Twin Paradox

[swansont]

So, one twin will see the other's clock running slower (showing a smaller value) throughout the journey. But the moment the twins get back together, the clocks will be synchronized. Does the synchronization happen in the end of the journey (in an instant) or sometime before, in a gradual fashion?

 

I haven't gone through the particulars, but it should happen at the last acceleration. While they are in different inertial frames, they should not agree.

 

 

 

Note that there are three different scenarios now being discussed in the thread. This is referring to both twins accelerating, and then moving apart and then returning.

[foodchain]

Right. Clocks will generally only agree when they are in the same frame.

 

That made things seem more clear to me.

 

What I wonder now is then can you apply time overall, say you have to different times such as in the twin paradox, but could you have a time that overlaps such?

 

Moreover could you have a clock for say our galaxy, and then one for the solar system? If I understand correctly it all goes back to the concept of a frame or time being relative or even possibly local or purely dependent on the environment that it has influence on?

 

Lastly, what if one twin was simply spinning at the speed of light, one foot away from the other twin, would this change the paradox at all, or does the paradox need in reality travel to occur?

[Mowgli]

If you accelerate one (change it's frame of reference) then they won't agree.

 

Right, but what happens if you accelerate both symmetrically? That is to say, they start from rest from one space point, and get back to the same space point at rest by accelerating away from each other for some time and decelerating on the way back. By the symmetry of the problem, it would seem obvious that the clocks should agree, neither would be dilated wrt the other.

 

Then again, during the whole journey, each clock is in motion (accelerated or not) with respect to the other one, and is supposed run slower than the other. So at what point during the journey does time dilation become time contraction?

[swansont]

Right, but what happens if you accelerate both symmetrically? That is to say, they start from rest from one space point, and get back to the same space point at rest by accelerating away from each other for some time and decelerating on the way back. By the symmetry of the problem, it would seem obvious that the clocks should agree, neither would be dilated wrt the other.

 

Then again, during the whole journey, each clock is in motion (accelerated or not) with respect to the other one, and is supposed run slower than the other. So at what point during the journey does time dilation become time contraction?

 

The acceleration isn't the same, though, since it's in the opposite direction. And once it has stopped (so that each is now in an inertial frame), they are in different frames. So even if somehow no net dilation were to occur from the acceleration, or you synchronized after it was done, you have two people moving at some v with respect to each other. They will each observe dilation in the other's clock.

[Mowgli]

Right, but what happens if you accelerate both symmetrically? That is to say, they start from rest from one space point, and get back to the same space point at rest by accelerating away from each other for some time and decelerating on the way back. By the symmetry of the problem, it would seem obvious that the clocks should agree, neither would be dilated wrt the other.

 

I think I didn't say it right. I meant, by symmetry arguments, at the end of the journey when the two clocks are together at the same point at rest with respect to each other, they have to agree.

 

Then again, during the whole journey, each clock is in motion (accelerated or not) with respect to the other one, and is supposed run slower than the other. So at what point during the journey does time dilation become time contraction?

 

During the journey, each clock is dilated with respect to the other. Since they have to satisfy the boundary condition that there should be no dilation at the end of the journey, when does the time contraction happen?

[KaiduOrkhon]

An Expansive 4-D Thought Problem With a Dilatory (mass-field) Solution:

 

The realm of the very small - microcosms - is said to host strong forces acting at very short distances; that are not considered to be related to large, 'weak forces of gravity', said to exist only in very large spaces and act at large distances in the very large - macrocosmic - spaces and times. So it is presently and dominantly considered, in the macrocosmic realm of the very large, exemplary, planetary-generated forces.

 

Gravity is thought not to occur - significantly - in the microcosmic realm of the very small. Whereas, gravity, like Gold, is actually where you find it, and how much of it you find; in large and *small, tenuous and *compact electromagnetic densities (*refer, nuclear binding forces). Moving in one of two possible - direction(s). Toward and/or away (impelling or repelling) from its material (4-D particle/charge) source.

 

Question: ‘Is matter expanding at the same rate of acceleration as light?’

 

Answer: ‘Yes, but, in a value of square (2). Consequently, the rate of acceleration is the same, but the expansion speeds vary with microcosmic (very small) and macrocosmic (very large) space-time, in a value of square.

 

Consider the (incorrect) distinction between electromagnetism & gravity as the status quo, i.e., the prevailing idea that microcosmic ‘nuclear binding forces’, ‘are not, and cannot be’ related to gravitational forces. This ‘disqualification’ of any unification of microcosmic electromagnetism with gravity is based on the false, prevailing and uncontested premise alleged in the ‘difference’ between large gravitational forces which cause planets to orbit, and the smaller forces which bind ‘particles’ together within the atomic nucleus - sometimes called ‘nuclear resinal forces’.

