Attribution of Reference Frame: A Dilettante's Question

[SteveF]

I can't find an answer on my dilettante question about how we attribute reference frame to complex objects, where different parts move with different velocity or where different parts experience different influence of gravitation.

For example, we can take a human's body. If we take the full body as a reference frame, we can talk about time dilation compared to some other object external to this body. But at the same time we can take the head as a reference frame and "compare" it to feet. Also we can take neurons from the top of the brain and compare to neurons from the middle of the brain etc. Does this mean that there is no treshold for "framing"?

 

[martinbn]

I think, first you need to learn what a reference frame is.

 

[Ibix]

A frame is a choice of a direction in spacetime to call "time" and choice of how to zero spatially separated clocks. You don't "attribute" a reference frame to any object.

It's certainly true that different parts of an object may have different speeds relative to a given reference frame. In that case, clocks at the different parts of an object may well tick at different rates (in fact, we can detect gravitational time dilation over distances small enough to know that a clock at your head height ticks at a different rate from one by your feet). The effect is too small for you to notice; in any circumstance where you could notice it you would have bigger problems.

There is no rule that requires all clocks on an object to tick at the same rate (which I think is the assumption underlying your questions).

 

[Orodruin]

To expand a bit on #2: A reference frame is an assignation of spacetime coordinates to uniquely identify events. In its essence, it has nothing to do with any object. It is just a computational aid.

 

[Mister T]

I can't find an answer on my dilettante question about how we attribute reference frame to complex objects,

You don't attribute reference frames to objects.

An object can be at rest in a reference frame, in which case we may refer to the reference frame as the rest frame of that object. But if different parts of an object are moving relative to each other, the different parts do not share the same rest frame.

 

[Nugatory]

You will often hear people saying things like “the reference frame of <something>” or “<something> is in this frame”. Strictly speaking these are incorrect, but we say them anyway because it’s awkward to keep saying “the reference frame in which <something> is at rest”.

The “<something> is in this frame” wording is especially misleading because it suggests that things may be “in” some frames but not others. In fact everything is always in all frames; they’re just not at rest in some of them.