Time dilation at an unchanging velocity

[ryuunoseika]

Help me settle an arguement:

Say you have two clocks, one moving at 2/3 the speed of light (for explantory purposes called "A") and another at rest ("B"). Which clocks tics faster?

 

[Doc Al]

Which clocks tics faster?

According to whom?

 

[ryuunoseika]

According to whom?

According to an observer that perceives B as stationary.

 

[Doc Al]

According to an observer that perceives B as stationary.

According to that observer, clock B clicks faster.

 

[ryuunoseika]

Thank you, i just won $10.

 

[ryuunoseika]

My friend still refuses to accept that he's wrong. I've been trying to explain it for two hours, maybe you can explain it to him better than i can.

He claims the clocks should be the same because they haven't accelerated or decelerated thus they're still in the same inertial reference frame. I've been trying to explain that that doesn't matter and that it's the second object's relative velocity that sets it off. I still don't see what he's trying to say.

 

[JesseM]

He claims the clocks should be the same because they haven't accelerated or decelerated thus they're still in the same inertial reference frame. I've been trying to explain that that doesn't matter and that it's the second object's relative velocity that sets it off. I still don't see what he's trying to say.

What does he mean by "in the same inertial reference frame"? The two clocks have different inertial rest frames. Obviously you can use a single inertial frame to analyze both, but the same is true of accelerating clocks, a "frame" is just a coordinate system. If your friend is confused about this issue, you might show him this little hypothetical dialogue between a student (bold) and teacher from p. 43 of Taylor and Wheeler's Spacetime Physics:

A rocket carries a firecracker. The firecracker explodes. Does this event--the explosion--take place in the rocket frame or in the laboratory frame? Which is the "home" frame for the event? A second firecracker, originally at rest in the laboratory frame, explodes. Does this second event occur in the laboratory frame or in the rocket frame?

Events are primary, the essential stuff of Nature. Reference frames are secondary, devised by humans for locating and comparing events. A given event occurs in both frames--and in all possible frames moving in all possible directions and with all possible constant relative speeds though the region of spacetime in which the event occurs. The apparatus that "causes" the event may be at rest in one free-float frame; Another apparatus that "causes" a second event may be at rest in a second free-float frame in motion relative to the first. No matter. Each event has its own unique existence. Neither is "owned" by any frame at all.

A spark jumps 1 millimeter from the antenna of Mary's passing spaceship to a pen in the pocket of John who lounges in the laboratory doorway (Section 1.2). The "apparatus" that makes the spark has parts riding in different reference frames--pen in laboratory frame, antenna in rocket frame. The spark jump--in which frame does this event occur? It is not the property of Mary, not the property of John--not the property of any other observer in the vicinity, no matter what his or her state of motion. The spark-jump event provides data for every observer.

Drive a steel stake into the ground to mark the corner of a plot of land. Is this a "Daytime stake" or a "Nighttime stake"? Neither! It's just a stake, marking a location in space, the arena of surveying. Similarly an event is neither a "laboratory event" nor a "rocket event." It is just an event, marking a location in spacetime, the arena of science.

 

[ryuunoseika]

ok, i think i get where he's going wrong now...

he says that if two objects are moving at different speeds, but not accelerating relative to each other then they are experiencing the same time and that only when one accelerates or decelerates relative to the other does time dilation become a factor.

then he went off on some rant about the twin paradox and that, relative to the twin in the rocket ship, the one on Earth is accelerating, thus the one in the rocket ship should be younger and the grounded should be younger.

he lost me again. i thinks he might just be stupid...

 

[DaveC426913]

he lost me again. i thinks he might just be stupid...

Cut him some slack. It is a very difficult subject to comprehend.

He has a point about the subjective viewpoint. At some point in his voyage (the outbound leg), the guy in the spaceship will see the guy and the clock on Earth moving slowly. So your friend is not entirely out to lunch.

The catch is that the guy in the spaceship must turn around. And to do this he will experience non-inertial acceleration. Which is what distinguishes him as the moving observer.

 

[JesseM]

ok, i think i get where he's going wrong now...

he says that if two objects are moving at different speeds, but not accelerating relative to each other then they are experiencing the same time and that only when one accelerates or decelerates relative to the other does time dilation become a factor.

then he went off on some rant about the twin paradox and that, relative to the twin in the rocket ship, the one on Earth is accelerating, thus the one in the rocket ship should be younger and the grounded should be younger.

Well, this is the classic mistake that leads people to think it's a genuine paradox, but it's wrong--inertial frames have a special role in relativity, the standard time dilation equation only works in inertial frames. The guy an the rocket has to objectively accelerate to turn around and return to Earth, it's objective because he'll feel G-forces when he accelerates, whereas an inertial observer feels weightless (here we're talking about special relativity where gravity is neglected, think of inertial vs. accelerating observers in deep space). So, the guy on the rocket knows it was him that accelerated and not the Earth, and so if he understands relativity he'll know that any frame where he remains at rest throughout the journey must be a non-inertial one, and thus the time dilation equation cannot be used in this frame to calculate the aging of the twin on Earth.

For more on the twin paradox, here's a good page to show him:

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html