Twin Paradox Proffered

          Fraternal twins, Alice and Bob, travel to a, very large, mass free region of intergalactic space. This region of space is so isolated that no curvature of TimeSpace is measurable except for the incredibly tiny mutual gravitational attraction between Alice's ship and Bob's ship. The engines of Bob's ship will not be turned on for the duration of this exercise.
          Alice and Bob synchronize their identical clocks to read zero as Alice starts her ship's engines.

The Standard Constant Speed Case:

  1. Alice's ship quickly reaches 60% the speed of light as she begins her outbound journey.
  2. Alice's ship travels a constant 60% the speed of light as she travels 6 lightyears distance.
  3. Alice's ship quickly comes to a stop 6 lightyears away from Bob.
  4. Alice quickly turns her ship around and reaches 60% the speed of light as she begins her inbound journey.
  5. Alice's ship travels a constant 60% the speed of light as she travels 6 lightyears distance.
  6. Alice's ship quickly comes to a stop next to Bob.

General Considerations:

Traveling at 60% the speed of light: β = 0.60 therefore:

  1. The time dilation factor is γ = 1.25
  2. The length contraction factor is γ-1 = 0.80

From Bob's point of view:

          Each way: Bob ages 10 years while he infers that Alice ages 8 years.
          Each way: Bob sees the distance as 6 lightyears and infers that Alice sees the distance as 4.8 lightyears.

Bob's Expectation:

          As they are reunited, Bob will be 4.0 years older than his twin sister, Alice.

From Alice's point of view:

          Each way: Alice ages 8 years while she infers that Bob ages 6.4 years.
          Each way: Alice sees the distance as 4.8 lightyears and infers Bob sees the distance as 3.84 lightyears.

Alice's Expectation:

          As they are reunited, Alice will be 3.2 years older than her twin brother, Bob.




As Alice reunites with Bob,

1: Bob will be 4.0 years older than Alice.
2: Alice will be 3.2 years older than Bob.
3: they will be the same age: Robert I. Price made a mistake . . . the putz.
4: they will be the same age because they are twins.
5: Other, please specify below or leave a comment in the usual c99p comments section.
Please Specify:

Poll Maker




          Be mindful of Not Henry Kissinger's adamant comment about there being a "no preferred observer" requirement in Relativity. If your reasoning fails on this point, your reasoning is fatally (as in: leading to failure or disaster) flawed.




Share
up
0 users have voted.

Comments

Turns out that they are not just twins, they are are quantum entangled twins, every last particle of their being being entangled between the two/one person(s).

However, as it turns out neurons function on quantum principles, and the entangled neurons give aliob the ability to experience both perspectives without their heads exploding. Giving boice the ability to see the past and future from the two differing perspectives.

However due to the entanglement their bodies reach a stable rate of time between the two time frames, causing them to both age at the same rate,The alice perspective being slowed down, and the bob perspective being sped up.

Hopefully their food stocks, and LSD supplies are entangled as well, because I haven't the foggiest what will happen to them if they are not!

up
0 users have voted.
Not Henry Kissinger's picture

(although you are not a putz.)

Here's why:

Each way: Bob sees the distance as 6 lightyears and infers that Alice sees the distance as 4.8

You have described Bob's point of view as being different from Alice's but all other things being equal they are actually the same.

From Alice's point of view it is Bob who is moving away from her at the rate you ascribe to Alice. So from her perspective it is Bob whose clock is moving more slowly and whose distance is truncated.

Basically they both observe the same thing about the other.

up
0 users have voted.

The current working assumption appears to be that our Shroedinger's Cat system is still alive. But what if we all suspect it's not, and the real problem is we just can't bring ourselves to open the box?

PriceRip's picture

Basically they both observe the same thing about the other.

up
0 users have voted.
sojourns's picture

a couple hits of acid. I'll be back with an answer in a few light years.

up
0 users have voted.

"I can't understand why people are frightened of new ideas. I'm frightened of the old ones."
John Cage

PriceRip's picture

up
0 users have voted.
sojourns's picture

I'm far too old to be undertaking chemically induced revelations.

up
0 users have voted.

"I can't understand why people are frightened of new ideas. I'm frightened of the old ones."
John Cage

very conundrum, and what he observed was that, preferred observer or not, the frames of reference are, in fact distinguishable: Alice experiences acceleration, and Bob does not. This acceleration, he averred, was what gave Alice a shortened experience of time, with respect to Bob's experience of time. (It would also increase Alice's mass perceptibly, per e=mc^2, so that she would need to burn ever more fuel to continue accelerating, but I've never been clear on the relativistic characteristics of acceleration-induced gain of mass.)

