# Problems with Proper Length and Proper Time in SR

1. Jan 11, 2014

### Yosty22

I have just started studying Special Relativity in class and the concepts of Proper Length and Proper Time are giving me some issues. I understand the basics of length contraction and time dilation, but the idea of this "proper" time and length is giving me problems. One example in particular that was bugging me:

To start, the textbook I have for class defines proper length of an object as: "the length of the object measured by someone who is at rest with respect to the object." That makes sense, but in this example, it confuses me. It goes on to say: "Consider a spaceship traveling with a speed v from one star to another and two observers, one on Earth and the other in a spaceship. The observer at rest on Earth (and also assumed to be at rest with respect to the two stars) measures the distance between the starts to be L_p, where L_p is the proper length."

It continues on to state that the observer on Earth observes the voyage taking Δt to complete and the observer on the ship observes the same journey taking Δt'. This makes sense to me due to time dilation, but the proper length confuses me. I understand that in this example, the Earth is at rest with respect to the two stars, but from the observer on the ship's point of view, would he too be at rest? To the observer on the ship, it would seem as if he is at rest and the stars are what is moving. Why does this disallow the observer on the ship to measure proper length, since, as the book suggests proper length is, he is at rest with respect to the object, it is just the object is moving to him in his reference frame.

Any help would be much appreciated.
Thanks in advanced.

2. Jan 11, 2014

### ghwellsjr

If the object is moving to him in his reference frame, then he is not at rest with respect to the object, correct?

3. Jan 11, 2014

### Yosty22

Ahh, I see. So I was reading and it seemed like proper length and proper time were always in difference reference frames. Is this always true? If so, is this how Einstein's first postulate holds? i.e. If they are always in difference reference frames, do they "cancel out" to ensure that all of the laws of physics hold as Einstein's postulate suggests?

4. Jan 11, 2014

### ghwellsjr

I'm not sure what you're talking about. Every object is in every reference frame so you should consider just one reference frame at a time. All the objects that are at rest in a particular Inertial Reference Frame (IRF) are not Length Contracted nor Time Dilated so their lengths are Proper Lengths and their times are Proper Times. All the other objects that are moving in the same IRF are Length Contracted (along the direction of motion) and Time Dilated (which means expanded). Length Contraction means that the lengths are smaller than the Coordinate Lengths and Time Dilation means the times take longer than the Coordinate Times, so in what sense are you thinking that something will "cancel out"?

5. Jan 12, 2014

### my_wan

No, both proper length and proper time are defined by the things in the same reference frame as the observer. The measurements of space and time of things moving relative to you not measurements of proper space or time for the object being measured.

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