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Lorentz factor
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== Numerical values == [[File:Lorentz factor 2.png|thumb|Lorentz factor {{mvar|γ}} as a function of fraction of given velocity and speed of light. Its initial value is 1 (when {{math|''v'' {{=}} 0}}); and as velocity approaches the speed of light {{nobr|(''v'' → ''c'')}} {{mvar|γ}} increases without bound {{nobr|({{mvar|γ}} → ∞).}}]] [[File:Lorentz factor inverse.svg|thumb|α (Lorentz factor inverse) as a function of velocity—a circular arc]] In the table below, the left-hand column shows speeds as different fractions of the speed of light (i.e. in units of {{mvar|c}}). The middle column shows the corresponding Lorentz factor, the final is the reciprocal. Values in bold are exact. {| class="wikitable" style="text-align:center;" |- ! Speed (units of {{mvar|c}}), <br/>{{math|''β'' {{=}} ''v''/''c''}} ! Lorentz factor, <br/>{{mvar|γ}} ! Reciprocal, <br/>{{math|1/''γ''}} |- | '''0''' || '''1''' || '''1''' |- | '''0.050{{fsp|2}}''' || 1.001 || 0.999 |- | '''0.100{{fsp|2}}''' || 1.005 || 0.995 |- | '''0.150{{fsp|2}}''' || 1.011 || 0.989 |- | '''0.200{{fsp|2}}''' || 1.021 || 0.980 |- | '''0.250{{fsp|2}}''' || 1.033 || 0.968 |- | '''0.300{{fsp|2}}''' || 1.048 || 0.954 |- | '''0.400{{fsp|2}}''' || 1.091 || 0.917 |- | '''0.500{{fsp|2}}''' || 1.155 || 0.866 |- | '''0.600{{fsp|2}}''' || '''1.25''' || '''0.8{{fsp|2}}''' |- | '''0.700{{fsp|2}}''' || 1.400 || 0.714 |- | '''0.750{{fsp|2}}''' || 1.512 || 0.661 |- | '''0.800{{fsp|2}}''' || 1.667 || '''0.6{{fsp|2}}''' |- | 0.866{{fsp|2}} || '''2''' || '''0.5{{fsp|2}}''' |- | '''0.900{{fsp|2}}''' || 2.294 || 0.436 |- | '''0.990{{fsp|2}}''' || 7.089 || 0.141 |- | '''0.999{{fsp|2}}''' || 22.366 || 0.045 |- | '''0.99995''' || 100.00 || 0.010 |} [[File:Lorentz_factor_log_log.svg|thumb|Log-log plot of Lorentz factor ''γ'' (left) and 1/''γ'' (right) vs fraction of speed of light ''β'' (bottom) and 1−''β'' (top)]]
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