Different Clock Rates Throughout Accelerating Spaceship

[1977ub]

Because the rocket must continually foreshorten more and more, Scotty is always moving faster than Kirk. It does not matter if one regards the rear of the rocket moving forward faster, or the front of the rocket moving slower to achieve foreshortening, rationally Scotty must move faster than Kirk.

This is important thing to remember and which I ran into earlier: "foreshortening" is in the eye of the beholder. There is no shortening for Kirk & Scotty the way there would be for an intertial observer nearby. And furthermore any foreshortening is only found after comparing notes with other observers in one's own frame. It could be argued to be "illusory" (not to put too fine a point on it.) Any shortening experienced by Kirk & Scotty is due to materials compressing I believe. This is one reason why I modified my model to cover two identically accelerating rockets one in front of another. This allows issues of how front / back see / measure the other without issues of materials, etc.

Even "universal speed of light" is relative. Sitting here, we are moving very close to "the universal speed of light" relative to some body somewhere (with its putative observers), without doing anything to make that happen.

 

[1977ub]

Related:
Two rockets differently placed along x.
Both accelerating identically according to RF.
AO1 (rear) 'sees' AO2's clock ticking faster and receding.
Presumably if AO1 puts a 2nd clock, initially synched with his own, on a stick and sends up forward,
attached to AO2 for a bit, he will see it ticking faster.
When he gets it back later, it will have ticked ahead of his own? Or returned to synch with his?

Either way, how does RF explain this?
I can see during clock's travel forward it is accelerating faster than AO1 or AO2.
Thus gamma is larger, clock moves slower than AO1 or AO2 clocks, as seen by RF.
It would arrive to AO2 reading slower than his own, then while set earlier than his own, begin ticking at same rate as his own.
Then when he sends it back, RF will see it accelerating more slowly than AO1 or AO2, lower gamma, faster ticking, and arrives back to AO1 back in synch with his?

Oh:
Since AO1, AO2 and 3rd clock appear to be continually slowing down throughout this exercise, presumably when clock3 is being sent back, this is during a period of greater gammas all around, and thus slower ticking all around, and so the ticks 'lost' during the travel forward are not all 'regained' on the trip back?

 

[jartsa]

Related:
Two rockets differently placed along x.
Both accelerating identically according to RF.
AO1 (rear) 'sees' AO2's clock ticking faster and receding.
Presumably if AO1 puts a 2nd clock, initially synched with his own, on a stick and sends up forward,
attached to AO2 for a bit, he will see it ticking faster.
When he gets it back later, it will have ticked ahead of his own? Or returned to synch with his?

Either way, how does RF explain this?
I can see during clock's travel forward it is accelerating faster than AO1 or AO2.
Thus gamma is larger, clock moves slower than AO1 or AO2 clocks, as seen by RF.
It would arrive to AO2 reading slower than his own, then while set earlier than his own, begin ticking at same rate as his own.
Then when he sends it back, RF will see it accelerating more slowly than AO1 or AO2, lower gamma, faster ticking, and arrives back to AO1 back in synch with his?

Oh:
Since AO1, AO2 and 3rd clock appear to be continually slowing down throughout this exercise, presumably when clock3 is being sent back, this is during a period of greater gammas all around, and thus slower ticking all around, and so the ticks 'lost' during the travel forward are not all 'regained' on the trip back?

A trip to the upper regions and then back at moderate velocity will cause a clock to gain ticks. This is why:

(I'm not going to consider 3 clocks, 2 should be plenty enough.)

RF sees the clock that moves upwards to run slower than a clock that stays at the rear.
RF sees the clock that moves downwards to run faster than a clock that stays at the rear.

The latter effect wins, because relativistic effects become larger as velocity increases.
(that's why not immediately starting the return trip causes even more ticks to be gained.)

 

[Wes Tausend]

...

I apologise. It will take a while to come back with fully intelligent questions and answers. I've recently retired and hoped that I will finally have time to pursue some basic layman questions about the Equivalence Principle that arose during science books I read long ago, before the internet. There is also a bit of domestic pressure to tackle home projects that have accumulated over the years rather than spend time on the internet. I will have to be devious.

Lacking advanced formal education, I think I may be in over my head here for the time being. The first post was simple enough for me to understand in terms of geometry. But I don't have enough of an advanced education to quickly understand some of the math language and acronyms used as this thread proceeded, so there is a language barrier for me to overcome that will take more time.

===

In reply to stevendaryl,

Apparently I may have been mistaken in my belief that the Equivalent Principle is fully equivalent. I took info such as this rendition of Einsteins statement, and subsequent development, quite literally.

