Different Clock Rates Throughout Accelerating Spaceship

[my_wan]

Einstein postulated that any experiment done in a real gravitational field, provided that experiment has a fairly small spatial extent and doesn't take very long, will give a result indistinguishable from the same experiment done in an accelerating rocket.

The text I put in red is the key the advisers here is telling you. The only time the results are 'perfectly' identical is when the spatial extent goes to zero. The clocks in the spaceship where placed to maximize this distance to articulate the effects of a non-zero spatial extent. Of course it is still a very tiny effect on a reasonably sized spaceship, which is why the quoted approximation works.

 

[Wes Tausend]

stevendaryl, jartsa, 1977ub,

Thank you all for a nudge in the right direction. I guess better understanding of General Relativity has been on my bucket list, and I've carried a misconception, or two, for a long time. So, Thanks again. Great thread.

Wes
...

 

[jartsa]

stevendaryl, jartsa, 1977ub,

Thank you all for a nudge in the right direction. I guess better understanding of General Relativity has been on my bucket list, and I've carried a misconception, or two, for a long time. So, Thanks again. Great thread.

Wes
...

Well you just have to add one small thing to the clocks in a rocket scenario:

The extra velocity of a clock at the rear of an accelerating rocket is not enough to explain the time differences observed inside the rocket.

But if we add the extra velocity of a clock that is carried from the rear to the nose, then the final time difference between that clock and a clock at the nose is fully explained by the velocity time dilation.

 

[nitsuj]

What do you get for a ceiling fan hanging/rotating in a "train" traveling at relativistic speeds?

Do you see that it is "distorted" and changing its shape? not merely "shortened" ?

We'd certainly be reminded of the simultaneity issues which accompany the shortening. That's all I meant.

I don't get the ceiling fan, Can I not trust that if I install a fan on my spaceship and go near c, that the fan will still hold it's geometry.

You seem to be telling me that physics isn't the same in all FoRs.

 

[1977ub]

I don't get the ceiling fan, Can I not trust that if I install a fan on my spaceship and go near c, that the fan will still hold it's geometry.

You seem to be telling me that physics isn't the same in all FoRs.

Here I refer only to the view from the "rest frame" - another inertial frame.

Just as the ladder shrinks, all kinds of other weird things happen - for me in the rest frame.

 

[nitsuj]

Here I refer only to the view from the "rest frame" - another inertial frame.

Just as the ladder shrinks, all kinds of other weird things happen - for me in the rest frame.

Ah I see, yea lots of weired things would happen for sure. However I cannot imagine all the invariants/equivalents and "see the fan" has wobble. I would think after accounting for all physical effects when transforming coordinates that the exact same geometry is calculated/found, and in turn the fan isn't wobbling, yet still perfectly balanced.

How I don't know, maybe via kinetic energy/mass the shorter blades still have the same mass as those perpendicular to motion.

 

[1977ub]

Ah I see, yea lots of weired things would happen for sure. However I cannot imagine all the invariants/equivalents and "see the fan" has wobble. I would think after accounting for all physical effects when transforming coordinates that the exact same geometry is calculated/found, and in turn the fan isn't wobbling, yet still perfectly balanced.

How I don't know, maybe via kinetic energy/mass the shorter blades still have the same mass as those perpendicular to motion.

One of the simplest implications of "c is the same for all observers" is that clocks which people on the train view as synchronized / simultaneous read different time as viewed in another frame. Imagine they have a ceiling fan with the blades lining up with the direction of motion "at a particular time". Just like in barn door example, those "same times" train-wise turn out to be different time rest-frame-wise. So the opposite ceiling fan blades will line up with the train's length dimension "At different times" rest-frame-wise and thus at any particular time rest-frame-wise the moving blades are generally not going to be opposite. This all derives from ladder/barn.

 

[1977ub]

Imagine a sphere which regularly and continuously stretches to twice its size and back again. If moving high % of c seen in RF, then the leading and trailing edge are noticed no longer to be puffing out in synchrony. In fact, if speed is just right, leading/trailing ends are "out of phase" so that as trailing edge is receding toward the middle, front edge is puffing out and vice versa. The length in the direction of travel could be nearly constant over time.

 

[SteveDave]

I know this is an older topic by now but if I were to accelerate myself (no ship of any kind) to c and i were holding a timepiece would it no then just be constantly stopped until I slowed back down? Also, would it then want to "catch up" to my postion relative to the surrounding Universe?

Again, I know it's an old topic but seems to me Time is only relevant to our position near the Earth as our time has only ever been measured in relation to ourselves. Just looking for some clairvoyance i suppose.

 

[SteveDave]

Also, this Barn/Ladder theory (after some research) makes sense but again imposes that all things are affected by the spacetime continuum and we know that is not true any longer thanks to the Hadron Collider setup. Please correct me if I am wrong.

 

[my_wan]

I know this is an older topic by now but if I were to accelerate myself (no ship of any kind) to c and i were holding a timepiece would it no then just be constantly stopped until I slowed back down? Also, would it then want to "catch up" to my postion relative to the surrounding Universe?

Again, I know it's an old topic but seems to me Time is only relevant to our position near the Earth as our time has only ever been measured in relation to ourselves. Just looking for some clairvoyance i suppose.

No, the timepiece you are holding will always go at a normal rate. This is because time slows for you, your body, thoughts, everything. So if time did stop for you then you would be stopped to so you will not notice.