Speed of Moving Object: Exploring Length Contraction & Time Dilation

[petm1]

What does the factor that you get when you plug the length contraction and time dilation of a moving object back into the form of meters/second represent?

 

[jtbell]

I don't understand what factor you're asking about. Can you give a specific example?

 

[HallsofIvy]

What does the factor that you get when you plug the length contraction and time dilation of a moving object back into the form of meters/second represent?

?? I have no idea what you mean. I think the factor you are talking about is \sqrt{1- \frac{v^2}{c^2}} but I don't know what you mean by "plug back into the form of meters/second".

 

[selfAdjoint]

I think the OP is asking this. You operate on the lengths and times of the traveling frame with some algebraic factor involving \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}. And does that factor have units of its own, and if so how do the transformed lengths and times get back to their own proper units? We ssee their transformed values, but their units should still be lengths like meters and times like seconds shouldn't they?

And the answer to that is that if you look at the expression for gamma, the only dimensionful amounts in it are the speeds v and c. And they only occur as their ratio, so their units are divided out. This means that gamma is a pure number, and no algebraic function of it alone can be anything but a pure number, so the transformed lengths and times have the same units that the rest frame amounts do.

 

[petm1]

Sorry, I had a small problem, house fire and when that alarm sounds I have to run, I didn't know that I had posted this instead of just previewing it until I read it the next day. Thanks for the effort and I will be more careful in the future.