Time & Mass: Newbie Questions from a Spaceship Observer

[Fyreth]

I'm having a hard time wrapping my head around some of the basic concepts.

Imagine a spaceship moving at a certain velocity relative to you. To you, his time is slower than yours. He guy in the spaceship doesn't know his time is slowed down.
If his time is slower than yours, it means that he thinks your time is faster than normal.

But if we turn it around the guy in the spaceship can say that you're moving at a certain velocity and therefore your time is slower than his and that you think his time is faster than normal.

So what's going on? Who seems slower to who?

And another thing. If mass increases with velocity and you're in a spaceship. Wouldn't you notice the increase of inertia?
Or, more likely, if mass is normal to you and your mass seems increased to the observer outside on top of the slowed down time. Would he think you're stumbling around weirdly while everything is alright to you?

Such a fun theory.

 

[bcrowell]

If his time is slower than yours, it means that he thinks your time is faster than normal.

No, each of you seems slow to the other.

I found this the hardest part of relativity to get when I first learned it.

The key here is that neither of you has any direct method of checking what you think about the other. Every method of checking what's going on involves the exchange of signals, which take time to propagate. A says B is slow, but B says A only thinks B is slow because of effects arising from the propagation of the signals back and forth.

 

[Chestermiller]

I'm having a hard time wrapping my head around some of the basic concepts.

Imagine a spaceship moving at a certain velocity relative to you. To you, his time is slower than yours. He guy in the spaceship doesn't know his time is slowed down.
If his time is slower than yours, it means that he thinks your time is faster than normal.

But if we turn it around the guy in the spaceship can say that you're moving at a certain velocity and therefore your time is slower than his and that you think his time is faster than normal.

So what's going on? Who seems slower to who?

Imagine that the spaceship is very, very, long, and that a whole team of observers is deployed along its length. Also imagine that you are not the only observer in your frame of reference who is observing the spaceship; there is a whole team of observers strung out along the direction of the spaceship movement. Now, your entire team focuses its attention on just one guy on the spaceship, and each of you records the time displayed on your clocks and the time displayed on his clock when he passes each of you. So there's one guy in the spaceship frame of reference that is being tracked by multiple guys in your frame of reference that he is sweeping past. After the measurements are made, the guys in your frame of reference get together and compare the data obtained. You then plot a graph of the times on the guy's clock on the vertical axis, and the times on your clocks as the horizontal axis. The slope of this line will be less than 1, suggesting to your team (as well as to the guy on the train) that his clock is running slower than yours.

Now let's flip the experiment. The team of observers on the spaceship focuses its attention on just one guy in your frame of reference ( you), and each of them records the time displayed on their clocks and the time displayed on your clock as they each sweep past you.
So there's one guy in your frame of reference (namely you), that is being tracked by multiple guys in the spaceship frame of reference. After the measurements are made, the guys in the spaceship frame of reference get together and compare the data obtained. They then plot a graph of the times on your clock on the vertical axis, and the times of their clocks as the horizontal axis. The slope of this line will be less than 1, suggesting to the spaceship team (as well as to yourself) that your clock is running slower than theirs.

Which team is right? Within the framework of the way these experiments are carried out (compare the italicized wording), both teams are right. How can this be? Your team of observers receives snapshots of reality at constant values of the time t displayed on your synchronized set of clocks, while the team of observers on the spaceship receive snapshots of reality at constant values of the time t' displayed on their synchronized set of clocks. Unfortunately, constant values of t at different locations in your frame of reference are accompanied by non-constant values of t' in the spaceship frame of reference at these same locations, and vice versa. This is all related to the non-uniqueness of simultaneity between inertial frames of reference.