The case for True Length = Rest Length

[PAllen]

By your ( standard ?) definition, yes.


We're looking at different paradoxes. In the one I'm talking about, the pole is shorter than the barn when they are compared at rest, but not so from the moving pole frame.

However, I'm doing some calculations and I might find that the one-length interpretation won't fly.

I think the 'standard' pole in the barn 'paradox' is the analogous to the alternate formulation I gave in my post #39. That is a rod with a rest length of 100 meters is hurtling towards a barn whose width is 10 meters. Assuming very rapid doors, you can open one door, let the rod in, close that door. Then open the other door to let the rod out. So briefly your 'true length' 100 meter rod has been enclosed in a 10 meter barn.

As I explained in my post #39, this would, in principle be possible. In the rod's frame, it would all look different: a barn door opens, then another opens; the really squashed barn than traverses the rod; then the door that opened first, closes. So the ordering of opening and closing has changed due to simultaneity differeences. However, the containment of the 100 meter rod in the 10 meter barn is awfully 'real' to the barn observer.

 

[JesseM]

Jesse, this goes back to my rotated cube. "The property" is the width of the cube face; "perceptions of the property" is the apparent, foreshortened width due to a partial rotation. Are you suggesting that if a cube is rotated a full 90 degrees then its face width is actually zero?

In my way of speaking, looking at how wide the face appears visually is not a valid method of measuring the property of "face width", though it is a valid way to measure separate properties like "apparent angular width" or "width of projection of face onto your visual plane". I would say that each property is defined in terms of how it is measured, if you use the wrong type of measurement for a given property you've just mixed up the definitions, you're not measuring your "perception" of the value of the property.

 

[JesseM]

At any given moment in this frame, the coordinate distance between ends of the barn really is shorter than the coordinate distance between ends of the pole,

But the barn is not in at rest in this frame which is why comparing the coordinates of the pole with the coordinates of the barn lead to the apparent paradox. If the measurements are adjusted for the relative velocity this erroneous conclusion is avoided.

Once again you have me confused with DaleSpam ;) Anyway, of course I understand the barn is not at rest in this frame, but why should that lead to any "apparent paradox"? In this frame the pole really doesn't fit entirely into the barn at any moment in time, as I said the seeming "contradiction" between what happens in the pole frame and what happens in the barn frame is resolved by realizing this is really just an issue of the relativity of simultaneity, that the order of the events "back end of pole enters rear of barn" and "front end of pole exits front of barn" is different in the two frames, thus there is no frame-independent truth about whether the pole was "really" ever entirely inside the barn. Perhaps you could be more specific about what you think the "apparent paradox" is here, and why you think the solution has anything whatsoever to do with "adjusting for the relative velocity"?

Perhaps tomorrow you could give a numerical example showing what this "correction" you're referring to would look like.

That's disingenuous - of course I mean the LT to change coordinates so you get a comparison 'as if' both objects are at rest in the same frame.

"Disingenuous" is a pretty strong word, are you suggesting I being intentionally deceptive and pretending not to know what you're talking about when I really do? I assure you that's not the case, I really have no idea what you mean by "correction" in this context, and your new clarification is equally confusing, I have no idea what it would mean mathematically to do "a comparison 'as if' both objects are at rest in the same frame". Again, if you can give me a numerical example perhaps I would understand what you're trying to say, but your verbal explanations don't correspond to any use of the Lorentz transform I can imagine.

I think further discussion about 'objective reality' belongs elsewhere and I believe I have given a definition adequate for this discussion.

I haven't been following every post on this thread, mostly just looking at the ones that were responses to my own comments, so can you tell me in which post you gave a definition of what you mean by "objective reality"?

 

[Mentz114]

I think the 'standard' pole in the barn 'paradox' is the analogous to the alternate formulation I gave in my post #39. That is a rod with a rest length of 100 meters is hurtling towards a barn whose width is 10 meters. Assuming very rapid doors, you can open one door, let the rod in, close that door. Then open the other door to let the rod out. So briefly your 'true length' 100 meter rod has been enclosed in a 10 meter barn.

As I explained in my post #39, this would, in principle be possible. In the rod's frame, it would all look different: a barn door opens, then another opens; the really squashed barn than traverses the rod; then the door that opened first, closes. So the ordering of opening and closing has changed due to simultaneity differences. However, the containment of the 100 meter rod in the 10 meter barn is awfully 'real' to the barn observer.