I don't entirely understand what you meant by,"But the two cases are different, if you perform precise measurements of g." Does that mean that the loss of apparent "weight" by Kirk will be present in both cases, but different, when the rocket is sitting on the ground as opposed to an inertial reaction in an accelerating rocket? What about the clock variation? Will time differences also be different when sitting on the ground as opposed to accelerating in the rocket? I am unable to see this.

Not knowing any better, regarding the Equivalence Principle not being equivalent, I think I worked out a simple relativity model where tidal forces are seemingly also included on the rocket because of Special Relativity, but have since found that that is a highly unusual perspective. It is easier to envision with a different, rather odd thought experiment. There is even a paragraph to this conventional "tidal shortcoming" towards the end of the wiki development section mentioned earlier.

===

In reply to jartsa,

Yes, the bending of the light should occur in both cases, whether the elevator is sitting still on the ground or being drawn up by cable. I am delighted we see it the same. But again, would it be a varied curve difference between the two?

===

In reply to 1977ub,

It is you I must apologise to most profusely for dragging your thread down to my level and slightly diverting it. Thank you for your tolerance.

I tend to regard foreshortening as a real phenomena that may even be easily observable in a very strange way. My thought was that regardless of motions throughout the endless universe, there is a theoretical average that is most at rest. Since the average rest might be any position and light must be at a relative constant speed to include all other observers, that is the philosophical reason any external observer (beholder) may regard themselves at rest.

To Kirk and Scotty, the rest of the universe is really foreshortening while they observe themselves to remain "uncompressed" in assumed current local time. They actually observe the external universe in an earlier, shorter condition. I know this may not make sense to you. It too, is hard for me to explain without a suitable visual descriptive thought experiment.

I do regard the speed of light as universal in a vacuum. Whereas "nothing may go faster than the speed of light in a vacuum", my thought is nothing can be observed to go faster than the speed of light in a vacuum. Perhaps most importantly, light cannot go slower in a vacuum.

In my opinion, the time-dilation/reverse-time-dilation in an accelerating rocket can best be explained by considering that all indicators of time involve additional motion to create an event (tick-tock). Since a vibrating atom, a pendulum, a reciprocating flywheel and all other event-creating clocks must have their own inherent motion, the time mechanism must have additional motion in addition to the forward motion of the spacecraft . But the closer to lightspeed the addition of motions become, the slower the periodic clock events must progress so they may theoretically gradually arrive at zero, the time-stop instant when all the total available "speed" is entirely used up by forward motion at "C", lightspeed. In the above case of Kirk vs Scotty at acceleration, one gentleman is traveling faster than the other, and their ever-slowing respective clock event motions cannot proceed at equal ticks until they both arrive at zero. I hope this makes sense.

...
Wes

 

[stevendaryl]

I don't entirely understand what you meant by,"But the two cases are different, if you perform precise measurements of g." Does that mean that the loss of apparent "weight" by Kirk will be present in both cases, but different, when the rocket is sitting on the ground as opposed to an inertial reaction in an accelerating rocket? What about the clock variation? Will time differences also be different when sitting on the ground as opposed to accelerating in the rocket? I am unable to see this.

Yes, the variation of "g" with height is different for a rocket sitting on the Earth and for a rocket accelerating through space. The variation of "clock rate" with height is different for a rocket sitting on the Earth and for a rocket accelerating through space. In both cases, "g" gets weaker as you go "higher", and in both cases, clock rates go up as you go higher. But the precise rate at which "g" changes and "clock rates" change with height is different in the two cases.

 

[nitsuj]

It could be argued to be "illusory" (not to put too fine a point on it.)

To your previous point it is "after comparing notes" & not optical observation (Penrose-Terrell rotation) that length contraction is observed.

The "ladder paradox" is imo great because it demonstrates the "strength" of that Principal of Relativity postulate (which seems to hold via RoS). How it "smushes" the two FoRs together; unlike that nasty twin paradox.

Here, clearly the ruler is "ticking more slowly"... Or is "shorter" in simultaneous terms, and of course the concept of "simultaneous" is the illusion; not the fact the ladder is actually shorter and fit(s) in the barn; such a fine line. But maybe made more clear by remembering we live in a continuum, and not a sequence of "simultaneity frames" of a mathematical nature.

 

[1977ub]

Here, clearly the ruler is "ticking more slowly"... Or is "shorter" in simultaneous terms, and of course the concept of "simultaneous" is the illusion; not the fact the ladder is actually shorter and fit(s) in the barn; such a fine line. But maybe made more clear by remembering we live in a continuum, and not a sequence of "simultaneity frames" of a mathematical nature.

"The ladder is actually shorter and fits in the barn" - this highlights the way we see an object has having permanent and synchronized areas or parts. The sleight of hand performed by the moving ladder is to have the back of the ladder arrive "soon" and the front of the ladder arrive "late" compared with how we think the whole of the ladder is traveling as a singular object.

