Time Dilation and Length Contraction. (1 Viewer)

[atar99dot95]

Why is it that, proper time and proper length are measured in different frames?
To be more specific, this question is in relation to muons.

For example:

An observer on earth measures the distance travlled by a muon. Why is it measured as proper length, not, contracted length; whilst, proper time is measured by the same observer?

Need some clarification.
Thanks.

 

[adomad]

i may be wrong..... just warning you...

proper time and proper length are measure by the observer in that is stationary relative to the moving frame of reference.

for example: a man (or woman) travelling on a rocket that is 15m long, at the speed of 0.5c, will measure their rocket to also be 15m long. and observer on earth will measure the length of the rocket to be less than the real 15m (proper length), but measure it to be 12.99m (contracted length). hence proper length is measure by the observer in the rocket and contracted length is measure by the observe on earth.

BUT, if the observer on the Earth had a 2m long broom stick, the person on the rocket will measure it to be 1.7m. so in this case, the earth observer will measure proper length and the person on the rocket will measure contracted length as the observer on Earth, relative to the rocket, is moving at 0.5c. same thing happens with time except it dilate.

for your question in regards to the Muon, the event can be seen in a way that we are moving towards the muon and the muon is stationary....
so in this case, we are the observer that measures proper time and length as we are stationary in our frame of reference and the muon is moving towards us.

this is why we can detect muons on the surface of earth even though they have a half life of 2 microseconds . because of their fast speed 0.998 c , time for the muon is dilated ( i.e. it lives longer) and length contracts ( hence the distance it has to travel is less that the proper length it has to travel).

some one correct me please , i don't think i got the hang of it yet

 

[xXmuffin0manXx]

Why is it that, proper time and proper length are measured in different frames?
To be more specific, this question is in relation to muons.

For example:

An observer on earth measures the distance travlled by a muon. Why is it measured as proper length, not, contracted length; whilst, proper time is measured by the same observer?

Need some clarification.
Thanks.

Proper time is measured by the person within the same frame of reference as the experiment or whatever. Say for example, Santa on his sleigh at 0.99c...To Santa, he would be measuring proper time whilst everyone outside his frame of reference, say for example, the elves...well they would be measuring dilated time.

On the other hand, the distance travelled by the muon from the same frame of reference would be the contracted length because the speed at which it travels would mean for the moving muon, it would measure a length that is less than the proper length..

So..we can't measure the proper length from within the same frame of reference as the moving muon..Henceeee..we can only measure proper length from an outside frame..mmm

so that answers "Why is it that, proper time and proper length are measured in different frames?"

*lol forgot about reading the above post..i dont think my answer realyl answered the question..

 

[adomad]

some one check my post, i want to know if i totaly understand the concept?? cheers

 

[xV1P3R]

The use of proper time and proper length sounds very awkward. With reference to the Lorentz transformation equations, rest time refers to the frame of reference in which the event occurs.

@adomad
Seems correct to me, though the bit about the muon:

time for the muon is dilated ( i.e. it lives longer) and length contracts ( hence the distance it has to travel is less that the proper length it has to travel).

The muon does not live longer per se, in its own frame of reference it still has a half life of 2 microseconds. But from out frame of reference (Earth), we perceive these 2 microseconds as dilated and so these 2 microseconds appear far longer to us than to the muon.