A Traveling Twin's Rest Frame?

Okay, let's play with this idea of the traveling twin's  "rest frame"  One trouble with the idea of any noninertial frame is that there is no unique way of prescribing its construction. 

But I think I understand how you are thinking of your construction...  Here is the link to WWoods diagram on Wikipedia: File:Twin 5.png

My impression of your "rest frame" is that you want to take these diagrams, and chop them along the lines of simultaneity and stitch together the result like so:

One reason I would object to that is that in this “rest frame of the traveling twin” all of the events that happen on earth between Event A and Event C are unrepresented.  Also, if the traveling twin were to look in the opposite direction, some events would cross the line of simultaneity in the other direction, and happen twice.

Let me suggest another version of this "traveling twin's rest frame."

As a solution, I would offer the following modification. 

Instead of stitching together the rest-frame along the line of simultaneity, what if we stitched it together along the line of x=-ct (e.g. the locus of events that are actually observed by the traveling twin at the instant of his acceleration when he looks toward earth.)

For that, we'll start with another diagram

File:Three frames.JPG

This diagram does not share the same labels as the earlier one.  Instead, event B here is the event-(stream) on earth observed by the traveling twin at the time of the turnaround.

Instead of chopping the two diagram along the line of simultaneity, I chop it along the line EB and combine them like this.

We still have this line from beginning-to end of the trip for the traveling twin represented as a straight line. But now it shows all of the events on earth observed by the traveling twin instead of skipping a bunch.

Also it has the advantage of actually showing, rather than hiding the discontinuity in the motion of the earth in the reference frame(s) of the accelerating observer.

By using t=0 as your stitching boundary, you have some observed events repeated twice, and some observed events not represented.  So your concept of an accelerating rest frame would be much improved if you used the locus of events t=−r/c of the past light-cone as our stitching boundary. 

Now, just to be clear, though.  Just because I can stitch together parts of two diagrams to make the world-line of an accelerating observer look straight, I still think it is probably better to just say he is "switching inertial reference frames" because even those events that are far in the observer's past are still in the locus of events affected by the Lorentz Transformation.

Upvote - Downvote - Comment: Why Nobody Grocks the Twin Paradox

Jonathan Doolin, Generator of Hypotheses (and College Physics and Astronomy Professor)

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What always really bugs me about these explanations of the twin paradox is that they usually seem to say "there's something different about the accelerating twin." But they are always very vague about what that difference is.

But the differences need not be vague.  Everything can easily be derived from the Lorentz Transformation equations, and there is no mystery to it. 

If you have an object receding from you at near the speed of light, it will appear to be moving, at a maximum, of 50% of the speed of light. 

Why?  (Answer this question for yourself, and if you agree, Upvote, if you don't agree, downvote, and post a comment.)

On the other hand, if you have an object approaching you near the speed of light, there is NO LIMIT to it's maximum apparent speed. 

Why?  (Answer this question for yourself.  If you agree, upvote.  If you don't agree, downvote, and post a comment.)

Now, when you look at a fast approaching, or fast receding object are you looking at where the object is now?  No.  You're looking at where the object WAS when it emitted or reflected the light.  That emission or reflection of light is an "event" which happened at a place and time in your perceptions.  It has physical coordinates of (t,x,y,z)  Space and time.

What happens when you accelerate toward a past event in Special Relativity?   It moves away from the observer, and back in time.  Again, do the math yourself.  If you agree, Upvote.  If you don't agree, Downvote and post a comment.)

But yes, if you accelerate toward an event in the past, Lorentz Transformation equations say it moves away and back in time.  That's good, because it makes everything consistent with what I said earlier: 

As the moving twin is moving away from the sun, he's going to see the sun moving away at less that half the speed of light.   When he turns around, he's going to see the image of the sun jump away from him--lurching away from him spatially.  And it will also (from his perspective) lurch backward in time... So the emission/reflection event happened much further away and longer ago.  So at the "instant of acceleration" is when the earth has suddenly aged in his point-of-view.