Without double-checking your math, I'm happy to assert that Bob WILL be older than Alice, but I'm not going to assume your calculations are correct.

Years ago I had a rather tart argument with someone at DailyKos about this, who insisted that in fact all frames of reference are equivalent under the relativistic paradigm -- and thus, there is no difference between saying that the earth spins on its axis, or that the universe revolves around the earth. (The discussion began with someone asserting that people who say that the sun revolves around the earth are exactly as correct as people who say that the earth revolves around the sun.) The other person threw out a couple of equations that I found unpersuasive, given the simple reality that arguing that the universe revolves around the earth would require all of the mass at the farthest reaches of the universe to be moving at very high speeds indeed, while being continually accelerated, somehow, by forces that, as i say, perhaps his equations somehow reconciled and explained. Thus, I argued, an observer standing on the earth can know that it is the earth that is spinning, and not the universe that is revolving.

up
0 users have voted.

The earth is a multibillion-year-old sphere.
The Nazis killed millions of Jews.
On 9/11/01 a Boeing 757 (AA77) flew into the Pentagon.
AGCC is happening.
If you cannot accept these facts, I cannot fake an interest in any of your opinions.

PriceRip's picture

          . . . or rather a reasonable facsimile (β = 0.8 rather than β = 0.6) complete with TimeSpace diagrams in a few days.

          I will also post a solution wherein Alice travels with constant acceleration, as a more "realistic" scenario.

up
0 users have voted.

as if physicists even today do not differ in their preferred interpretation/"solution"/explanation/"way of understanding". typically, the preferences seem to, ahem, revolve around an individual's particular perspective on where the conundrum lies, and whence it arises, which is satisfyingly relativistic in itself.

I note that you assert that Alice and Bob make certain inferences; but these inferences can only be based, not merely on their observations, but on their knowledge of the structure of the experiment and their (or at least, Alice's) erroneous understanding of time-space dilation under relativistic motion. to the extent that the inferences are based on actual observation, you have elided the question of who is making what observation, and how. Bob's inference of Alice's experience requires that Bob actually have some way of measuring Alice's speed, as well as the distance to her target. Similarly, Alice's inference requires that Alice have some way of measuring either the speed at which she is moving away from Bob, or the speed at which she is approaching her target. We can imagine that, in advance of the experiment, they agree on some clever scheme such as each of them focusing a laser beam at the other; when Alice observes the "appropriate" red-shift in the light from Bob, she will know she is traveling at the predetermined speed. But what is the appropriate red-shift? How will they calculate it? And will Bob observe the same red-shift, or a greater or lesser? Etc.

Consider alternatively, structuring the experiment so that Alice moves her specialized space ship to a distance of 1000000km from Bob, and then fires up engine 1 to propel herself perpendicular to the line from her to Bob, and fires up engine 2 to maintain her distance at 1000000km. In other words, for lack of "real" gravity, she will use a secondary perpendicular engine to keep her in orbit around Bob at a constant distance. Knowing her distance from himself (established by any number of trivial means), Bob can know her speed in his frame of reference simply by tracking the angular rate of her trajectory. So, what in heaven's name will Alice now make of her situation? Her distance from Bob does not change (in bob's frame of reference) ... but how exactly does she know that ... and does it change in her own frame of reference? Indeed, how does the ship manage to control itself in the necessary fashion? Hmm, that's a confusing mystery isn't it? Tell you what: We'll build an enormous circular magnetic rail system in space, 1000000km in radius, and Alice's ship will whoosh along it, zooming along at .6c as understood by Bob, (who could be sitting at the center of the circle of iron, or docked on its outer rim, without changing the outcome) or indeed, by the rail system itself, which can be engineered to keep Alice racing over its course at just the rate desired.

Now there is nothing left for Alice to infer. She knows precisely what her speed is in Bob's frame of reference, and she knows precisely what Bob will perceive to be her distance traveled as well as the time she has spent traveling.

