Twins Paradox

When EACH looks at the other, from their own inertial rest-frame, they each have no sensation of motion. Therefore, they see the other planet as moving at 0.6c and expect Special Relativity (SR) effect of Time Dilation, due to what they each see as the OTHER planet moving toward or away from them. For this velocity of 0.6c, we can easily calculate that this is a factor of 0.8 regarding time passage. As each grows up, they therefore EACH see the other as aging more slowly (0.8 times as fast) than they age. We are going to momentarily neglect the fact that the two might see each the other as having been born before or after themselves, and ONLY consider the INTERVAL while they constantly watch each other. During an interval when they each live 30 (Earth) years, they each see that the other has only lived 24 (Earth) years!. This is true of BOTH of them! There can be no doubt of this because EACH of them is in a rest-frame coordinate system which is not accelerating, and which each therefore considers to be "stationary", such as we tend to do here on Earth.

This alone negates any possibility that the popular Twins Paradox could be valid! They BOTH see the other person and planet as having aged slower than themselves! The Twins Paradox was incorrectly built upon the premise that requires that only one (who happens to be on Earth) would sense this, when a viewed traveler was moving at a high but constant velocity away from or toward the Earth. The people who promote the Twins Paradox simply ignore the fact that the traveler on the spaceship IS TRAVELING AT CONSTANT VELOCITY and therefore would see the same Time Dilation effect when looking at the Earth. Imagine that he lived on a planet instead of a spaceship, where you might see it as much more obvious that HE would be the one who felt he was on a stationary planet. This simple example shows that the (constant velocity) traveler must experience the same perception, where the Earth twin (and everything else on Earth) MUST be perceived by him to be happening more slowly than in his own life! The Twins Paradox cannot be credible, as the reality is clearly that BOTH have to experience the same sensation!

We will return to our example momentarily, but we wanted to note here that a similar situation could exist where the relative velocity of the two planets was 0.999999 of the speed of light. The Time Dilation factor is 700 to one for this relative speed. The result would be that baby A would age to 60 years while he watched Baby B only age one month! OK, you might be willing to swallow that, but at the same time, Baby B was also constantly looking at Baby A. He would only see Baby A age by about one month in his entire life of 60 years. Both of these situations could actually be true, but the necessary circumstances are very bizarre. And they could NEVER decelerate to the same speed to ever meet, without one or both of them dying of old age first!

Back to our example described above: This is all completely true, because each is in a non-accelerating (inertial) rest frame, and so SR applies. We now have BOTH of them seeing the other as having aged six years less than they did! (These comments and this analysis are NOT going to include an additional complicating factor of the fact that the light image of events on either planet takes some time to propagate the distance they happen to then be apart. In principle, we are going to consider the specific situation in each case where an event occurred as the high-velocity-differential planets happen to pass each other very closely at that very high velocity, so that the distance apart is small enough such that the propagation time of the light images is very small.)

On that 30th birthday which they each celebrated while watching each other celebrate their 24th, they had previously decided to get to a situation where they are both moving at the same velocity. They realize that once they accomplish that, all SR and GR effects will end, and they will then age at exactly the same rate as each other, from both their points-of-view.

They realize that there are three obvious different ways they could do this: (1) A gets in a spaceship and accelerates to the velocity of B; (2) B gets in a spaceship and accelerates to the velocity of A; or (3) each get in spaceships and accelerate HALFWAY toward the other's velocity. Whether they are next to each other or far apart does not then matter, because once they have no relative velocity to each other, no relativistic effects of either SR or GR would apply. To confirm, once at that common velocity, they will then both see the other as aging exactly at the same rate they do themselves. That is the ONLY situation where they could actually establish whether one is older than the other! In any situation where they are either moving at relative velocities to each other (SR) or accelerating (GR), they will appear to age at different rates to each other, and no such valid comparison of ages would be possible.

Remember that BOTH of them WATCHED the other as having aged six years less than themselves aged! How could this be resolved if they should manage to meet? They cannot BOTH think that the other is younger then!

This situation has been set up with maximum symmetry, such that when they would meet, or equivalently, be traveling at the same relative velocity, they must certainly find themselves to have corrected those perceptions regarding aging. That eliminates any so-called paradoxes!

This specific situation is one of many similar situations which show that the popular ideas of what is called the Twins Paradox is simply wrong! That premise ONLY considers the situation from ONE of the two perspectives, and totally ignores the other, and then applies one very incorrect assumption, to arrive at an alleged way where it is presented that one could travel vast distances across space without aging much! It is such an attractive concept that it has become universally accepted as valid, even being included in a huge number of textbooks. But it is simply not true! That description is also quite illogical, as we have already started to see above, but there is a perfectly logical explanation for all the actual experiences both SEE and EXPERIENCE, as well as what any outside observer would see of each of them. It is presented here.

