Undergrad Who is Moving Faster: Planet or Probe?

[calinvass]

Neither time really slows down. Time as experienced by you is a measure of the length of your path through spacetime, and the planet and probe took different routes with different lengths. That's all there is to it. I think you are just confusing yourself thinking about frames, especially as you are implicitly using non-inertial frames, and talking about "imaginary frames" (which makes no sense - all frames are imaginary, when all's said and done).

Yes, you were right. I was using multiple frames attributed to objects that are always at rest in those frames of reference, except for the clocks and frames moving relative to each other. That generated confusion and contradictory ideas.

 

[GeorgeDishman]

If we go to the probe reference frame, the planet will appear as leaving the probe, and clock on board we can suppose is runs slower. But then the probe will need to do something to come back and it will need to catch the planet. This way in the probe reference frame the probe will not be at rest anymore but moving faster than the planet previously moved in the probe reference frame. So we get the same result. We can ignore the acceleration.

It's a good idea when starting with SR to think primarily of inertial reference frames. You can start with a frame in which the probe is initially at rest and the planet is moving, the planet-based clock therefore ticks at a lower rate in that frame. To catch up though, the probe must then accelerate and move faster than the planet which means that although both clocks are now "ticking slowly" in the chosen frame, the probe's clock is affected to a greater degree. When the probe catches up with the planet, it therefore shows a lesser total elapsed time, by the same amount as would be calculated in the planet's rest frame of course.

 

[calinvass]

There is a different version of a thought experiment without using acceleration by introducing a third object, sincronizing clocks, like in a relay race. Basically, one probe passes by, synchronizes its clock with the planet, then meets another probe, in the opposite direction,same speed, synchronizes clocks again. The third probe, passes by the planet again and they read their clocks.

 

[GeorgeDishman]

That's right, and if you consider the picture from the first probe, the second probe is moving much faster than the planet in order to catch up. It's the same as what I said but avoids the need for an engine burn.

 

[Herman Trivilino]

Suppose we have a single planet in the entire universe and we send a probe through space. There is a clock on the probe and one on the planet. The probe will fly at a constant speed relative to the planet then it comes back.

In order for the two clocks to end up at the same place at least one of them will have had to change direction. If only one of the two clocks changed its direction of motion (in your example it's the one on the probe) then that's the one for which a smaller amount of time will have elapsed.

 

[Dale]

As usual at this point I disagree. A reference frame is something real. You can take the corner of your lab and the clock on the wall as a reference frame as the most simple example. Physics is after all an empirical science and deals with the quantified description of real things you can measure with the adequate measurement devices. That can be a simple yard stick to measure distances up to a ultraprecise interferometer like LIGO to measure tiny distortions of its arms by hitting gravitational waves, but it's a material things that defines reference frames.

No, it isn't. It is convention which defines reference frames. You can take the same material objects making the same measurements and adopt a convention assigning any coordinates you like. As usual, one good example is the GPS Earth centered inertial frame in which none of the material measurement devices are at rest.

 

[vanhees71]

Sure you can use one frame and relabel it with other coordinates, but to fix a frame to begin with you need material objects to define one frame.

 

[Dale]

to fix a frame to begin with you need material objects to define one frame.

The material objects alone certainly don't define the frame, it clearly also requires a convention in addition to the material objects.

 

[Herman Trivilino]

Sure you can use one frame and relabel it witah other coordinates, but to fix a frame to begin with you need material objects to define one frame.

You can use one set of objects to define a coordinate system and relabel it with other coordinates to define a different coordinate system. But the coordinate system is the frame, not the objects. If the objects were the frame you couldn't use the same objects to define two different frames.