In this section, we will define the concept of proper time<\/strong> and we will explain in detail the twin’s paradox<\/strong>.<\/p>\n\n\n\n Proper time\\( \\tau\\) is the time measured by clocks at rest in a system moving relative to another, To derive the formula of proper time we will simplify the notation and restrict the derivation to the case of a boost in \\(x\\) direction with velocity \\(v\\),<\/p>\n\n\n\n\\begin{align}\n x’ &= \\beta(x-vt ) \\nonumber\\\\\n y’&=y\\nonumber\\\\\n z’&=z\\nonumber\\\\\n t’&= \\beta\\left(t-\\ds\\frac{v}{c^2}x \\right)\\\\\n\\beta&=\\ds\\frac{1}{\\ds\\sqrt{1-\\frac{v^2}{c^2} }}\\\\\n\\label{Lorentz}\n\\end{align}\n\n\n\n The Lorentz equations for a clock in the primed system, and centered in the origin, read<\/p>\n\n\n\n\\begin{align}\n 0 &= \\beta(x-vt ) \\nonumber\\\\\n t’&= \\beta\\left(t-\\ds\\frac{v}{c^2}vt\\right)\\label{l1}\n\\end{align}\n\n\n\n which gives immediately the proper time \\(\\tau\\) measured in the prime system,<\/p>\n\n\n\n\\begin{equation}\n \\tau= \\sqrt{1-\\frac{v^2}{c^2} } t \\label{proper}\n\\end{equation}\n","protected":false},"excerpt":{"rendered":" Introduction \\(\\def\\ds{\\displaystyle}\\) In this section, we will define the concept of proper time and we will explain in detail the twin’s paradox. Proper Time Proper time\\( \\tau\\) is the time measured by clocks at rest in a system moving relative to another, To derive the formula of proper time we will simplify the notation and […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"nf_dc_page":"","ocean_post_layout":"","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"0","ocean_second_sidebar":"0","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"0","ocean_custom_header_template":"0","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"0","ocean_menu_typo_font_family":"0","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"0","footnotes":""},"_links":{"self":[{"href":"https:\/\/physicsandmusic.com\/wp-json\/wp\/v2\/pages\/13431"}],"collection":[{"href":"https:\/\/physicsandmusic.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/physicsandmusic.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/physicsandmusic.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/physicsandmusic.com\/wp-json\/wp\/v2\/comments?post=13431"}],"version-history":[{"count":6,"href":"https:\/\/physicsandmusic.com\/wp-json\/wp\/v2\/pages\/13431\/revisions"}],"predecessor-version":[{"id":13599,"href":"https:\/\/physicsandmusic.com\/wp-json\/wp\/v2\/pages\/13431\/revisions\/13599"}],"wp:attachment":[{"href":"https:\/\/physicsandmusic.com\/wp-json\/wp\/v2\/media?parent=13431"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Proper Time<\/h1>\n\n\n\n