A VERY interesting conclusion exists in all of this. Say that you wanted to go to a planet circling Alpha Centauri. Traditional thinking is that you would want to accelerate as fast as you could, so you could spend the bulk of your time traveling at the highest possible velocity, to get there quickest. However, that is not the case here! Speed does matter, but in a rather odd way. It is ONLY important the FASTEST you had traveled during the trip, and any concept of "average velocity" does not have any meaning! We will show below that you could have a rocket with minimal power, where it was only capable of less than one gee of acceleration, your rocket would get up to a maximum velocity of 0.6c or 0.8c by the halfway point of the trip, after which you immediately start decelerating all the rest of the way. OR, you could have a rocket with a ferociously powerful engine, where it accelerated you very quickly to that desired 0.6c or 0.8c, at which point you would coast for most of the trip, and then rapidly decelerate near the end. In BOTH of these cases, you would get to that planet in exactly the same total amount of time! (This will be thoroughly discussed later).

This discussion actually has a very simple conclusion, that the well-known effects of Special Relativity, specifically Time Dilation, is counter-balanced by OPPOSITE effects which occur during the acceleration and deceleration required to GET to that differential relative velocity. And, interestingly, where BOTH the Earth and the traveler has the SR Time Dilation perception that the other is aging more slowly, it is also true that BOTH have the opposite perception during acceleration (of either of them) where they see the other as aging FASTER than they are!

We can consider each of the three possibilities that our two men might do, and think about their individual experiences! The first two situations are actually identical, from logic perspectives, and we will examine them first. They are also simpler to conceptualize.

Case 1 or 2: Either one accelerates to match the Velocity of the other

An (incorrect) assumption in the Twins Paradox thinking is that the well-known Time Dilation ("a perception of slow aging") of Special Relativity (constant relative velocity) would also occur due to the acceleration effect (which is General Relativity).

There is no question that SR and Time Dilation occurs, as it is easily confirmed by simple experiments, such as some first performed in the 1920s regarding cosmic-ray created Muons in the Earth's high atmosphere. Those Muons are known to have very accurately known rest-lifetimes (0.000002212 second), where they are capable of traveling less than half a mile (at the maximum of 186,000 miles per second) before they disintegrate into other particles. Yet, enormous numbers of such Muons manage to make it all the way down to the Earth's surface and to laboratories where it is easy to confirm that they are making it distances of 20 to 60 miles! Time Dilation due to the extreme high velocities of those Muons is the only explanation for such experimental results of Muon detection in laboratories.

But virtually all Physicists have simply assumed that whatever happens in SR also occur in GR. The math of GR is immensely involved, and few people have even attempted to solve the GR equations, and those few people have claimed that GR causes Time Dilation, after INCOMPLETELY solving the equations. It is clear that they are wrong about that!

Keep in mind that as he starts the trip, they EACH have seen the other having aged 6 years less than themselves, which obviously cannot still be true when they meet or even get to the same relative velocity. In one way or another, logic requires that they then agree on whatever the reality is. They will NOT be able to BOTH believe that the other is younger than themselves!

What necessarily occurs is this: The non-accelerating observer would have a normal life where he aged six years (from age 30 to 36) while the other was traveling. But he would see the other seem to experience an OPPOSITE effect to Time Dilation! In fact, he would see the traveler experience a total of twelve years (from age 24 to 36) DURING that (acceleration) trip! The non-accelerating observer would have seen him seem to be constantly moving in high-speed motion for the whole trip, seeming to live life at double the normal speed!

The traveler would not have noticed ANYTHING unusual, and would have instead have experienced a trip that took him six normal years (from age 30 to 36) to complete, with a constant acceleration for the entire time. He would have watched the non-accelerating one appear to age twelve years (from age 24 to 36) during that trip.

Once he stops accelerating, that effect would end, and they would see each other as then aging at EXACTLY the same rate. The non-accelerating one would have seen each age a total of 36 years during the whole story, either his own 30 + 6 years or the traveler's 24 + 12 years. He would see NEITHER as having had any Twins Paradox advantage regarding the rate of passage of time. Yes, he would have seen that effect during the constant-velocity (SR) years, but then he would have seen it counteracted during the acceleration years (GR), where the total of his perception would be the same for himself and for the traveler.

This results in both of them not having any illogical results, and in fact, they even both would agree that a total of 36 years had gone by while they had observed each other. The primary difference would be that they each saw a different distribution of years before and during that trip.

No "paradox" exists at all!

The non-accelerating one therefore starts out seeing that the other start the trip as being six years younger, but then watches as the traveler accelerates and ages at essentially double-speed, to age 12 years during those perceived six years of travel.

