To outside observers, the overall sizes of objects traveling at relativistic speeds are..... larger or smaller or same size?

Objects traveling at relativistic speeds appear smaller to outside observers. This phenomenon is known as "relativistic length contraction" or "Lorentz contraction." According to Einstein's theory of special relativity, as an object's velocity approaches the speed of light, its length in the direction of motion appears to contract from the perspective of an observer at rest relative to the object.

To understand why this occurs, we can use the Lorentz transformation equations. One such equation is the length contraction formula:

L' = L * sqrt(1 - (v^2/c^2))

In this equation:
- L' represents the measured length of the object from the perspective of an observer in motion relative to the object
- L represents the proper length of the object when at rest
- v is the relative velocity between the observer and the object
- c denotes the speed of light in a vacuum

From the equation, we can see that when v approaches c, the term (v^2/c^2) gets closer to 1, causing the square root to approach 0. As a result, the measured length (L') of the object appears contracted compared to its proper length (L) for observers in motion relative to the object.

Therefore, according to the theory of special relativity, objects traveling at relativistic speeds are observed to be smaller by outside observers.