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Relativistic Length Contraction

Length contraction is the phenomenon of a decrease in length of an object as measured by an observer who is traveling at any nonzero velocity relative to the object.

The observed moving length equals the stationary length times a factor that decreases as the velocity approaches the speed of light.

Formula

QuantityVariable["l", "Length"] == Sqrt[1 + Quantity[-1, "SpeedOfLight"^(-2)]*QuantityVariable["v", "Speed"]^2]*QuantityVariable[Subscript["l", "0"], "Length"]

symbol description physical quantity
l moving length "Length"
v velocity "Speed"
l0 stationary length "Length"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Relativistic Length Contraction"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Relativistic Length Contraction"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Relativistic Length Contraction"], {QuantityVariable[ \!\(\*SubscriptBox[\("l"\), \("0"\)]\),"Length"] -> Quantity[1, "Meters"], QuantityVariable["v","Speed"] -> Quantity[3.`*^7, ("Meters")/("Seconds")]}]
Out[3]=

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