The traveler therefore ACTUALLY spends 6 years of his life during that journey, but the non-accelerating one sees him age 12 years during that journey.

There are alternate ways of describing this, but they are all actually the same.

The end result of this is that the acceleration would cause each of them to see the other one as experiencing fast aging, aging 12 years while his own clock shows the passage of six years. This is exactly the opposite effect of SR regarding the Time Dilation perception by EITHER inertial non-traveler, whether on Earth or in a constant velocity rocket. Therefore, they agree upon meeting that there is nothing peculiar about their ages!

There are some slight adjustments to this, primarily due to the relative velocity that exists during all parts of this trip, so certain, generally minor, SR Time Dilation effects are also present.

It is important to note that NO previous history of accelerations has any effect in this. They had each lived their entire lives on their non-accelerating, inertial, planets. They each start out at the trip beginning as seeing the other as having aged six years less than themselves. But when they meet, ONLY a General Relativity acceleration has occurred during this trip and a direct result is that an effect of fast aging resulted. This is therefore actually equally valid for any of the three possibilities of their meeting which are possible.

Note that the "perception of age saving" due to the SR period of travel CAN BE entirely and perfectly cancelled out by a "perception of rapid aging" during the GR acceleration. But the SR result is cumulative over however many years they choose to watch each other, and the GR result has a peculiar cumulative effect over the period of the constant acceleration. If, for example, they had waited 60 years instead of 30, then the age differential would have become twelve years instead of six. Depending on the rate of acceleration during the trip, it may or may not have an effect to counter-act six years of effect or twelve years of effect.

During SR, we all know that an apparent SLOWING of time occurs, Time Dilation. But THIS reasoning establishes that, during GR, Relativistic acceleration, there is necessarily an apparent SPEEDING of time that occurs. Traditional Physics has denied that such an apparent "speeding of time" ever happens, insisting instead that Time Dilation also applies during GR acceleration. But the example above clearly shows that if GR caused TD, the two would then EACH meet a person who was MORE than six years younger than themselves, which is obviously impossible. They can be the same age, or one of them can be older when they meet, they cannot be both older than the other!

The Remaining Case, where both accelerate to a velocity halfway between that of their two planets

We have the same initial situation, where both have seen the other age six years less than they have, which must be resolved. If we assume that they both have identical rockets, in other words, identical accelerations, then from above, we have a situation where the effect of the OTHER's GR acceleration will cause an apparent rapid aging by three years in the other. His own acceleration has a separate GR effect of causing a separate three years of aging in the other. This results in the other seeming to age an extra six years, three plus three, during the pair of trips. This counteracts the initial fact that the other was seen as six years younger than the observer, which then results in the situation where they are both the same age when they are both traveling at the midway velocity of 0.3c from both planets. They would both agree that this is the case, and in fact, it also matches the initial observation of the impartial observer who had initially been traveling at the 0.3c and had seen what he considered simultaneous births on the two planets. The fact that they now meet, at that velocity, and they ARE exactly the same age agrees with that.

Again, no paradoxes whatever!

We have chosen some of the simplest possible situations to try to make this all most understandable. It is actually not necessary that the cumulative effect of the GR time speeding is identical to the cumulative effect of the SR time slowing, except for very specific situations. Most specifically, if an "entire round trip" is considered, then they must necessarily exactly balance each other out, where there is no net advantage or disadvantage regarding time. (Examples are shown below) (Exactly opposite what the Twins Paradox says occurs!) Trips are also limited by the total trip time required having to be greater than that of the speed of light. For most other real situations, the GR and SR cumulative effects could be different.

The consequences of this are enormous. When this is all carefully and thoroughly analyzed, an ENTIRE trip (acceleration, cruising and deceleration to the initial inertial rest frame) results in a very different conclusion than if only the SR portion of a trip is considered. In that second case, a Twins Paradox story actually seems to be reasonable, where they would meet being many years different in age. However, a correct explanation of such a real trip must necessarily include periods of apparent rapid aging (during GR acceleration) as well as the very well known period of slowed aging (during SR cruising). An entire trip then necessarily involves (as seen from the initial location, i.e., Earth) first a perceived rapid aging during acceleration, then the well-known perceived slowed aging during the SR constant velocity part of the trip, and finally another perceived rapid aging during deceleration. A careful analysis of the ENTIRE trip always results in the total trip taking the "correct" total amount of time. There IS no "time benefit" due to taking fast trips and coming back. The "Twins Paradox" story would therefore actually result in the twins being EXACTLY the same age when they meet again!

IF the entire trip occurred in the conditions of SR, of constant velocity, THEN the Twins Paradox could be true. But that is certainly not the case, as enormous accelerations and decelerations are necessary. And that changes everything!