So now, suppose that Bob has a little radio beacon sending out regular pings at a predetermined rate of 1 per second, at a predetermined frequency of 1Ghz. Will Alice perceive the rate of the pings to be 1 per second? 1.25 per second? 0.8 per second? Something else? Will she perceive the frequency of the waves to be 1Ghz? 1.25Ghz? 0.8Ghz? Something else?

if you really want to start fucking with people's heads, instead of putting alice on a rail, put her in a pod at one end of a 2,000,000 km lever, with a perfectly counterweighted pod on the other end, and mount the whole thing onto your gigantic "wheel", mostly just for the hell of it, and accelerate the lever by pushing the pods using magnets in the rim of the wheel, and spin it up to 200 or 300 rpms, and put little blinky lights all along the lever, all of which you start blinking at the same moment, but using their own clocks, before you start anything spinning up at all ... and then shine lasers pulsed at a given rate from the center of the lever down its hollow tube out to the pods, where the light is reflected off a mirror and sent back, where some of it is detected at the center and the rest allowed to zip along back to the opposite pod ... and ask yourself ... WHAT THE FUCK IS GOING TO BE OBSERVED, AND BY WHOM? how does a 2,000,000km lever behave when it is experiencing a continuum of differential time/inertial frame of reference at relativistic scales all along its extent from its fulcrum (axle) to its load (life pod)?

up
0 users have voted.

The earth is a multibillion-year-old sphere.
The Nazis killed millions of Jews.
On 9/11/01 a Boeing 757 (AA77) flew into the Pentagon.
AGCC is happening.
If you cannot accept these facts, I cannot fake an interest in any of your opinions.

PriceRip's picture

          . . . in that we all get the same answer to the question as it is written.

          i find it a bit perplexing that you refer to "the solution" as if physicists even today do not differ in their preferred interpretation/"solution"/explanation/"way of understanding". typically, the preferences seem to, ahem, revolve around an individual's particular perspective on where the conundrum lies, and whence it arises, which is satisfyingly relativistic in itself.

          The "Twin Paradox", as it was originally presented, highlights the expectations of the pair of observers applying time dilation and length contraction in a straight forward manner. As I noted "Except for one very exceptional observation," they seem to be moving symmetrically. The reality is: Alice's observations of Bob's motion are not at all symmetric to Bob's observations of Alice's motion.
          The key is that Alice feels an acceleration as she starts the journey, when she turns around at the far point, and finally as she comes to a stop as she reunites with Bob. Bob however experiences no such accelerations. In the 1980s I had an online exchange with N. David Mermin of Cornell University concerning this very point. He insisted that I was ignorant of the true nature of the conundrum, and I responded by pointing out that at least I was not being belligerently ignorant in this case. We did not have any further online exchanges.


Bob has a little radio beacon sending out regular pings


          The solution, I will be posting soon, includes this explicitly.
up
0 users have voted.
Not Henry Kissinger's picture

in the sense that it is a change in the rate of TD.

But that rate change is mirrored is in Bob's observation of Alice accelerating away from him just as it appears to Alice that Bob is accelerating away from her.

The fact that she may feel the acceleration and he doesn't has nothing to do with their observations of each other's clocks.

up
0 users have voted.

The current working assumption appears to be that our Shroedinger's Cat system is still alive. But what if we all suspect it's not, and the real problem is we just can't bring ourselves to open the box?

explanation -- which is the one that I noted was given me by my professor, and the one that i find most comprehensible -- is not universally admired; beyond which, not all of the "acceleration" explanations are precisely the same.

my (somewhat naive) take on it is that the non-acceleration-based explanations can seemingly all be transformed into acceleration-based explanations, rather analogously to the way that certain physical phenomena appear to be either magnetic or electric in character, depending on the perspective of the observer -- which is, of course, one of the oddities that helped inspire Einstein's formulation of relativity and his fruitless search for the GUT. so in that sense (and iff my naive take is correct), then yes, "there is only one correct solution," but that seems a bit like saying there is only one correct algorithm for solving the Traveling Salesman problem, since each correct algorithm for solving the TS problem can be transformed in polynomial time to any of the others, so they are really all the same, so there's really only one.

ultimately, some of the more knotty phenomena predicted by special and general relativity have never been adequately and comprehensibly explained in any terms other than mathematical equations. physicists -- cosmologists in particular -- like to talk about the universe being infinite as if that were something meaningful outside the realm of abstract calculations. Newton and Leibniz showed us how to deal with the infinite when it applies to convergence of infinitesimals, but at the other end of things, the concepts often seem to break down -- as in the paradox of the "well-defined" funnel-like shape that has infinite surface but finite volume, presenting the ponderer with a hypothetical "object" that can be filled with a finite amount of paint, but can only be painted with an infinite amount of paint. mathematicians (and physicists) tend to shrug away such amusing problems as curiosities of no particular significance. Nonetheless, when a physicist states that the already-endless universe is continually getting bigger, we are outside the realm of mere curiosity, and dealing with a fundamental inadequacy of language (and the cognition that feeds back into language) to contain the concepts in play. I literally do not know what this is supposed to mean. When, where, and how did this expandable infinitude manifest itself? Presumably, the universe has always, from the instant of its inception, been exactly as infinite as it is now -- else, there must have been some magical moment when it somehow transcended itself and became infinite. The problem, I believe, is that physicists are using the word "infinite" in a way that is not at all congruent with ordinary intuition as to what they mean. They do this sort of thing often, it seems to me. The popular "explanation" -- or perhaps "illustration" is a better term -- of ever-expanding curved space, via the metaphor of the surface of a balloon is utterly unsatisfying, because it explains nothing and illustrates very little. Most generally, I do not know how physicists operationally define this limitless universe -- and I'm not sure they know either.