 

In this sense, contemporary physical science still dwells in the archaic conceptual world of *Ptolemic-*Aristotelean dualization of ‘earthly & heavenly motions’ - *when it was thought that the unidentified forces of the far flung universe and heavens were apart from - unrelated to - the unidentified forces acting on earth; until the time of Newton, who proved that large forces in the universe were the same forces acting on and near earth. That the fall of an apple was governed by the same forces that caused the moon to orbit the earth, and the earth’s orbit around the sun...

 

It is said that the electromagnetic force reciprocating between an electron and a proton is 1039 times the gravitational force; the gravitational force between these two ‘particles’ alleged to be ‘too weak’ to be measured’ at this microcosmic level.

 

The nuclear force which is distinquished from gravity ‘because’ it is 1039 times stronger, is (microcosmic - 'earlier Moment A') gravity (unrecognized and unacknowledged by physicists): this is due to the (4-D continuum) fact that the value(s) of time is covariant with the moment(s) of space it (time/motion) occurs in...

 

Allow this pie plate chart design diagram < to represent the Moments A, B, and C, 4-D expansion of any given physical or spatial system, where the left-most intersection of the two lines represents earlier Moment A (the convergence of the 4-D space-time continuum emerging from out of the infinite microcosms) the right-most opening representing later Moment C, advancing into the infinite macrocosms, with the middle of this pie plate chart representing Moment B - the 'eternal now' - of the considered 4-D continuum. (The actual shape of which would account for acceleration, in a profile structure such as Riemannian geometry's representation of a 'gravity sink' <Refer 'rubber sheet analogy'; featuring Riemannian geometric shapes>).

 

The value of a linear, square or cubic mile of space on (earlier) Moment A earth, is not the same value as that same mile measured on (later) Moment B earth, or on (latest) Moment C earth.

 

When a motorist on Moment A earth drives his automobile at the speed he measures as 60 miles per hour, he is not traveling 60 of Moment B miles per Moment B hour...

 

Moreover, the velocity of 18 & 1/2 Moment A miles per second, traveled by Moment A earth around Moment A sun, is not the same velocity as compared with the 18 1/2 miles per second traveled by Moment B earth around Moment B sun...

Neither is the 365 1/4 days of Moment A year the same interval in time - in this case determined by the completion of an orbit around the sun - as the 365 1/4 days of Moment B or Moment C (providing that these moments could be and were compared with each other).

 

The velocity of light - C - in this continuum, correspondingly varies from one moment to the next, while remaining constant, relative to the space-time moment from which it originates and with which it is associated. This principle of relative velocity is what allows for an 'optical', or 'event horizon', for example.

 

When the ‘mini person’ inhabitant of Moment A earth may look ‘up’ along the positive (future) side of the 4th dimension of time, and see themselves at (later) Moment(s) B or C, they would see their own image as an incredibly huge, slow moving giant; if this slow moving giant of Moment A mini-person’s future could look ‘down’ along the past side of their continuously accelerating 4-D projection, they would then observe themselves as a tiny, very fast moving ‘mini-person’.

 

There is no way for Moment A mini-person (thinking in 3-D conceptual physics) to know that their 3 dimensions of space, and consequently their time will be relatively larger (spatially) and slower (chronologically) at (future) Moments B and C.

 

Conversely, there is no way for that same giant, slow moving person in (later) Moments B and C to know that the spatial dimensions and time of their entire (Moment A) universe was correspondingly more contracted in space, having proportionately smaller durations of time, at Moment A.

 

The false assumption is that the value of space is the same with the passage of time; that, if Moment A earth was compared to Moment B and C earth, it (the earth) would have the same uniform size and density in space, when compared with itself at different moments in time.

 

Newton contemplated a 4-D continuum but did not anticipate that the values of space and time would vary with different spaces and times of that continuum.

 

The ‘here and now’ dimensions of ‘space and time’ appear - and are 3-dimensionally conceptualized - to be uniform and unchanging. The law of conservation of mass-energy is not infringed upon, since this expanding continuum is always the same amount of energy distributed over an ever increasing space; maintaining uniform relative density.

(Among other issues, a reinstatement of the presently abandoned Steady State and Unified Field theories is being considered here.)

 

 

The omni-directional acceleration of the apparently static (‘non-expanding’) 3 dimensions of space along the 4th dimension of time (the 4-D space-time continuum) reveals a contracted micro-space accompanied by a correspondingly and inevitably contracted micro-time. and a dilated macrospace accompanied by an equally and correspondingly dilated (‘slowed down’) macro-time.