(Video explanation added, November 7)

The video explains what is meant by "if you have an object receding from you at near the speed of light, it will appear to be moving at a maximum of 50% of the speed of light." 

It also explains why the distance traveled by the earth in the second leg of the inbound  frame is much greater than the distance traveled by the earth in the first leg of the outbound frame

Updated 7 Nov • View Upvotes

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Jonathan Doolin

I thought I would provide this reference... This is a free video game which I think does a pretty good job of showing what relativistic motion really "looks like"

A Slower Speed of Light

You can see as you play it that accelerating forward makes objects in front of you appear to move away, and when you accelerate backwards, the objects in front of you appear to come closer. 

Some people think of this phenomenon as an "optical illusion" but it isn't.  The images are coming from the actual coordinates of actual light-reflection events.  Are these coordinates observer dependent?  Yes.  Are these coordinates frame dependent?  Yes.   Are these differences illusory?  NO.

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Erik Anson

You seem to be suggesting that SR is a matter of light travel delay effects. I'm assuming that you know that that isn't the case, but your answer focusing on them so much that readers may be confused.

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Jonathan Doolin

You find my willingness to explore the traveling-twin's point-of-view confusing.  I should ask, are you actually finding it confusing, surprising, unbelievable, or incorrect? 

Confusion is when you are unaware of all the facts; or you may have some of them wrong; so they don't all fit together.  Surprise is when you see something that you didn't expect. 

For people able to accept surprises, putting an emphasis on that surprise can often clear up the confusion. 

Most of the literature on the twin paradox does not discuss any observations made by the traveling twin, except for an obsession with the traveling-twin's clock. There is a widespread unwillingness to analyze the twin paradox from the traveling-twin's point-of-view.  I think that the traveling-twin's observations are relevant to the twin paradox question, and describing them will greatly increase the "surprise" but greatly decrease the "confusion".

So I'm trying to present the most surprising asymmetry of the problem (other than the well-known fact that their clocks don't match up at the end):  Namely, the way the earth JUMPS AWAY from the accelerating twin when he/she accelerates towards it.  This fact deserves EMPHASIS because it is SURPRISING.  (Not DEEMPHASIS because it is CONFUSING.)

The fact that the earth JUMPS AWAY from the traveling twin on turnaround, is a fact that I expect many readers to find surprising...  I strongly suspect that even some people who consider themselves experts on the subject are unaware of this fact, since it doesn't seem to appear anywhere in the literature I've seen; although it does show up quite prominently in the video game from MIT.  A Slower Speed of Light
(They do this without words, and it actually looks pretty natural.)

But just to make it clear, this JUMPING AWAY is NOT a result of light-travel-delay-effects.  It is an effect of switching inertial reference frames.  By the Lorentz Transformations this happens whenever you take any distant observed event  and accelerate toward it.  That event jumps away from you backward in space, and backward in time.

What is the most logical explanation of the twins paradox in special theory of relativity?

What always really bugs me about these explanations of the twin paradox is that they usually seem to say "there's something different about the accelerating twin." But they are always very vague about what that difference is.

But the differences need not be vague.  Everything can easily be derived from the Lorentz Transformation equations, and there is no mystery to it. 

If you have an object receding from you at near the speed of light, it will appear to be moving, at a maximum, of 50% of the speed of light. 

Why?  (Answer this question for yourself, and if you agree, Upvote, if you don't agree, downvote, and post a comment.)

On the other hand, if you have an object approaching you near the speed of light, there is NO LIMIT to it's maximum apparent speed. 

Why?  (Answer this question for yourself.  If you agree, upvote.  If you don't agree, downvote, and post a comment.)

Now, when you look at a fast approaching, or fast receding object are you looking at where the object is now?  No.  You're looking at where the object WAS when it emitted or reflected the light.  That emission or reflection of light is an "event" which happened at a place and time in your perceptions.  It has physical coordinates of (t,x,y,z)  Space and time.

What happens when you accelerate toward a past event in Special Relativity?   It moves away from the observer, and back in time.  Again, do the math yourself.  If you agree, Upvote.  If you don't agree, Downvote and post a comment.)