I've been analysing diagrams of the pole-barn type scenarios, especially the ordering of events in the frames. Then I started adding light rays to work out what the obervers see and I was struck by how quickly the information reaching the observers gets out of date ( at relativistic speeds ). So, while I'm not so adamant about the 'one-length interpretation' it's not quite dead yet. I'm going to work on the diagrams and analysis rather than post here for now and maybe have something worth reporting later.

Thanks for your inputs.

 

[Mentz114]

Once again you have me confused with DaleSpam ;) Anyway, of course I understand the barn is not at rest in this frame, but why should that lead to any "apparent paradox"? In this frame the pole really doesn't fit entirely into the barn at any moment in time, as I said the seeming "contradiction" between what happens in the pole frame and what happens in the barn frame is resolved by realizing this is really just an issue of the relativity of simultaneity, that the order of the events "back end of pole enters rear of barn" and "front end of pole exits front of barn" is different in the two frames, thus there is no frame-independent truth about whether the pole was "really" ever entirely inside the barn. Perhaps you could be more specific about what you think the "apparent paradox" is here, and why you think the solution has anything whatsoever to do with "adjusting for the relative velocity"?

Once again, I apologise. Your remarks are apposite and for now I'll give the same response I give to PAllen in my previous post.

(the post you're looking for is #78, I think)

This "thus there is no frame-independent truth about whether the pole was "really" ever entirely inside the barn. " is pretty much what I was beginning to think, but I'm not sure yet. I'll have to draw some more light beams.

Rather than repeating my arguments I'd like to work on it. I'll get back to you, thanks for your inputs.

Also thanks to other respondees and the OP, I don't have the time to reply to all of them, unfortunately.

 

[PAllen]

I've been analysing diagrams of the pole-barn type scenarios, especially the ordering of events in the frames. Then I started adding light rays to work out what the obervers see and I was struck by how quickly the information reaching the observers gets out of date ( at relativistic speeds ). So, while I'm not so adamant about the 'one-length interpretation' it's not quite dead yet. I'm going to work on the diagrams and analysis rather than post here for now and maybe have something worth reporting later.

Thanks for your inputs.

That would be great! I've made some attempts at this without ever carrying it through to a conclusion; but enough to see that what a movie shows would be quite different from the same data interpreted by removing light delays with standard conventions. Also, note that you can remove issues of interpreting light signals (at least in thought experiments) by such direct means as a hypothetical sheet of detecting tissue across each door opening (separate from the doors), attached to recording clock 'right there' so no time delay. Then, irrespective of what an observer would 'see' from any single vantage point, they could put all their data together and find it hard to avoid concluding they had momentarily trapped the 100 meter rocket in the 10 meter barn.

However, be all this as it may, I actually favor the idea of rest length being special for a sufficiently rigid body, and that it is reasonable to treat it as a property of the object. For larger and larger bodies, sufficient rigidity breaks down both in the real world and in theory (1 light year born rigid rulers, anyone?). What I also think is that other lengths observed for the object are also real in the only way that matters to me: what you would measure and reasonably conclude from your measurements.

My analogy is to a cylinder with arbitrary cross section. If someone says, without qualification, 'what is the cross section of that cylinder?' , we all assume an orthogonal slice and discuss the resulting shape and area. We do this even though if we actually cut the cylinder at an angle, we don't pretend that the result we got is an illusion and not real. Furthering this analogy, the more irregular the shape (rather than a cylinder), the more it breaks down to talk about any standard cross section. The analogy to space time seems very direct to me. A rigid body is the analog of the cylinder (cylindrical world tube), while not rigid bodies are like messy objects.

 

[ghwellsjr]

You started your thread with this sentence:

I wanted to discuss Lorentzian length contraction (and time dilation, for that matter).

How about we talk about time dilation now since you said you wanted to. Do you have the same attitude about the rate at which clocks at rest tick versus moving clocks? Do you make the claim that the tick rate of a moving clock is an illusion and that the true tick rate is that of the rest tick rate?

Rjberry, I'm still waiting for a response from you to my questions posed in post #75.