 

This is the reason that Einstein called ‘Space and Time’ :

Space-Time.

 

This is the cause of what Einstein calls ‘Non-absolute time’, and 'non-absolute space'.

 

It is also the cause of what Einstein calls ‘time dilation’. The value of time is determined by the value of space it occurs in. Larger moments of 4-D space result in relatively slower time, when compared with the value of time in smaller moments of 4-D space.

 

The Twin Paradox Re-visited:

A popular example of relativistic non-absolute time (time dilation phenomenon) is known as the 'twin paradox'. One of two twin brothers remains on coordinate system earth, while the other twin departs the earth in a spacecraft vehicle, approaches the velocity of light; remains in deep space sustaining high velocity for what his senses and instruments measure as 30 days; then returns to earth to learn that his earthbound twin brother and everyone else on earth (who was his age upon his departure) is considerably more aged than himself.

 

There is no conceptual explanation for this, however, the mathematics of relativity indicate that time dilation is a true effect of greatly increased velocities. The twin paradox becomes conceptually comprehensible with the application of the issued , expanding mass-field concept:

 

When an object - a space-craft and its contents accelerates faster than the coordinate system from which it originates and with which it is normally associated (a system of relatively uniform space and time; in this case, the earth), the spacecraft and its contents are distributed over a greater area (its mass value increases with its velocity). Consequently it becomes an independent coordinate system, having relatively larger values of space and proportionately slower experiences of time than its original coordinate system, earth.

 

In a spacecraft nearing the velocity of light the individual hairs on the heads of it's astronauts may (for example) be dilated (enlarged) to the diameter of a large redwood tree (relative to the dimensions of space recognized on coordinate system earth). Yet, the astronauts detect no change of spatial values relative to themselves or their ship and its contents, including all of its time measuring instruments, because everything on board is proportionately dilated in 4-D (mass-field) space-time. For example: It takes these mass field dilated astronauts several of earth's relatively micro-spatial hours - and one of their relatively macro-spatial seconds - to sneeze. Upon returning to coordinate system earth, they must slow their speed, and in so doing they proportionately decrease their size and mass values.

 

Upon disembarking the now 'normal sized' spacecraft, they learn that many years have passed on earth, while they and their instruments have experienced, recorded, and can account for only a month of time in space.

 

To the knowledge of this record, up to the time of this writing, there is no conceptual account for 'non-absolute time', 'time dilation' or the 'twin paradox' that popularly accompanies it.

 

The (stubbornly unrecognized and denied) ever enlarging value of physical space is a ‘non absolute space’, which causes ‘non-absolute time’ (and is also the cause of the conventionally considered - 'Hubble red shift' - expansion of materially unoccupied space.

 

The fundamental import of this discussion is that THE VALUE OF GIVEN UNITS OF TIME (seconds, hours, days, weeks, months, years) IS ENTIRELY DETERMINED BY THE 3-D VALUE (size) OF THE SPATIAL MOMENT IT (time / motion ) OCCURS IN.

http://forums.delphiforums.com/EinsteinGroupie

or http://forums.delphiforums.com/kaiduorkhon

(This is not a business solicitation of any kind)

[Edtharan]

Right, but what happens if you accelerate both symmetrically? That is to say, they start from rest from one space point, and get back to the same space point at rest by accelerating away from each other for some time and decelerating on the way back.

Without actually doing the calculations (I don't really know enough of the math to do it), the out bound acceleration, both travellers will see the other's clock slowed down. However, on the inbound acceleration they would see the other traveller's clock sped up. This increase in speed will negate the dilation of the out going motion.

 

This will mean that at the end of the journeys, both travellers clocks will agree because they have both been slowed down and sped up by the same amounts.

[MolotovCocktail]

Alright, I put the article about the Twin Paradox on WiSci. It is a stub and is incomplete though, so feel free to edit it. I'm going to continue to add to it.

[MolotovCocktail]

and one more thing, the information I put on there is based on what I read here, so I put the link to this subsection for references

[Robonewt]

Some questions

 

If the two observers see the same effect (Clocks running slow) when Betty accelerates away from Adam, then they will surely both see the same effect (Clocks running behind but at a faster rate) when Betty accelerates back towards Adam and also the same again through the deceleration processes.

 

Visually there would be no way to tell who was moving, so the experience should be equivalent for both.

 

How does this create a difference in the clocks when they return?

 

If you want to include the force as a distinction then it has to be valid in all accelerations and decelerations and so would affect the experience had by Betty in all instances, losing the simultaneity in every case.