But yes, if you accelerate toward an event in the past, Lorentz Transformation equations say it moves away and back in time.  That's good, because it makes everything consistent with what I said earlier: 

As the moving twin is moving away from the sun, he's going to see the sun moving away at less that half the speed of light.   When he turns around, he's going to see the image of the sun jump away from him--lurching away from him spatially.  And it will also (from his perspective) lurch backward in time... So the emission/reflection event happened much further away and longer ago.  So at the "instant of acceleration" is when the earth has suddenly aged in his point-of-view.

Geometric-Point-of-View and Experiential-Point-of-View

Why do people think the Earth orbits the Sun? Can geocentricity be disproved?

I think in the rush to say "No! The earth orbits the sun!" there may be another root question that gets missed, which is whether our point-of-view as people on the planet's surface is valid at all.

If you've ever played a first-person video game, you may have noticed that all of the all of the action seems to center around a first-person point-of-view.  Can that first person point-of-view be disproven?

But can my personal point-of-view be disproven?  From my own point of view, the stars move around the sky in 23 h 56 minutes.  The sun lags behind them, going around the sky every 24 hours, and the moon lags behind even further still, being lapped by the sun every month.

Can you disprove my point-of-view?  My point-of-view is as valid as any other point-of-view, so long as it doesn't cause me to draw any invalid conclusions. 

If I say, "It appears that the sun and stars are going around the sky once each day" that is a valid statement, but when I conclude "By Newtonian Mechanics, they should be flung outward into space, so Earth's pull must be so great that it is holding them in place." Now I've made a false conclusion.  There are many false conclusions that might be intuitively drawn by saying that the earth is at the center of our universe, just as there are many false conclusions that might come from saying "I am the center of the universe."

However, that doesn't change the fact that our own points-of-view, regardless of the false conclusions they may cause us to draw, are the only points-of-view we actually have.  So the geocentric perspective is not invalid, but the geocentric conclusion that the sun orbits the earth in 24 hours because of Earth's gravity has certainly been disproven.

Robert Frost

No.  That argument could be made if only the Sun and Earth exists.  Since we have a rover driving around on Mars, we can indisputably say that egocentrism is false and heliocentrism is correct.

Jonathan Doolin

I'm arguing for the validity of a point-of-view; e.g. "my point-of-view is a valid one"

You're arguing against egocentrism, e.g. "my point-of-view is the only valid one" That's an entirely different argument.

Robert Frost

I'm saying point of view is irrelevant.

Jonathan Doolin

Oh, in that case, then I really disagree with you.  You claim that we sent a rover to Mars, and you use that to make some kind of claim, but then you go on to claim that point-of-view is irrelevant.  It's a logically inconsistent argument.  You're using the point-of-view of the Mars lander, as something relevant, then saying that the point-of-view of the Mars lander is irrelevant.

David Veshapidze

That point of view, if it's also a belief, is caused by the ignorance if the subject and there is no point of trying to disprove the hypothesis to a person who stubbornly believes that.  Now, I am hoping your argument is purely a philosophical one and in that case, heliocentricity only matters to an average person for the sake of being knowledgeable.

If one lived in a house all their life, never leaving, with climate controlled, constant temperature and humidity, it wouldn't matter to them whether it was raining, snowing or sunny outside. Such person could believe the entire universe was at 72 degrees temperature, despite what the outdoor gauges were showing, but that would not make them right, just stubborn  and ignorant.

Jonathan Doolin

Ah.  I think here I was referring to "point-of-view" not so much as belief, but perspective. 

As a matter of perspective, it makes very much sense to use right-ascension and declination.  Declination is very much tied to the Earth's equator.  Nothing to do with the ecliptic.  Right Ascension is measured in hours because the stars move one hour per hour, relative to the earth.  However, they are tied to a point in space, which could be called geocentric  Because the point in the sky where the sun crosses the earth's equator is zero right-ascension.  However, the coordinate of right ascension isn't really geocentric or heliocentric--it's measured against the whole backdrop of stars.