 

[PAllen]

I've been analysing diagrams of the pole-barn type scenarios, especially the ordering of events in the frames. Then I started adding light rays to work out what the obervers see and I was struck by how quickly the information reaching the observers gets out of date ( at relativistic speeds ). So, while I'm not so adamant about the 'one-length interpretation' it's not quite dead yet. I'm going to work on the diagrams and analysis rather than post here for now and maybe have something worth reporting later.

Thanks for your inputs.

I have a suggestion that might be of interest. Instead of pole/ barn, consider the following based on my equivalent variant in post #39; this provides several different types of measurements at once:

100 meter rest length rocket going near c left to right (close enough to c that its contracted length is less than 10 meters). Assume the rocket has fins signficant wider than the body of the rocket.

Imagine tissue like detecting membrane and associated clocks. These can directly measure the passage of nose and fins of the rocket. These are placed 10 meters apart.

Also imagine barriers shooting up and down as in post #39 adjacent to the tissue detectors, but with cameras on them positioned to take head on / tail on pictures of the rocket when the barriers are fully up.

So now we have the sense of containment from barriers, direct measurement of rocket nose tail passing, plus a very interesting pair of images.

I think these end on cameras or more relevant than side cameras, though that would be interesting too.

(The right image would show the rocket from well before it reached the left barrier. The left image would, all the same, show a distorted picture of the tail).

 

[rjbeery]

How about we talk about time dilation now since you said you wanted to. Do you have the same attitude about the rate at which clocks at rest tick versus moving clocks? Do you make the claim that the tick rate of a moving clock is an illusion and that the true tick rate is that of the rest tick rate?

Depends what you mean by "illusion". You might take it to mean that the measurement itself is false, rather than simply differing from the true value of the property being measured, but that isn't right (or rather, that's not what I mean). When I say illusion I mean that the property of an object being measured isn't its "true" value, but that doesn't mean that the "illusion" has no physical consequences. As an example, I had to fit an ottoman through a door the other day which would not fit because the ottoman was wider than the doorway. I rotated the ottoman, such that its foreshortened length was able to fit. Did I actually change the length of the ottoman, or was its foreshortening "illusory"? The illusory effect of foreshortening has physical consequences.

Another example: analyze the color of a binary star and you'll find that it alternates between being redshifted and blueshifted as it orbits its partner. Is it "actually changing color", or is it "an illusion"? The answer that most people would give is that the apparent color change is an illusion...yet the blueshifted color has more energy than the redshifted color nonetheless. Therefore the illusory effect of wavelength shifting has physical consequences. Ask yourself why we feel it's proper to correct for Doppler induced red- and blue-shifting caused by relative motion but NOT to correct for SR-related length contraction caused by relative motion...

When we make measurements we must consider perspective before assigning "true" values to the object under consideration. The whole point of this thread for me is to point out that "perspective" includes relative speed, and that leads me to conclude that "true" length is that which is measured locally and inertially to an object. In the end it's nothing more than a (possibly unnecessary) semantic convention but I find the logic to be sound.

 

[ghwellsjr]

Depends what you mean by "illusion".

I meant whatever you meant at the end of your first post:

Considering SR in this light, one could make the case that objects DO have an absolute length, that being their maximally-measured inertial length, and that any Lorentzian contraction is in fact an illusion.

Would you also make this claim:
Considering SR in this light, one could make the case that clocks DO have an absolute time, that being their minimally-measured proper time, and that any Lorentzian dilation is in fact an illusion.

You are using the words "true" and "false" and "illusion" and "actually" and "apparent" and "absolute" when applied to lengths of moving objects. I'm asking you to use whatever you mean by those words (and I don't care what you mean) and tell me if you believe those same words apply to times on moving clocks.

 

[rjbeery]

I'm asking you to use whatever you mean by those words (and I don't care what you mean) and tell me if you believe those same words apply to times on moving clocks.

Restricted to SR, which is the scope of what we're discussing, the appearance of moving clocks ticking slowly is an illusion. Proof of this is that the effect is reciprocal, in the same way that if you and I are not facing squarely to each other we could both make the claim that the other guy is narrower. It's a bit nonsensical to assign any true or intrinsic value to a measured property if it leads to a logical contradiction.

 

[bobc2]

rjbeery and mentz114, you seem to be looking for some aspect of a 3-D object that could be considered a "True" or objective property. Maybe a concept of 4-D objects (rod or beam) or properties such as 4-Vectors could work for you.

