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Is there a way using the various unit commands to convert units to values that correspond to the speed of light being 1 and unitless. 10 Joules is the immediate quantity in question.

Also I wonder if Solve could be used to do this.

Could some one direct me to some instructions in how to use tis editor. I Answered my own question but this editor is hard for me to decipher.

UnitConvert[Quantity[10, "Joules"]/(Quantity["SpeedOfLight"])^2] // N

The Answer is 1.11 X 10-16 KG Gave up on this editor so I will just type it out. Momentum of a car, 3 X 10^4 Unitconvert[3010^4 kg m s^-1]->30 X 10^3 kg m /s Coefecient of s is -1 so coeffecient n below is 1 UnitConvet[3010^3 [= kg m /s]*(1/Quantity["SpeedOfLight"])^n (n=1) 0.000100069 kg

larry
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  • What have you tried so far? Can you, please, include this code in your question? – CA Trevillian Apr 17 '21 at 20:03
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    What's wrong with UnitConvert[Quantity[10, "Joules"]/Quantity["SpeedOfLight"]]? – Adam Apr 17 '21 at 20:54
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    I think by setting c = 1 = 299792458 m/s, the OP wants a second to meter conversion or vice versa. With that conversion you can eliminate either meter or second for the joule conversion – Bill Watts Apr 17 '21 at 22:20
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    To define an energy unit based on c, you must also choose a unit of mass, either explicitly or implicitly. – John Doty Apr 18 '21 at 01:07
  • As @JohnDoty points out, you need to fix an entire system of units, not just one (speed of light). In SI units, we choose kilograms, meters, and seconds as the three base units for dynamics. You can choose any three you like; but they have to be three in number (for dynamics). So choosing the speed of light as a base units is fine but needs to be complemented by two others, for example the kilogram and the meter, or Planck's constant and the electron's mass, or really any other pair. See this answer for more examples. – Roman Apr 18 '21 at 06:54
  • As an example of the aforementioned solution, the command unitConvert[Quantity[10, "Joules"], makeUnitSystem[{"SpeedOfLight", "PlanckConstant", "ElectronMass"}]] gives a conversion to $1.221432857\times10^{14} m_e c^2$. The need for a mass unit (here, the electron mass; but could be anything) becomes explicit. – Roman Apr 18 '21 at 07:05
  • You solution of UnitConvert[Quantity[10, "Joules"]/(Quantity["SpeedOfLight"])^2] // N is right on the money since you are essentially dividing Joules by $1^2$, but I'm not quite sure what you mean about problems with the editor. – Bill Watts Apr 19 '21 at 21:32

1 Answers1

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A simplified version of what I said in the comments:

As @JohnDoty points out, you need to fix a unit of mass. Together with the unit of speed (in your case, the speed of light), the conversion becomes:

SpeedUnit = "SpeedOfLight";
MassUnit = "Kilogram";
UnitConvert[Quantity[10, "Joules"], MassUnit*SpeedUnit^2] // N
(*    1.11265*10^-16 kg c^2    *)

SpeedUnit = "SpeedOfLight";
MassUnit = "PlanckMass";
UnitConvert[Quantity[10, "Joules"], MassUnitSpeedUnit^2]
(    5.11210^-9 mP c^2    )
Roman
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