# Time Dilation and Length Contraction the same thing?

Are these really just two ways of explaining the same thing?

## Answers and Replies

ghwellsjr
Gold Member
No, they are not the same thing.

Time dilation is where all times for a moving clock/observer are longer than for the frame in which they are considered.

Length contraction is where lengths only along the direction of motion are shorter than for the frame in which they are considered.

Are these really just two ways of explaining the same thing?
Both are different aspects or outcomes of the theory of relativity.
The length contraction doesnt actually have anything to do with actual change in physical properties of an object..Its the measurement that is important here.
Length of an oblect in an accelerating frame may seem to be ,or is measured to be shorter in the direction of motion to an observer in an other frame of reference.
Time inside such an accelerating frame may seem to be slowed down for an outside observer in another frame,whereas an observer inside the accelerating medium may not see any such effects.

Both are results of how Lorentz transformation work. It's pointless to ask for verbal descriptions; you should look up the Lorentz transformations; those equations tell of how it works; you need to learn to read the equations as there is no satisfactory no-math verbal dissection of that whole into parts like time dilation, length contraction, and relativity of simultaneity.

The length contraction is actually more of a result of relativity of simultaneity; the coordinate along the direction of motion is expanded just like time is dilated (with same gamma factor), but the coordinate intervals taken *at same moment* are contracted. To measure length of a moving object you need to measure positions of it's ends at same time, and the 'same time' is different for different observers.
This is important to understanding things like "ladder paradox".

I forget which frequent poster said it, but they called length contraction and time dilation two sides of the same coin.

I can't determine if the "coin" is distance or speed, perhaps there is little difference in this context.

ghwellsjr
Gold Member
I forget which frequent poster said it, but they called length contraction and time dilation two sides of the same coin.

I can't determine if the "coin" is distance or speed, perhaps there is little difference in this context.
That would be DaleSpam:
You cannot have time dilation without length contraction, they are two sides of the same "coin" (the Lorentz transform).

Ah, thanks George.

I should clarify then (now that it's been "coined"), Dalespam is not implying anything other then you can't have one without the other.

Both are results of how Lorentz transformation work. It's pointless to ask for verbal descriptions;

The length contraction is actually more of a result of relativity of simultaneity; the coordinate along the direction of motion is expanded just like time is dilated (with same gamma factor), but the coordinate intervals taken *at same moment* are contracted. To measure length of a moving object you need to measure positions of it's ends at same time, and the 'same time' is different for different observers.

I think that is a very good verbal description. One of the most concise descriptions I've read (just a little too general).