When Einstein first proposed Relativity, he gave several pre-conditions, which required Relativity in order for them to be true. They are:

• (1) that anyone in the Universe who does the same experiment, in an (inertial) non-accelerating environment, must get the identical results of any identical experiment of any other inertial environment;
• (2) that no one could ever experience any discontinuity of time;
• (3) that no one could ever experience any discontinuity of space;
• (4) that no one could ever get the experience of traveling faster than the speed of light; and
• (5) the sum of this is that the Universe must be able to "make logical sense" to any person in any environment.

The Twins Paradox story violates at least one of these!

The easiest way to see this is to temporarily set aside Physics and Relativity, and simply consider the actual experiences of the traveling twin. Here is the standard Twins Paradox story, with the addition of a single introductory sentence!

Twin brothers have lunch together on Earth, while carefully determining the actual distance to Alpha Centauri, where they each get a result of a distance of 4.3 light years away.

One of the twins immediately gets in a spacecraft and accelerates extremely rapidly. He has a forward window in the spacecraft, and he sees that Alpha Centauri is a distance of three light WEEKS away from him. So, it then makes complete sense to him that his entire trip takes only three weeks of his life! Once on a planet around Alpha Centauri, he is then about 4.2 years YOUNGER than his twin on Earth. He says hello and goodbye, and travels back to Earth. Again, he "gains" another 4.2 years, so when he re-meets his twin brother, he is now 8.4 years YOUNGER than his twin!

He and his brother carefully measured the distance to AC as being 4.3 light years, but then an hour later, HE saw AC as being only 0.06 light year (3 light-weeks) away! THAT is not possible! It represents what Einstein called a discontinuity in space, and such things violate Physics and Relativity. It also requires the traveler to have the personal experience of having traveled nearly 4.3 light years of actual distance in just a three-week trip, meaning that he could allegedly then go into Court to Testify that he had just personally traveled around 75 times faster than light travels! In fact, Relativity was DEVELOPED specifically so that no person could ever experience such a discontinuity of space, or of time, or of believing that he/she was traveling faster than the speed of light. The Twins Paradox involves a required assumption, where at least one of these is violated. Therefore, even though Relativity, including Special Relativity and General Relativity, and Time Dilation and all the other consequent effects are TRUE, the Twins Paradox definitely is NOT TRUE!

Some of the attempted explanations invoke some very peculiar ideas! One claims that the Twins traveler actually would be the 8.6 years younger than his brother when them meet again BUT that all of his body processes would still have gotten "older" and he would die just as if before! Where could someone come up with such a silly idea? Such things are easily shown to be silly if a trip to a star 100 ly away was involved. His earth brother would therefore have to be over 200 years old when he arrived back on Earth, while he might only be 25. Is he supposed to instantly die of old age at 25 on returning? Silly!

A major reason for such errors is that it seems often true that the SR and GR portions of the trip are freely interchanged, and that results in the wrong conclusions. One popular claim is that the two twins do NOT both experience the effects of Time Dilation because they are "actually not in symmetrical situations, because the one had gone through accelerations". That statement is foolish, because if ONLY the constant velocity portion of the trip is considered, as though there is no "memory", the two actually ARE in perfectly symmetrical situations, each feeling that he is in an inertial rest frame with the other rapidly moving. It is an error to invoke that an acceleration that occurred at some previous time could or would alter experiences during SR! (The very first example presented here shows that. It would not matter whatever accelerations those two planets experienced prior to the babies' births, only their SR lifetimes have effect.)

There have been countless experiments, such as the muon experiments at CERN in 1966, which confirm that Time Dilation occurs for constant velocity motion near the speed of light. Time Dilation is certainly true for SR conditions. But those muons disintegrated while still at that relativistic velocity, and NOT after the muons were slowed to non-relativistic velocities. So NO conclusions regarding GR can be gleaned from such experiments, only regarding SR. I must admit, though, that the fact that those muons were traveling in circular paths means that they actually were under constant (lateral) acceleration seems to me to indicate that an additional complication must have existed for those analyses.

Notice that NO assumptions have been applied here, and ONLY the personal experiences of the individuals have been considered. When Physicists have neglected that first sentence (which I added), then they always immediately start citing equations on why the Twins Paradox is true. But they invariably neglect to consider the discontinuity in space that would therefore be required, and which my added paragraph makes clear. THEN it is appropriate to start doing the math!

This certainly sounds very peculiar! How could two people be looking at each other and BOTH see that the other has clocks that are advancing more slowly than his own? But it is certainly a reality of the situation. THAT is actually pretty easy to see, too. The "symmetric situation" that this presentation started with certainly shows it to be an unavoidable fact.