I similarly find the most common "proofs" concerning the infinity of integers to be ... unconvincing. For example, the "proof" that there are "exactly" as many positive integers as even positive integers is no more compelling to me than the alternative and equally straightforward "proof" that there are "exactly" twice as many positive integers as even positive integers; and the inherent problem in both, I believe, is that infinity is a rather dubious concept that thwarts most (or even all) systems of logic. Similarly, Godel's Theorem rests on suspending one's intuition and accepting the Cantor diagonal argument as TRVTH. The infinite and the countably infinite -- what, I wonder, are their equivalents in the realm of physical "reality".

Not that there's much we can do about any of it, anyway.

up
0 users have voted.

The earth is a multibillion-year-old sphere.
The Nazis killed millions of Jews.
On 9/11/01 a Boeing 757 (AA77) flew into the Pentagon.
AGCC is happening.
If you cannot accept these facts, I cannot fake an interest in any of your opinions.

PriceRip's picture

          quite frequently creates the scenario you suggest in your third paragraph.

up
0 users have voted.
PriceRip's picture

I had a rather tart argument with someone at DailyKos

up
0 users have voted.
PriceRip's picture

It would also increase Alice's mass perceptibly

          The mass of a moving object does not change as a function of speed.

          The notion of mass increase with velocity just will not go away. This untruth is the result of some very sloppy thinking. Like the The Lernaean Hydra this nonsensical myth just keeps popping up no matter how many times it is cut from the body of knowledge.

up
0 users have voted.

from the body of knowledge, but i can tell you that 35 years ago this "nonsensical myth" was being taught as a fundamental fact by some very, very smart physicists to some very, very smart engineering undergraduates at one of the most elite public engineering universities in the country, which would certainly go a long ways towards explaining its persistence.

up
0 users have voted.

The earth is a multibillion-year-old sphere.
The Nazis killed millions of Jews.
On 9/11/01 a Boeing 757 (AA77) flew into the Pentagon.
AGCC is happening.
If you cannot accept these facts, I cannot fake an interest in any of your opinions.

PriceRip's picture

          I have been fighting this "meme" for more than 45 years. In fact I argued this point with many "very smart physicists . . . at [various] public . . . universities in the country" and quite frankly I am a bit tired of dealing with it. Further, I am sorry so many "very, very smart engineering undergraduates" and others were subjected to this selfsame asinine perversion of Simple Physics. My job is so very hard anyway, and this just make it that much harder.

          But, then who am I to question my "betters", right? Sigh indeed!

up
0 users have voted.

who has more than once found my arguments dismissed on the grounds that Dr. I.R. Famous, Ph.DDDDDDDD has published a broad array of well-received and oft-cited and much-applied contrary opinion, I can only say that I feel your pain.

up
0 users have voted.

The earth is a multibillion-year-old sphere.
The Nazis killed millions of Jews.
On 9/11/01 a Boeing 757 (AA77) flew into the Pentagon.
AGCC is happening.
If you cannot accept these facts, I cannot fake an interest in any of your opinions.

Not Henry Kissinger's picture

He mentions it early on in a Brief History of Time, which was very popular.

FWIW, I don't buy the mass increases with speed theory either.

Just another in a long string of absurdist theories which tries to reconcile data that General Relativity can't otherwise explain.

up
0 users have voted.

The current working assumption appears to be that our Shroedinger's Cat system is still alive. But what if we all suspect it's not, and the real problem is we just can't bring ourselves to open the box?

PriceRip's picture

          It's not a theory. It was never a theory. Initially this was just a sloppy interpretation (for the great unwashed) of the equations used to describe relative kinematics. Then this lazy pattern of expression slithered into the weltanschauung and became "real" to many of the community. So now it's progeny have infected much of Physics.

          Well, I will just carry on, even though few really care. Reality sucks.

up
0 users have voted.
lotlizard's picture

I assume everyone here interested in string theory and the like is already familiar with Tim Blais’s Queen parody “Bohemian Gravity” . . .

up
0 users have voted.
PriceRip's picture

          An IP address registered as being in Berlin was detected by the Poll Maker server.

up
0 users have voted.