 

 

Secondly, what would A or B actually see with regards to the clocks? If the speed of light is always C regardless of the frame of reference then it would always take 1 second of local time to see the second hand move on the other clock. You would not be able to see the apparent change of rate of the clock, because light would always bring it to the observer at the same rate as it was sent.

[swansont]

Some questions

 

If the two observers see the same effect (Clocks running slow) when Betty accelerates away from Adam, then they will surely both see the same effect (Clocks running behind but at a faster rate) when Betty accelerates back towards Adam and also the same again through the deceleration processes.

 

Visually there would be no way to tell who was moving, so the experience should be equivalent for both.

 

How does this create a difference in the clocks when they return?

 

When they return? There are a few different scenarios depicted in this thread, so one has to be sure to not apply this solution to the other scenarios. In the one you describe, Betty accelerates and Adam does not, so Betty's clock will be slow at her return. She shifted inertial frames during the acceleration (typically one only includes the turnaround acceleration in the simplest version of this; one can assume synchronization after Betty gets up to speed at departure and the comparison made before she changes speed upon her return) and that's when the shift in simultaneity occurs.

 

 

If you want to include the force as a distinction then it has to be valid in all accelerations and decelerations and so would affect the experience had by Betty in all instances, losing the simultaneity in every case.

 

 

Secondly, what would A or B actually see with regards to the clocks? If the speed of light is always C regardless of the frame of reference then it would always take 1 second of local time to see the second hand move on the other clock. You would not be able to see the apparent change of rate of the clock, because light would always bring it to the observer at the same rate as it was sent.

 

You seem to be mixing constant c sending a signal with the time interval of a set of signals. The light may get to you at c, but the interval between two signals can still change — a simple Doppler shift shows that, even in the non-relativistic limit.

[KaiduOrkhon]

Please correct me if I'm wrong, but isn't time dilation a relatively long established fact proven with cesium clocks and fairly conventional flights near and around the earth? (Please refer to message #9 by Molotov Cocktail on page 1.)

[Norman Albers]

Swansont, can acceleration be handled as a differential succession of velocity states, with, heaven forbid, NO NEW PHYSICS? In radiative accelerations you have to do that analysis, no?

[Robonewt]

When they return? There are a few different scenarios depicted in this thread, so one has to be sure to not apply this solution to the other scenarios. In the one you describe, Betty accelerates and Adam does not, so Betty's clock will be slow at her return. She shifted inertial frames during the acceleration (typically one only includes the turnaround acceleration in the simplest version of this; one can assume synchronization after Betty gets up to speed at departure and the comparison made before she changes speed upon her return) and that's when the shift in simultaneity occurs.

 

Are you saying that the difference between the two clocks when Betty returns is dependant only on the acceleration that Betty experiences and not the length of time she travels at a high but constant speed?

[swansont]

Are you saying that the difference between the two clocks when Betty returns is dependant only on the acceleration that Betty experiences and not the length of time she travels at a high but constant speed?

 

No. The time difference will depend on the time spent traveling at v. The shift in simultaneity occurs when she changes inertial frames; that's when the symmetry of the two observers is broken.

[swansont]

Swansont, can acceleration be handled as a differential succession of velocity states, with, heaven forbid, NO NEW PHYSICS? In radiative accelerations you have to do that analysis, no?

 

I can't recall having occasion to work out such a problem, but you can do it.

 

http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html

[Robonewt]

So we have 3 different phases of acceleration that Adam experiences and we can work out the effects on Adam.

 

Phase 1: Acceleration away

Under this movement both Twins will see the other's clocks running slow.

 

Phase 2: Acceleration towards

Under this movement Adam will see Betty's clocks running fast and Betty will see Adams clocks running slow.

 

Phase 3: Deceleration

Under this movement both Twins will see the other's clocks running fast.

 

You will notice that in Phase 2 acceleration Adam's clock is different to Betty's clock. It is this phase of the journey that causes the difference in the clocks. And this phase that causes the difference in their ages.

 

This effect does not occur under constant motion (but turning around is not constant motion).

 

If phase 2 causes a difference in the ages, why doesn’t Phase 1? In both, Adam experiences acceleration, why does one cause a different effect than the other?

 

If the effect does not occur under constant motion, why does the size of time difference also depend on the amount of time spent at near light speeds?

[Norman Albers]

Robonewt, you are right if you're thinking it depends on the length of the trip. The acceleration distinguishes the two frames, but the time difference comes with steady velocity too. Mess with the equations, and think about "long strings of lights or clocks".