In Special Relativity, we have a situation where one person (our traveler) is moving at very high speed, away from or toward the other. The Twins Paradox proponents have always considered the Earthbound twin as experiencing "normal time" and all descriptions are based from that perspective. However, that is not the only available perspective! Say the Twins Paradox traveler does NOT have any memory and simply wakes up, or is born (on an extremely long trip) and looks out the window, to see the Earth hurtling away at a constant extremely high speed. From HIS perspective, and his experience, he is "experiencing normal time". But he sees his brother and the Earth receding at very high speed, so HIS view of his brother clearly shows (by Special Relativity) that his brother (and everything else on the Earth) is experiencing "slower time". Since the two brothers have been constantly staring at each other for the whole trip, that means that they EACH must see the other as aging more slowly than he does, during the entire constant velocity, Special Relativity portion of the trip. This HAS to be true! Otherwise, he would be required to have experiences that violate Relativity.

This is required because neither twin is then experiencing any acceleration. They EACH therefore see themselves as being in the "inertial rest-frame", while the other is therefore rapidly moving away from or toward them.

As odd as it sounds, THAT does not actually violate anything, because when the entire trip is considered, there is a perfectly logical and mathematical explanation and description, from BOTH viewpoints, and without having to invoke any weird assumptions!

The actuality of the situation is then necessarily that, yes, during the Special Relativity constant-velocity parts of the trip, there IS the Time Dilation that we all can easily calculate. However, when the ENTIRE TRIP is considered, it turns out that he necessarily lives a total of exactly the same amount of time that his twin brother does on Earth. (At different points of the trip, one or the other brother is older or younger, because of the differential aging effects of Time Dilation of Special Relativity and this "Time Compression" effect of General Relativity, but whenever they are both in the same rest-reference frame, they are exactly the same age! So, when he gets back to Earth, he and his brother meet and are EXACTLY the same (correct) age!

A basic premise, on which several fields of Astrophysics are based, is therefore incorrect! This is troublesome, but certainly true.

A Detailed Trip

As an experienced traveler, the traveling twin carries a LogBook. While he is still with his twin brother on Earth, about to get in the spaceship, he makes the first Entry, where he and his brother each confirm that Alpha Centauri is 4.3 light years away. For clarity and simplicity, I enable him to never need to sleep during the entire journey to AC. The Twins Paradox would claim that he would arrive at AC maybe 10 weeks later (of his watch's time), the entire point of the Twins Paradox! So he would later write in his LogBook his arrival at AC, ten weeks after leaving Earth. He has (allegedly) now arrived at a location 4.3 light years (225 light-weeks) from where he was 10 weeks earlier, AND he has not slept, so nothing WEIRD could have happened to him. In his personal experience, he could then confirm that he just covered that distance at around 22.5 times the speed of light! AND he even has a LogBook to prove it! If he was taken into Court, he could even testify to those facts! And he could even submit his LogBook as evidence! He (allegedly) experienced ten weeks of life (due to the Special Relativity effect of Time Dilation) and is now, provably, is over 22 times as far away as even light could have gotten! (This is obviously impossible, and is another proof of why the Twins Paradox story is wrong, even though the Time Dilation on which it is based is absolutely true.)

Physicists seem to want to completely ignore the parts of the trip other than the Special Relativity, constant-velocity part! And, if ONLY that part is considered, YES, he would essentially experience what the Twins Paradox would claim. But that is NOT the whole trip! There is also another assumption that Physicists seem to ready to make, regarding whether the Time Dilation of SR also applies to GR (General Relativity) during acceleration. That assumption is clearly wrong, as demonstrated in the examples above, where the exact opposite effect is seen.

Not even considering any Physics yet, try writing ANY Log Book entries, going from 4.3 l.y. to zero remaining distance, in ten weeks of recordings. If you did it "equally", (as in the example Weekly Log Book shown at the right) then during EACH of his weeks, he would see the remaining distance decrease by around 0.43 l.y. (or around 23 light-weeks per week), a clear violation of exceeding the speed of light! If you try to tweak the numbers, yes, you could have PART of the trip appear to him to comply with the speed of light, but then other parts have to be even greater violations! (as seen below)

As long as he does not sleep, and does not go insane, there is NO possible set of LogBook entries that could show how he could go (in HIS experience) 4.3 light years distance in just ten weeks! A discontinuity of either time or space would be required. But Physics and Relativity do not allow such discontinuities, or exceeding the speed of light, in ANY reference frame. Therefore, he cannot possibly arrive at AC in ten weeks of his time as the Twins Paradox insists. In fact, he cannot arrive there, in any possible way, in less than 4.3 years total time (for the one way trip). This proves that the Twins Paradox is entirely wrong (except for its references regarding Time Dilation during the Special Relativity portion of the trip, which IS true!)

