Relativistic Time, Length, Mass

[weirdobomb]

Reposting to this section of the forum instead of the Introductory Physics homework section.

So let's say a guy travels at 0.5c in a spaceship from planet 1 to planet 2.

Am I right in saying that:

proper time = time measured inside space ship
proper length between planets = length the guy measures from start to end while on the space ship
proper mass of his android phone = the mass the android phone while on the space ship


pulled from textbook:

m is the proper mass, that is, the mass measured by an observer at rest with respect to the mass

does this mean that the observer maintains a constant distance from the mass?

 

[PeterDonis]

lets say a guy travels at 0.5c in a spaceship from planet 1 to planet 2.

More precisely, the guy travels at 0.5c *relative to the planets*. Velocity is relative.

proper time = time measured inside space ship

The proper time for the guy in the space ship, yes. Proper time is a property of a particular observer following a particular path through spacetime.

proper length between planets = length the guy measures from start to end while on the space ship

Not really, no. "Proper length" is usually used to refer to the length between two points (in this case the "points" are the two planets) measured in a frame in which the points (the planets in this case) are at rest. The guy is not at rest with respect to the planets, so the length he measures between them will be contracted; i.e., it will be shorter than the "proper length" as I defined it above.

proper mass of his android phone = the mass the android phone while on the space ship

If "proper mass" means "rest mass", which is what it looks like your textbook is using it to mean, then the proper mass of the phone is the mass measured by the guy who is carrying the phone with him on the ship, since the phone is at rest relative to him.

does this mean that the observer maintains a constant distance from the mass?

Since he has to be at rest relative to the mass, yes, he will be at a constant distance from it. I'm not sure why that matters, though.

 

[weirdobomb]

Then if the guy after he gets off the spaceship writes down the time he experienced on the trip and I, who was always at rest with the planet, take that time to calculate how much time elapsed for me, would the result I get be called the dilated time?

 

[PeterDonis]

if the guy after he gets off the spaceship writes down the time he experienced on the trip and I, who was always at rest with the planet, take that time to calculate how much time elapsed for me, would the result I get be called the dilated time?

Normally, no, it would be the other way around: the time elapsed for the guy in the spaceship would be called "dilated" relative to the time elapsed for you, at rest with the planet. If you are inclined to respond that that terminology doesn't really make sense, you're right. But that's the standard terminology.

 

[weirdobomb]

Yes it's weird since dilated should mean longer, which corresponds to me who is outside the spaceship experiencing a longer length of time. I guess I'll just memorize this example.

 

[TumblingDice]

...the time elapsed for the guy in the spaceship would be called "dilated" relative to the time elapsed for you, at rest with the planet. If you are inclined to respond that that terminology doesn't really make sense, you're right. But that's the standard terminology.

I'm grinning just a bit because the terminology makes sense to me, and wondering if I should be worried.

From dictionary.com: dilate: to spread out; expand.

Running with this perspective, time dilation is expanded time - spread out - so less time lasts longer.

 

[ghwellsjr]

Yes it's weird since dilated should mean longer, which corresponds to me who is outside the spaceship experiencing a longer length of time. I guess I'll just memorize this example.

I'm with TumblingDice on this one, especially if you make some spacetime diagrams which will make it obvious that in the mutual rest frame of the two planets, the space ship's time is "spread out". Here the two planets are depicted in blue and red while the spaceship is shown in black. The dots mark of one-year increments of Proper Time for each object:

Now we can use the Lorentz Transformation process to see what the same scenario looks like in the rest frame of the spaceship during the "trip":

As you can see, now it is the planets' times that are dilated. And you can also see the distance between the planets in this frame is contracted from 4 light-years in the first frame to just under 3.5 light-years.

However, you said that the guy on the spaceship makes measurements and these diagrams don't show how he makes those measurements. Have you considered how he might make those measurements that would agree with the information depicted in the diagrams?