Length contraction or Lorentz Contraction

In summary, Lorentz contraction states that an object contracts to an observer when moving at high speeds.
  • #1
thecow99
31
0
As I understand it, Lorentz Contraction states an object "contracts" relative to it's velocity to an observer.

So at a high velocity of speed, the meter stick (carried by the object moving relative to the observer) appears to contract (to the observer) and the observer measures less distance traveled than the object.

This seems to counter time dilation.

If the object is measuring a larger distance traveled from A to B it would seem the object would would measure an increase in observed time, not a decrease.

If object is moving at .99C and it contracts the measured distance from A to B would increase for it, which would logically say would take more time.

How am I misinterpreting this? I know the object experiences less time but a greater distance? Huh?

Cheers!
 
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  • #2
The Object is measuring a smaller distance traveled from A to B. You see the object contract, the object sees you contract. It's symmetric. Always contraction of length, never dilation of length. Likewise, always dilation of time, never contraction of time.
 
  • #3
Eh, my stupid brain...

The meter stick doesn't contract in it's own frame of reference. Should have guessed that!

I kind of get it now. So when time dilation occurs, the moving object experiences less space traveled because in it's frame it "time" was constant.

Wait.. is that why you can't get a frame at C? Because at C everything would exist in the same place at the same time?
 
  • #4
thecow99 said:
.. is that why you can't get a frame at C? Because at C everything would exist in the same place at the same time?


Yes, I believe so. It requires an outside observer with a lower relative velocity to see light as traversing a distance.
 
  • #5
To work through these questions properly, you need to consider the relativity of simultaneity as well as time dilation and length contraction. When someone says "This rod is one meter long" they're being a bit sloppy in their wording - it would be more precise to say "I found where the two ends of the rod were at the same moment, and then I measures the distance between those two points, and found them to be one meter apart".

Note that this definition does not assume that the rod is at rest relative to the person making the measurement. It also makes it clear that, because observers moving relative to each other have different definitions of "at the same moment", they will measure different lengths.
 

1. What is length contraction?

Length contraction, also known as Lorentz contraction, is a phenomenon in which an object appears shorter in length when it is moving at high speeds relative to an observer.

2. How does length contraction work?

According to the theory of relativity, as an object's speed increases, its length in the direction of motion will appear to decrease. This is due to the time dilation effect, in which time appears to slow down for objects in motion.

3. What is the formula for length contraction?

The formula for length contraction is L = L0 / √(1-v²/c²), where L is the contracted length, L0 is the rest length, v is the relative speed of the object, and c is the speed of light.

4. Can length contraction be observed in everyday life?

Length contraction can only be observed at speeds close to the speed of light, which is not possible in everyday life. However, it can be observed in particle accelerators and other high-speed experiments.

5. How does length contraction relate to time dilation?

Length contraction and time dilation are two sides of the same coin, known as the space-time continuum. As an object's length appears to contract from an observer's perspective, time also appears to slow down for that object. This is due to the fact that the speed of light is constant for all observers, regardless of their relative motion.

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