It is interesting that the ONLY time that the Twins Paradox argument makes sense is during the Time Dilation, Special Relativity portion of the trip! But FOR THE ENTIRE TRIP, it cannot make sense!

The Traveler's Personal Experience

View from the Earth Observer

The total trip, as seen from Earth, would therefore be seen as taking (1 + 236 + 1) or a total of 238 weeks. The Earth observer would personally age 238 weeks during the entire period of observation, the same total interval. But he would see the peculiar fact that he would see the traveler apparently experience extremely rapid aging for one week, then very little aging for the next four years, and then another week of extreme rapid aging.

Both of them would therefore agree that the traveling twin aged a total of 238 weeks during the entire trip, BUT ONLY ONCE THE TRAVELING TWIN HAD SLOWED BACK DOWN TO THE INITIAL EARTH VELOCITY, to be in the rest-frame of the Earth, even though the traveler was then at Alpha Centauri.

Notice that during the SR portion of the trip, the traveler experiences 8 weeks of life, while the Earth would see his brother travel for 236 weeks during that time potion of the trip, which is exactly what the Time Dilation consequence of SR says. During that part of the trip, yes, the Earth twin therefore ages 236 weeks while the traveling twin ages only 8 weeks. But when the GR consequences are included regarding the acceleration and deceleration, we find that both age a total of 238 weeks during the entire trip!

Actually, the Earth twin would see the traveling twin appear to age incredibly rapidly during that week of acceleration, then being 115 weeks older rather than the one-week-older the Earth twin has become! So, at the moment of the end of the acceleration, the Earth twin would see his brother as being 114 weeks OLDER than he was. But then the traveling twin is seen as aging only 8 weeks while the Earth twin experiences 236 weeks of life (the very well known part!). This results in the Earth twin THEN seeing his traveling twin as having become 114 weeks YOUNGER than himself, just as deceleration began. By the way, at the exact midpoint of the trip, they would see each other as exactly the same age! But the traveling twin would be seen to again appear to age extremely fast during the deceleration, actually aging 115 weeks while the watching Earth twin ages only a week. Again, the net result is that both of them live through 238 weeks of existence during the entire trip.

Note that they are in complete agreement that the traveling twin aged 115 weeks during acceleration, then 8 weeks more during the cruising, and then 115 weeks more during the deceleration. They both therefore absolutely agree that the traveling twin ages a total of 238 weeks during the one way trip.

The Earth Observer's Experience

The Traveler's View of the Earth Twin Brother

By the end of the acceleration (which he measures as taking 115 weeks of his time), he will have seen his twin brother on Earth appear to age about one day short of 119 weeks. So, at that moment, he would see the Earth twin as roughly 4 weeks older than himself.

Notice an odd effect here. At the end of the acceleration phase, BOTH of them see their twin brother as then being OLDER than themselves! The Earth twin sees his brother as then 114 weeks older than himself, while the traveler sees his brother as then being about 4 weeks older than himself.

During the next eight weeks of his time, the Traveler travels at constant velocity, in SR conditions. With a constant velocity, there is no way to claim that one or the other is the one that is actually moving, and so Special Relativity must apply similarly from both viewpoints. So the Traveler sees a similar Time Dilation effect occurring to his brother on Earth as his brother sees of him! During those next 8 weeks of the Traveler's time, he would watch his Earth-bound brother only age about two days. They EACH would see their twin brother aging far slower than themselves. In fact, with the specifications we have made for this trip, they EACH would see their twin brother aging only around 1/30 as fast as they were aging themselves! The traveler would see the Earth twin age about two days during eight weeks of observations, and the Earth twin would see the Traveler age about eight weeks during 236 weeks of observation. (THIS is the explanation of how BOTH brothers could see each the other as aging about one-thirtieth as fast as themselves, during the entire SR portion of the trip, in complete compliance with what Time Dilation formulas indicate.) Note that they EACH saw their brother as being older than they were at the start of the cruising (SR) portion of the trip; that at the exact halfway point of the trip, they also both see that they are momentarily the exact same age; and then they both see the other brother as having become younger than they are just prior to the deceleration. During his deceleration, the traveler would again see his Earth brother age just shy of 119 weeks, while he ages 115 weeks. As he measures it, once he is at Alpha Centauri and in a rest-frame with us, his Earth brother will appear to him to have aged (119-weeks + 2 days + 119- weeks) a total of 238 weeks, just like all other perceptions also give.

Note that BOTH of them see a "fast aging" effect during the GR accelerations and the Time Dilation "slowing" during the SR constant-velocity cruising. No one else seems to have ever noticed and described this necessary situation.

