Relatively confused

[Shadow]

We've just started tackling relativity in our physics class, and there's a thought experiment I've come up with that I can't seem to resolve. Say you have an empty infinite universe, and in that universe are two objects, A and B, which are moving at some velocity relative to each other. Since there are no reference points except for the two objects, from A's frame of reference it is B that is moving and A that is stationary and from B's frame the opposite, ie. A is moving and B is stationary. Since time dilates due to velocity, in A's frame of reference B's time will be slower and from B's frame of reference A's time will be slower. But that can't be, since it would mean that time in one reference frame must be both slower and faster than time in the other frame. So which part am I thinking wrong about?

[ydoaPs]

We've just started tackling relativity in our physics class, and there's a thought experiment I've come up with that I can't seem to resolve. Say you have an empty infinite universe, and in that universe are two objects, A and B, which are moving at some velocity relative to each other. Since there are no reference points except for the two objects, from A's frame of reference it is B that is moving and A that is stationary and from B's frame the opposite, ie. A is moving and B is stationary. Since time dilates due to velocity, in A's frame of reference B's time will be slower and from B's frame of reference A's time will be slower. But that can't be, since it would mean that time in one reference frame must be both slower and faster than time in the other frame. So which part am I thinking wrong about?

This sounds like a modified twin paradox. With no acceleration breaking symmetry, both frames do in fact see the other as being slower than their own.

[swansont]

time in one reference frame must be both slower and faster than time in the other frame.

 

Only slower.

[Sisyphus]

To spell it out:

 

In frame in which A is at rest, time is passing more slowly for B. In the frame in which B is at rest, time is passing more slowly for A.

 

It sounds in impossible, I know, but it actually does work out.

[timo]

As a matter of fact it's closely related that the two observers each see the other one as moving faster. Except that no one seems to find that one paradoxical.

[Shadow]

This sounds like a modified twin paradox. With no acceleration breaking symmetry, both frames do in fact see the other as being slower than their own.

Could you elaborate? I'm new to relativity and am not very good at deducing facts in physics, so I can't see the correspondance with the twin paradox

 

As a matter of fact it's closely related that the two observers each see the other one as moving faster. Except that no one seems to find that one paradoxical.

I always thought that was just a concequence of himan perception...is there a name/term I could search for to find out more?

[timo]

In the twins' paradox the crucial point from which the presumed paradox stems is that the twins each see the other twin's time as passing slower, same as your observers A and B do. So unless you've been misunderstood the scenario you talk about is indeed part of the twins' paradox (except that there one usually goes one step further and let them meet at the same point to compare their self-measured times).

 

Considering my statement: I doubt you'll find more about it on the net - no one sells relativity so cheap, I think. I'm also not sure if it's really helpful to you, it was also meant for the others. But let me elaborate a bit:

You said

, in A's frame of reference B's time will be slower and from B's frame of reference A's time will be slower. But that can't be, since it would mean that time in one reference frame must be both slower and faster than time in the other frame.

 

now imagine you had said

, in A's frame of reference B's velocity will be faster and from B's frame of reference A's velocity will be faster. But that can't be, since it would mean that velocity in one reference frame must be both slower and faster than time in the other frame.

 

What's the difference? Well, one difference is that we both know that in the 2nd question, the hypothetical one, the only confusing thing is the way you expressed the question. I guess we both understand pretty well how non-relativistic velocities can depend on the reference frame - everyone has learned to understand that at some point in their childhood. The difference to your actual question is not so big from a physical or logical point of view: it's merely that not everyone (read: no one) has learned relativity in their childhood. That's in fact pretty much the only fundamental difference (that I can think of at the moment). <there is a lot that I could say here but I think I'll better cut it short to restrict the confusion I might be causing with this non-mainstream comparison>.

 

Btw.: Considering the question whether a different passing of time is an effect of human perception: it is an effect of human perception in the very same sense as the different velocities (in your hypothetical question) are. So I'd tend to say "no, it's not". It's an effect of different frames of reference.