaqbj, ohg ur pna’g lrg frr gung vg unfa’g (orpnhfr bs gur fcrrq bs yvtug). Fb vg’f culfvpnyyl vzcbffvoyr sbe gur oebbz gb or evtvq rabhtu gb fgbc uvz trggvat cnfg gur erne jvaqbj, orpnhfr gung jbhyq zrna genafzvggvat vasbezngvba snfgre guna gur fcrrq bs yvtug. Bar jnl be nabgure, gur oebbz unf gb pbzcerff.
http://en.wikipedia.org/wiki/Ladder_paradox
Thanks for both answers, now I feel I understand it. Also thanks for the wikipedia link.
Gur zntvpny oebbz qbrfa’g orunir nppbeqvat gb gur ynjf bs fcrpvny eryngvivgl.