Lorentz Contraction Formula

[nycmathguy]

Calculus
Section 2.3

Help....

 

[MathLover1]

In the theory of relativity, the Lorentz contraction formula

expresses the length L of an object as a function of its velocity v with respect to an observer, where L0 is the length of the object at rest and c is the speed of light.
Find lim(v→c− L and interpret the result. Why is a left hand limit necessary?

A left hand limit is necessary because the velocity cannot be greater than the speed of light.

and since we know c > 0

Now, as

So. =0

thus,

As the object’s velocity increases towards c, it’s length decreases towards 0.

 

[nycmathguy]

In the theory of relativity, the Lorentz contraction formula

View attachment 3020

expresses the length L of an object as a function of its velocity v with respect to an observer, where L0 is the length of the object at rest and c is the speed of light.
Find lim(v→c− L and interpret the result. Why is a left hand limit necessary?

A left hand limit is necessary because the velocity cannot be greater than the speed of light.


View attachment 3019

and since we know c > 0

View attachment 3021

Now, as View attachment 3022

So. =0

thus, View attachment 3023

As the object’s velocity increases towards c, it’s length decreases towards 0.

Thank you so much. I had no idea that this question is so involved. You said the following:

So. = 0.

What = 0?

 

[MathLover1]

c^2-v^2=0 because v^2->c^2

 

[nycmathguy]

c^2-v^2=0 because v^2->c^2

Ok. I see what you mean.

How about the link below? I tried it failed to understand how it's done.

Find Delta...2