Consider again the pole and barn example that PAllen presented earlier. I've tried to sketch it below in a way that would emphasize the concept of 4-dimensional objects. Incidently, I've used a symmetric spacetime diagram (both objects moving in opposite directions at the same relativistic speed with respect to the black coordinates in order to obtain the same distance scaling for both red and blue coordinates.

It is clear that both observers (red and blue) witness very real phenomena, and when viewed in four dimensions there is no argument at all about whose observations are correct--they both are (and no need to make corrections for one's view, although blue could do a Lorentz transformation if he is curious about what the red guy is experiencing).

Notice you could raise other four dimensional questions such as, "what is the 4-Vector magnitude between events A and B (the blue and red guys would both get the same answer)?

 

[ghwellsjr]

Restricted to SR, which is the scope of what we're discussing, the appearance of moving clocks ticking slowly is an illusion. Proof of this is that the effect is reciprocal, in the same way that if you and I are not facing squarely to each other we could both make the claim that the other guy is narrower. It's a bit nonsensical to assign any true or intrinsic value to a measured property if it leads to a logical contradiction.

Why do you say "restricted to SR"? Are you leaving open a loop-hole through which you can explain the Twin Paradox?

 

[rjbeery]

Why do you say "restricted to SR"? Are you leaving open a loop-hole through which you can explain the Twin Paradox?

It's because SR effects produce measurements that are apparently contradictory and reciprocal (i.e. each party concludes the other's watch is slower), similar to mutual foreshortening. When you involve acceleration you break that reciprocity.

 

[ghwellsjr]

You can analyze the Twin Paradox from any frame of reference. They all agree that each party views the other party's clock as running slower than their own during the entire trip and yet when they re-unite, the traveling twin's clock has progressed a lesser amount of time. The reciprocity is not broken just because one of them accelerated.

You can also analyze the Twin Paradox without using any frame of reference and without using Special Relativity. You can analyze it simply from the observations of each other's clocks during the trip using Relativistic Doppler. Again, they always see each other's clock as running slow compared to their own in a reciprocal manner and yet when they re-unite, the traveling twin's clock has progressed a lesser amount of time.

SR does not make or create the way nature works, it's merely one way to describe and analyze it.

 

[rjbeery]

They all agree that each party views the other party's clock as running slower than their own during the entire trip and yet when they re-unite, the traveling twin's clock has progressed a lesser amount of time. The reciprocity is not broken just because one of them accelerated.

This is incorrect. If acceleration did not determine which twin was aging slower we could consider the "traveling" twin to be motionless and the other twin to be on a giant, Earth-shaped spaceship. You're not realizing that labeling one of them as "traveling" is equivalent to requiring that they undergo acceleration (i.e. at the very minimum to turn around and head back to their sibling).

 

[ghwellsjr]

You missed my point. I said that the acceleration of the traveling twin does not break the reciprocity of each twin seeing the other's clock as always running slower than their own. That's what you said in post #104. If after acceleration, the traveling twin saw the stationary twin's clock as running faster, then your comment might have some merit.

So I don't know what it was in my statement that you quoted that you believe is incorrect. Could you be more specific?

 

[rjbeery]

So I don't know what it was in my statement that you quoted that you believe is incorrect. Could you be more specific?

Sure...

You missed my point. I said that the acceleration of the traveling twin does not break the reciprocity of each twin seeing the other's clock as always running slower than their own.

This part is wrong. Reciprocity exists UNTIL the return trip begins; during the acceleration involved in turning around, the reciprocity is broken and both parties will now realize that "something is amiss". Otherwise, the following statement leads to a direct and obvious logical contradiction:

Again, they always see each other's clock as running slow compared to their own in a reciprocal manner and yet when they re-unite, the traveling twin's clock has progressed a lesser amount of time.

Please explain specifically how this would happen if the traveling twin kept a keen eye on his twin's clock for the entire trip; are you suggesting that "just as he lands" his Earth-bound twin's clock instantly LEAPS FORWARD in time to his amazement?

