{"id":1007,"date":"2023-04-07T08:29:38","date_gmt":"2023-04-07T08:29:38","guid":{"rendered":"https:\/\/qpr.ca\/blogs\/physics\/?p=1007"},"modified":"2023-04-07T08:36:00","modified_gmt":"2023-04-07T08:36:00","slug":"lorentz-expansion","status":"publish","type":"post","link":"https:\/\/qpr.ca\/blogs\/physics\/2023\/04\/07\/lorentz-expansion\/","title":{"rendered":"Lorentz Expansion!"},"content":{"rendered":"\n
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A Quora question asks:<\/div>\n
Two guns on Earth D metres apart fires simultaneously at a metal plate moving by at close to light speed. Is the distance between the two bullet holes in the plate length contracted?<\/span><\/strong><\/div>\n
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It depends on who thinks the guns fired simultaneously.<\/div>\n
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If, as seems most likely, the question means that those Earth-based guns were synchronized by someone on Earth with them, then the distance between the two holes, as measured by any observer stationary with respect to the Earth, is (and remains) exactly equal to the distance between the two guns. Since the plate appears contracted to these Earth-based observers, if it was marked with units of length in its own rest frame those markings would appear closer together to the Earth-based observers and so there would be more of them between the holes than the number of length units measured on Earth.<\/div>\n<\/div>\n
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In other words the distance between the holes would appear to be<\/strong><\/div>\n<\/div>\n
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greater<\/em> from the point of view of someone travelling with the plate.<\/strong><\/div>\n
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It may seem puzzling that this happens despite the fact that from the traveller\u2019s point of view the distance between the guns is \u201clength contracted\u201d and so appears to be less<\/em> than that measured between them on Earth.<\/div>\n<\/div>\n
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The puzzle is resolved by the fact that from the point of view of the traveller the guns did NOT fire simultaneously. The one making the front hole appears to the traveller to have gone off earlier. (And it is a worthwhile exercise for anyone seeking to learn about relativity to work through the calculation needed to show that the delay is by exactly the right amount for the forward movement of the plate to create the observed bigger distance between the holes).<\/div>\n
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Alternatively, if the traveller thinks the guns went off simultaneously, then the Earth-based observers think there is a delay. (And again, working out the details is a worthwhile exercise for any beginning student of the subject.)<\/div>\n
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P.S. The question of whether or not a length or object is \u201clength contracted\u201d does not really make sense without any mention of which observer is doing the measurement.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n

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Source: (1000) Alan Cooper’s answer to Two guns on Earth D metres apart fires simultaneously at a metal plate moving by at close to light speed. Is the distance between the two bullet holes in the plate length contracted? – Quora<\/a><\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

A Quora question asks: Two guns on Earth D metres apart fires simultaneously at a metal plate moving by at close to light speed. Is the distance between the two bullet holes in the plate length contracted?   It depends on who thinks the guns fired simultaneously.   If, as seems most likely, the question … Continue reading Lorentz Expansion!<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,4],"tags":[47,5,6],"topics":[11],"class_list":["post-1007","post","type-post","status-publish","format-standard","hentry","category-all","category-quora-answers","tag-length-contraction","tag-relativity","tag-special","topics-special"],"_links":{"self":[{"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/posts\/1007","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/comments?post=1007"}],"version-history":[{"count":3,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/posts\/1007\/revisions"}],"predecessor-version":[{"id":1015,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/posts\/1007\/revisions\/1015"}],"wp:attachment":[{"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/media?parent=1007"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/categories?post=1007"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/tags?post=1007"},{"taxonomy":"topics","embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/topics?post=1007"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}