Anyway, right ascension and declination are valid ways to describe the universe even though both are tied in some ways to a geocentric feature.  You could define declination from the ecliptic instead, but it would make it much harder for astronomers to find anything.  Using declination measured from the equator allows astronomers in the northern hemisphere, for instance, to use the North Star as a reference point, and just measure from there. 

That was the point I was trying to make about perspective... 

But as for this hypothetical man in the 72 degree room:

If he has outdoor gauges in his perspective, the readings of the gauges lie within his point-of-view.  If he doesn't look at the gauges, he remains ignorant.  If he doesn't trust the gauges, he is stubborn. 

Now the willfully ignorant person, who simply refuses to look at the gauge--there's little point in trying to prove or disprove anything to him... He doesn't care about evidence. 

But what if you have two people; one who trusts the gauges, and the other who doesn't trust the gauges.  Neither of them have any idea how the gauges work.  Which one, then, is ignorant and which one is knowledgable?

Both of them are ignorant, because neither one of them knows how the gauges work.  If they are both stubborn, then they should both be stubbornly trying to figure out how the gauges work, rather than getting in a fight over which one is more ignorant.

David Veshapidze

My gauges metaphor was to illustrate our current scientific knowledge of the movement of celestial bodies that allows us, with extreme precision, to launch aircraft and land on a tiny strip of land millions of miles away (mars), or perform a 7,800 mile flyby billions of miles away (Pluto) following a complex series of gravity assist maneuvers.

Person who trusts the gauges, does not just have "faith" in them, the gauges are the proven scientific facts that's we put in practice - He//she knows how the gauges work. The second person disregarding the gauges is willfully ignorant because they deny the science.

Jonathan Doolin

We seem to have agreed, in principle that point-of-view in terms of geometric perspective is generally valid for all observers.  If I see a house from one direction, and you see a house from another direction, we're both seeing the same house--but the differences we see are real and our point-of-view is valid.

As far as the other situation goes, you've listed TWO beliefs of the scientist in the room, not one.  The first is the belief that the gauges are correct.  The second is the belief that the second person "is willfully ignorant because he denies the science. "

The "willfully ignorant" person has given up on reading temperature gauges because he's found that all, within his experience, have behaved the same.  But they were all working fine, just never exposed to different temperatures.

 The scientist has given up on the "willfully ignorant," because he's found that all, within his experience, have behaved the same.  But they were all working fine, just never exposed to different ideas.

Stars in the Far Arms of Galaxies Move Just as Quickly as Those in the Mid-Arms

From a Quora Question:
Why are stars in the far arms of galaxies moving just as quickly as those in the mid-arms


It happens to be close the one year anniversary of this video I made last year:

The velocity distribution depends on the matter-distribution.  So if most of the matter is condensed at the center, (like the solar system; more than 99% of the matter lies within the sun) you have one velocity curve.  If you have more uniform matter distribution, you'll have a different velocity curve.

Rigid body:  ω(r)=const;v(r)∝r; 


Uniform mass distribution: ω(r)∝1r√;v∝r√
Google graph of sqrt(x)
(Near the center of galaxies this is close to what you have)

Mass Concentrated at Center : ω(r)=1r3√;v∝1r√
Google graph of 1/sqrt(x) 
(Near the edges of galaxies, this is close to what is expected for the velocity curve, assuming we can actually observe everything that is there.)

What ends up being observed toward the edges is somewhere in between the last two.
Outer Galaxy Observation: ω(r)∝1r;v(r)=const

Now, when physicists credit "Dark Matter" to being the cause of this phenomenon, do they mean by "Dark Matter" simply something they cannot see (For example, could it simply be cold gasses (Though monatomic hydrogen can be detected by the 21 cm line, for instance, diatomic hydrogen might manage to hide, simply by not emitting anything if it is cold enough.) that aren't hot enough to have an emission spectrum,), or do they mean by "Dark Matter" something fundamentally different from ordinary matter?  (Stationary neutrinos, undiscovered noninteracting materieals.)