 

[ghwellsjr]

Reciprocity exists UNTIL the return trip begins; during the acceleration involved in turning around, the reciprocity is broken and both parties will now realize that "something is amiss"

The traveling twin will observe during his turn around that the ticks from the stationary twin's clock suddenly come in faster than his own but applying Relativistic Doppler Factor, he calculates that the time dilation is identical to what it was before. The stationary twin has no knowledge of the traveling twin's turn around until long after it has occurred at which point he will also observe a similar change in tick rate but it also calculates to the same time dilation factor as before. Both twins observe exactly the same time dilation of the other twin during the entire trip (except for the insignificant time it takes for the turn around and for the take off and for the landing).

Please explain specifically how this would happen if the traveling twin kept a keen eye on his twin's clock for the entire trip; are you suggesting that "just as he lands" his Earth-bound twin's clock instantly LEAPS FORWARD in time to his amazement?

I already explained some of how this works in the first part of this post but the rest of the story is that each twin keeps track of the other twin's clock by counting the observed ticks. During the outbound half of the trip, the traveling twin counts so many ticks coming in from the stationary twin at a low rate and during the inbound half of the trip, he counts a much larger number of ticks coming in from the stationary twin at a much higher rate. In contrast, the stationary twin counts the ticks coming in at a low rate from the traveling twin for way more than half of the trip and then near the very end he counts them coming in at a high rate. You have to take into account the light travel time. Since the traveling twin counted high rate ticks from the stationary twin for a much longer percentage of the trip (one half of the trip, to be precise) than the stationary twin counted of the traveling twin, the traveling twin's total count of the stationary twin's clock is much higher than the stationary twin's count of the traveling twin's clock. Nothing happens instantly during any portion of the trip and neither twin is amazed by what happens. It's all very logical, reasonable, understandable and systematic.

 

[rjbeery]

Nothing happens instantly during any portion of the trip and neither twin is amazed by what happens. It's all very logical, reasonable, understandable and systematic.

I don't believe the twin paradox is anything but logical, reasonable, understandable and systematic. The contradiction arises if you try to claim that it isn't the acceleration of the traveling twin that causes the age differential.
Have you ever seen a "lines of simultaneity" analysis of the twin paradox? It looks something like this:
[URL]http://upload.wikimedia.org/wikipedia/commons/c/ce/Twin_Paradox_Minkowski_Diagram.svg[/URL]
See that "gap" in the stationary twin's world from the traveling twin's perspective? If you study this for a bit you'll realize that ALL of their relative age differential exists because of this gap. (Note: the only reason the stationary twin appears to age "instantly" is because the graph shows, as most do, that the traveler turns around "instantly". A more reasonable rate of acceleration while turning around would produce a period of extremely fast aging for the stationary twin, yet one devoid of an unnatural gap.)

Both twins observe exactly the same time dilation of the other twin during the entire trip (except for the insignificant time it takes for the turn around and for the take off and for the landing)

This analysis shows that your dismissal of the "insignificant time it takes for the turn around" is precisely what is wrong with your description and understanding.

 

[bobc2]

This analysis shows that your dismissal of the "insignificant time it takes for the turn around" is precisely what is wrong with your description and understanding.

rjbeery, I think you might consider the twin example from a little different perspective. Here is a spacetime diagram that simplifies the analysis by using the symmetric spacetime diagram for the trip out. We compare times with the use of the hyperbolic calibration curves for the trip back when the speeds are different (otherwise it would defeat the ability to compare distances and times directly). Both twins experience the same proper time lapse at their respective number 9 stations. But, owing to the short cut taken by the round trip twin on the return flight (blue goes faster to catch up with red), you can see the proper times would be quite different when they get back together. Red has moved 17 proper time increments and blue has only moved through 13 proper time increments.

It is clear that shortcut taken by the twin doing the round trip accounts for the difference in age, not the turn-around acceleration. All the turnaround does is to give the round trip twin interesting variations in his view of the other twin's clock (as has already been pointed out in ealier posts). We can show the respective views each has of the other's clocks on the return trip if necessary (someone else could probably do that since I'm running out of steam).

 

[rjbeery]

Here is a spacetime diagram that simplifies the analysis by using the symmetric spacetime diagram for the trip out.

Bob, with respect, I LOL'ed at this one.

Anyway, you are correct in a sense; it isn't the acceleration per se, it's the frame change. Have you ever played the game Portal? Super fun. Anyway, you have a gun that can open "portals" on any flat surface. You create two of them, and then you can travel between them instantly. Jump through one, and your momentum is carried through the other. The physics really plays with your head, especially when jump through the floor and enter through a vertical wall (and your momentum continues), or you place one directly on the floor below the other in the ceiling (so you fall "for eternity").