The "gee whiz" nature of all many beginner-level SR descriptions leaves out some of the complexities that would remind one of the simultaneity issues.

The "shortened" train with "slower" clocks for instance - if we think of all the things on a moving train that are not static, then the simple idea of things simply being "shorter" gets muddled - after you really work out the ladder paradox you see this - for instance if there is a ceiling fan, the blades are no longer coordinated and opposite, but flop around like psychedelic beagle ears [edit: and this is not an optical illusion, if resting observer could poke fingers down from above at the right times he'd "feel" the misshapen fan]. If there is an axle running under the train, it is twisted like a peppermint stick. If instead of a "ruler" traveling at a high rate, we were to think of a movie screen, then in addition to noting it seems shortened, we'd have to note that the action at the trailing end is from a part of the film a bit later than the leading end - by seconds or millennia or whatever.

 

[nitsuj]

"The ladder is actually shorter and fits in the barn" - this highlights the way we see an object has having permanent and synchronized areas or parts. The sleight of hand performed by the moving ladder is to have the back of the ladder arrive "soon" and the front of the ladder arrive "late" compared with how we think the whole of the ladder is traveling as a singular object.

The "gee whiz" nature of all many beginner-level SR descriptions leaves out some of the complexities that would remind one of the simultaneity issues.

The "shortened" train with "slower" clocks for instance - if we think of all the things on a moving train that are not static, then the simple idea of things simply being "shorter" gets muddled - after you really work out the ladder paradox you see this - for instance if there is a ceiling fan, the blades are no longer coordinated and opposite, but flop around like psychedelic beagle ears [edit: and this is not an optical illusion, if resting observer could poke fingers down from above at the right times he'd "feel" the misshapen fan]. If there is an axle running under the train, it is twisted like a peppermint stick. If instead of a "ruler" traveling at a high rate, we were to think of a movie screen, then in addition to noting it seems shortened, we'd have to note that the action at the trailing end is from a part of the film a bit later than the leading end - by seconds or millennia or whatever.

Should have also mentioned I like the Wikipedia Ladder Paradox description, specifically the diagram that reads like a Sunday comic strip.

I don't understand how comparative motion is "slight of hand". In what sense does the "back of the ladder arrive "soon" and the front of the ladder arrive "late""? I can only assume you mean the ladders FoR. The one that's equally valid as the barn FoR.


this highlights the way we see an object has having permanent and synchronized areas or parts.
Is that length? In either case yes, the barn doors closing is a "permanent"/simultaneous "area or "parts". And of specific coordinates, coordinates unlike the ladders. both "fall under" principle of relativity.

I can't follow that last paragraph, more comic strip, less big block of words.

 

[jartsa]

...
Yes, the bending of the light should occur in both cases, whether the elevator is sitting still on the ground or being drawn up by cable. I am delighted we see it the same. But again, would it be a varied curve difference between the two?

A scientist in a closed accelerating elevator can not be sure that he is in an accelerating elevator, and not standing still on the ground on some planet that has very homogeneous gravity field. That's what the equivalence principle says.

Clocks and accelerometers behave so that it is possible that there is either a real gravity field, and no acceleration, or acceleration and no gravity field.BUT an inertial observer will observe that clocks inside an accelerating rocket do NOT behave like clocks a in a gravity field. The time dilation difference between clocks at different positions is "too small".

For example the case of the non-contracting rocket: No time dilation difference at all between clocks at different positions.Addition: An accelerometer in a rocket with constant proper acceleration looks the same from any frame: It looks like a stopped clock.

Addition2: Oh yes the question was about the bending of light. Well a bending light beam is an accelerometer. So light beams bend the same way in an accelerating rocket and in a gravity field.

 

[1977ub]

I can't follow that last paragraph, more comic strip, less big block of words.

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" ?

[edit/added]

Let's say there is an apparatus set up to make sure that both barn doors close simultaneously as seen by barn frame. There is a single post which is held above the barn and it rotates regularly [on its axis, like an axle]. Large planks are attached at either end and the whole thing rotates so that the two planks cover the barn doors together. Since the ladder perspective sees the two doors covered at different times, this suggests that the post which rotates overhead is measure in ladder frame to be grotesquely twisted like a peppermint stick. This same desynch along a relatively moving frame applies to anything that might exist in the frame, such as a ceiling fan or a TV screen. For those moving relative to this frame, things nearer the direction of motion are set "later" than those toward the rear. Anything like a ceiling fan will be distorted and the blades will no longer be opposite.

[more]

What if a ruler were more like a candle? If it existed for a few minutes, started small, then grew in width as it changed color, then disappeared.

In a moving frame, it would appear to start as a spec and grow out to its full length. but the time it fully existed in the front, the color would be very different in the back, and the width would be greater. finally it would disappear from the back to the front.

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

 

[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.