Whether it is his actual transit time, the amount of time the Earth twin experiences, or either brother's record of the other's life, 238 weeks would have passed during the entire trip! There IS NO "Twins Paradox" in the popular sense!

These four different perspectives seem extremely different from each other, but the main fact is that they each represent exactly the same total amount of time for the entire trip, and they also each record the same basic facts.

This explanation fully agrees with all the Special Relativity effects of Time Dilation, as can be seen by EITHER of the two twins during the period of no acceleration. (All other attempts at description can ONLY apply to the view from the Earth-bound observer, and they all violate Relativity when the view from the traveler is considered.) However, it requires a change in the assumption regarding what happens during GR, the accelerations and decelerations. It has always been assumed that Time Dilation occurs during GR just like it does during SR. But this reasoning shows that during GR, there must necessarily be an OPPOSITE effect from Time Dilation, which I guess could be called Time Compression! The equations of GR are extremely complex, and mathematically proving that was harder than I had expected! But the solution has been found and confirmed, and the equation which describes this Time Compression is actually very similar to that of Time Dilation.

An interesting consequence of this is that there must always therefore be an identifiable inter-relationship between rate of acceleration, the interval of that acceleration, and the maximum relative velocity, such that an SR effect of Time Dilation is always exactly canceled out by an equal and opposite GR effect of "Time Compression" during the necessary acceleration and deceleration. A strict mathematical treatment identifies exactly what that relationship between SR velocity and GR acceleration is. g, the gravitational constant, appears to be significant in it, as somehow CAUSING the rate that we see time pass!

It might seem as though such choices might create an immense number of resulting effects, but that is not the case. In fact, regarding the amount of total time for an entire trip, the ONLY factors which are important are the known distance of the trip (such as in light years) and the MAXIMUM velocity, at ANY point along the trip! It turns out that there is no advantage in using the most powerful rocket engine to get the spaceship up to that maximum speed quickly, with the possible expectation that an entire trip at a high speed might require less total time. Some examples below show that is not the case! In fact, the most EFFICIENT trip is one with the SMALLEST possible rocket engine where the maximum desired speed is achieved at the exact halfway point, where deceleration is then immediately begun.

Here are some various ways of making a trip to Alpha Centauri. This identifies one of the three required parameters, 4.3 light years as the total distance of the one-way trip. Most of these are practical examples which do not require getting right near the speed of light, and they generally also require acceleration rates that the human body can withstand.

The first set are specifically selected for having a maximum velocity of 0.6 c, as recorded from the Earth. Each of these trips therefore would show the expected Time Dilation during Cruising of a factor of 0.80. These examples show the effect of different rocket engine power and therefore acceleration rates. Note that really powerful rocket engines could be operated for a short period of time, which would then allow cruising at constant velocity for much of the trip. For each situation, we provide a description of the entire trip from first an Earth observer, and then a DIFFERENT description of the entire trip as recorded by the Traveler himself. The time interval of the acceleration, and then the cruising and then the deceleration is DIFFERENT from the two perspectives. So is the distance covered in each segment and the acceleration which would be measured. However, the TOTAL TRIP is always exactly the same as seen by both, regarding the total distance covered and the total time taken for the trip.

Trip to Alpha Centauri, maximum velocity 0.6c

Taking about seven years, with maximum speed just above half the speed of light.

Notice that the Earth observer would see apparent accelerations that no human could withstand, but that the Traveler actually experiences very reasonable accelerations. Notice also that the Earth observer would see the entire acceleration occur in just over one day, while the Traveler would actually experience nearly nine months of acceleration.

SLOW Trip to Alpha Centauri, maximum velocity 0.1c

Forty years, with maximum velocity around 30,000 km/second

FAST Trip to Alpha Centauri, maximum velocity 0.9999c

Taking about 4.3 years, with extreme maximum velocity!

Notice that in only around 10 minutes of watching, the Earth observer would see two birthday parties!

He would record more of the trip as having occurred during acceleration and deceleration, while the Earth observer would record more of it as having occurred during the cruising phase.

We can also see that he arrives at Alpha Centauri 2617.6 days after leaving Earth, which is easily predicted by using the maximum velocity as though it was always the velocity, or 1567 light-days (same as 4.3 light-years) divided by 0.6, getting 2617.6 days for the trip.

There appears to be a "basic acceleration" which is 4.42968 meters/second², which is somehow the basis for all other accelerations! Motion at that acceleration may somehow cause time to pass at a basic rate! Equivalently, per Einstein, being in a gravitational field which has that value for the gravitational acceleration might somehow provide a basic rate of time passage. The fact that Earth has an acceleration due to gravity of more than double that might mean that time passes for us at a rate DIFFERENT, and calculable!