Anyway, my point is that if we could get our hands on one of these guns then producing an asymmetrical time dilation between two observers without either one of them accelerating would be possible. Until then, frame changing is synonymous with accelerating!

 

[bobc2]

Until then, frame changing is synonymous with accelerating!

I certainly agree with you that the round trip twin did accelerate during the turnaround. However, the spacetime diagram implies a relatively insignificant increase in proper time during the turnaround. We could have shown a magnification of the turnaround to indicate that the g-levels for the blue guy would not be as high as might be inferred from my diagram. But, again, the length of the world line (curve) during turnaround for the blue guy would be relatively insignificant.

Besides, it is obvious that it is the high speed at the end of the acceleration that provides the short cut through spacetime. We're not doing anything like sending the blue guy off to the neighborhood of a black hole. In any case we keep the acceleration under control so as to keep the problem in the realm of Special Relativity.

 

[ghwellsjr]

You asked me:

Please explain specifically how this would happen if the traveling twin kept a keen eye on his twin's clock for the entire trip; are you suggesting that "just as he lands" his Earth-bound twin's clock instantly LEAPS FORWARD in time to his amazement?

I explained to you what the traveling twin's keen eye would see of his twin's clock during the entire trip. I said that during the outbound half of the trip, he will see his twin's clock ticking at some rate slower than his own. Then after he turns around, he will see his twin's clock ticking at some higher rate than his own. The sum total of all the ticks is the amount of aging the stationary twin experienced.

And then I also explained what the stationary twin's keen eye sees of the traveling twin's clock. I said that for way more than half of the trip, he sees the traveling twin's clock ticking at some rate slower than his own (the same slow rate that the traveling twin sees during the first half of the trip). Then I said that near the end of the trip, he sees the traveling twin's clock ticking at some rate higher than his own (the same high rate that the traveling twin sees during the last half of the trip). The sum total of all the ticks is the amount of aging the traveling twin experience.

The fact that the stationary twin counted low rate ticks for much more than half of the trip illustrates how he sees the traveling twin as aging less than himself.

But then you responded by saying that all of the differential aging occurs during the acceleration at turn around which has nothing at all to do with what the twin's keen eye sees. Why do you ask me to explain what he sees and then complain about something that has nothing to do with what he sees?

You also asked me if I can see something in a graphic but the graphic is broken. All I can see is a framed box with an X in it. So I cannot respond to your questions but it really doesn't matter because as I already explained, you haven't shown what either twin sees which is what you asked me to explain.

And keep in mind, I explained what each twin sees without bringing Special Relativity into the picture. You can also explain the Twin Paradox, as I said before, by using any frame of reference. But you have to be careful to illustrate in that frame what each twin actually sees and it will be exactly the same as I described without using SR. It doesn't matter which frame you use to analyze a scenario, they all agree on what each observer sees.

So my simple question to you is: do you deny my description of what the twin's see?

 

[JesseM]

But then you responded by saying that all of the differential aging occurs during the acceleration at turn around which has nothing at all to do with what the twin's keen eye sees.

Did rjbeery ever say that exactly? If so, in which post? I thought rjbeery was just arguing that the acceleration explains why one twin has aged less in total when they reunite, which is not the same as saying all the differential aging occurred "during the acceleration". Neither of what either of you are saying about the twin paradox seems incorrect to me so I don't quite understand what you're disagreeing about, either I misunderstood something about your arguments or you guys are misunderstanding each other...

 

[GrayGhost]

Sure...

This part is wrong. Reciprocity exists UNTIL the return trip begins; during the acceleration involved in turning around, the reciprocity is broken and both parties will now realize that "something is amiss". Otherwise, the following statement leads to a direct and obvious logical contradiction:

Please explain specifically how this would happen if the traveling twin kept a keen eye on his twin's clock for the entire trip; are you suggesting that "just as he lands" his Earth-bound twin's clock instantly LEAPS FORWARD in time to his amazement?

Well, during periods of twin B inertial motion, the reciprocity always exists and can be observed. However when twin B undergoes proper acceleration, it's another story ...

The overall experience per twin B is twin A's wildly spinning distant clock during periods of twin B's own proper acceleration. However, this "overall experience" is the superposition of 2 relativistic effects ...

(1) the reciprocity of slower ticking clocks, and

(2) the change in relative simultaneity between the 2 POVs.​

So, the reciprocity of moving clocks always holds mathematically (as ghwellsjr stated), however the change in relative simultaneity counters that effect (from B's POV), twice over ... and so the reciprocity of moving slower-ticking-clocks cannot be observed, and can only be deduced as the superposition of 2 relativitic effects that concurrently concur.

That said, I see you and ghwellsjr both as correct. However, if you think that relative clock rates are illusionary effect, in this you are mistaken. Whether inertial or undergoing proper acceleration, what a clock presently reads dictates its real time and thus the proper time experienced by the clock since the 1st of 2 spacetime events.

GrayGhost

 

[bobc2]

And keep in mind, I explained what each twin sees without bringing Special Relativity into the picture. You can also explain the Twin Paradox, as I said before, by using any frame of reference. But you have to be careful to illustrate in that frame what each twin actually sees and it will be exactly the same as I described without using SR.

ghwelsjr, I was pretty much following everything you've been saying, except I don't follow what you mean about not using special relativity to explain the twin paradox. I've always understood the twin example as following from application of the knowledge of special relativity (I did rely upon it in my spacetime diagram above--post 102).

 

[Mentz114]

I've made some attempts at this without ever carrying it through to a conclusion; but enough to see that what a movie shows would be quite different from the same data interpreted by removing light delays with standard conventions. Also, note that you can remove issues of interpreting light signals (at least in thought experiments) by such direct means as a hypothetical sheet of detecting tissue across each door opening (separate from the doors), attached to recording clock 'right there' so no time delay. Then, irrespective of what an observer would 'see' from any single vantage point, they could put all their data together and find it hard to avoid concluding they had momentarily trapped the 100 meter rocket in the 10 meter barn.

I had a good look at the barn-pole scenario and this is what I got. I hope I haven't made an error but I'm sure someone will tell me if I have.

 

[ghwellsjr]

But then you responded by saying that all of the differential aging occurs during the acceleration at turn around which has nothing at all to do with what the twin's keen eye sees.

Did rjbeery ever say that exactly? If so, in which post? I thought rjbeery was just arguing that the acceleration explains why one twin has aged less in total when they reunite, which is not the same as saying all the differential aging occurred "during the acceleration". Neither of what either of you are saying about the twin paradox seems incorrect to me so I don't quite understand what you're disagreeing about, either I misunderstood something about your arguments or you guys are misunderstanding each other...

First off, I appreciate that you agree with me that my description of what each twin sees is correct and that my statement that each twin views the other one as experiencing time dilation during the entire trip is correct.

But, rjbeery does not agree with you or with me. I'm trying to figure out exactly what he disagrees with me about. That's why I asked him at the end of my post you referenced if he denies my description of what each twin sees.

But to answer your question about where he said that all the differential aging occurs during the acceleration at turn around:

(Note: the only reason the stationary twin appears to age "instantly" is because the graph shows, as most do, that the traveler turns around "instantly". A more reasonable rate of acceleration while turning around would produce a period of extremely fast aging for the stationary twin, yet one devoid of an unnatural gap.)

 

[PAllen]

I had a good look at the barn-pole scenario and this is what I got. I hope I haven't made an error but I'm sure someone will tell me if I have.

Didn't spot any errors. However, see my post #98 for more aspects of the situation. In your scenario, a key point is to imagine cameras on the inside of each barn door taking pictures every nanosecond, previously synchronized to extreme precision (in the barn frame). These cameras will have a period where one photographs the front of the rod and the other the back. However, the camera snapping the approaching rod will see it extending out the barn (or in my more extreme scenario, before it has even entered the barn). All the same, the other camera will simultaneously show the back of the rod. Also, the readout from my proposed tissue detectors will clearly show the rod inside the barn. As, for the cameras, it is easy to understand that the camera snapping the approaching rod is showing a very stale image, and thus concluding that the two cameras together 'prove' the rod was in the barn.

This all shows the even in one frame, you better clearly define how you measure something and how you interpret those measurements. Different, perfectly reasonable choices can lead to different results.