On planets with stronger or weaker g, the intrinsic rate of time passage might be different than for us! The implications of that seem somewhat frightening! But continuing the theme, it might suggest that SR and GR happen to be "special cases" of a single larger set of equations! This seems to have potential importance regarding Minkowski's space-time concepts. The traditional Minkowski description is not compatible with the existence of gravitational attractions, and this might enable some future compatibility there. I find that intriguing!

I composed a separate presentation which suggests that NASA send an atomic clock to be placed on the surface of the Moon (or Mars). Atomic clocks have been in orbit many times, but apparently none have ever been placed on the surface of either the Moon or Mars. It seems like a very important experiment to do. Einstein emphasized the equivalency of the acceleration due to gravitation and the acceleration due to rocket propulsion. Therefore, whatever the effect of General Relativity on the rate of passage of time, there should be clear and measurable differences between the surface of the Earth and the surface of the Moon, due to a factor of about six in the surface gravity. In fact, calculations seem to show that the rate of time should be SIGNIFICANTLY different on the Moon or on Mars than on Earth, by about 1/13 of a second difference per year! It is difficult to comprehend the implications of such findings!

The reason why the theories regarding the effects during General Relativity appear to all fail in having Time Dilation seems to be related to slight flaws in the Metric Theory behind General Relativity. A number of mathematical simplifications and assumptions were applied in order to make the set of ten General Relativity equations more soluble. These simplifications were known then to cause slight approximations in General Relativity concepts. Interestingly, those simplifications were primarily initiated in the early 1960s, virtually concurrently with the rise in popularity of the Twins Paradox story! Many alternative Metrics have been presented since Einstein presented his, and I am unaware if any have ever been carefully examined regarding whether they could have opposite consequences from Time Dilation during General Relativity. It seems like an area worth investigating. I have a feeling that General Relativity will win out, but that some flaw in those assumptions and approximations is responsible for the "inverse conclusion" regarding GR and TD.

I have determined that, for a full trip where the initial and final velocities are identical, the equations used above, for both Special and General Relativity are given by the following equations:

Three basic parameters must be chosen for them:

• trip is the actual distance of the trip, in light years
• vmm is the maximum velocity during the entire trip, in meters/second
• proportion is the portion of the trip which is during acceleration

The equations:

• Earth seen acceleration time: trip * 365.25 / vmm * proportion / 2
• Earth seen distance during acceleration: trip * proportion / 2
• Earth seen acceleration measured: (vmm² * c) / (trip * 365.25 * 86400 * proportion / 2)
• Earth seen cruise time: trip * 365.25 / vmm * (1 - proportion)
• Earth seen cruise distance: trip * (1 - proportion)
• Earth seen cruise (maximum) velocity: vmm
• Traveler measured acceleration time: trip * 365.25 / vmm * (1 - (1 - proportion) * SQR(1 - vmm ^ 2)) / 2
• Traveler measured acceleration distance: (trip * (1 - (1 - proportion) * SQR(1 - vmm ^ 2))) / 2
• Traveler measured acceleration rate: (vmm * c) / (trip * 365.25 * 86400 / vmm * ((1 - (1 - proportion) * SQR(1 - vmm ^ 2)) / 2)
• Traveler measured cruise time: trip * 365.25 / vmm * (1 - proportion) * SQR(1 - vmm ^ 2)
• Traveler measured cruise distance: (trip * (1 - proportion)) * SQR(1 - vmm ^ 2)
• Traveler measured cruise (maximum) velocity: vmm
• Total Trip time: trip * 365.25 / vmm
• Total trip distance: trip

These equations are all simplified versions of the Integral Calculus equations which actually apply. Their forms are obvious, and would be needed for any situations where the rate of acceleration changes during a trip. These simplified forms are given here because most real future space journeys are likely to have constant acceleration during powered portions of a trip.

These analyses are all based on COMPLETE trips, where an observer begins with no significant velocity or acceleration from an observed object, then there is a period of acceleration, followed by a period of coasting/cruising, followed by a period of deceleration down to the initial conditions of velocity and acceleration. Most phenomena detected tend to only have had the Special Relativity, constant velocity portion of such movement analyzed. These equations can be applied to a particle that BEGAN (as far as we knew) with massive velocity or acceleration, but then the treatment of the analysis has to be somewhat different.

Reasons for the Previous Errors regarding GR and Time Dilation

Implications

Pulsars and other very rapidly perceived phenomena

Black Holes, Accretion Disks, etc

Perceived Brightness

Possibly some of the great difficulties of Physics dealing with Quasars, Pulsars and the like might turn out to be far simpler to resolve. We have generally assumed that if an object sends us the radiation equivalent to 10 million stars, it must be quite huge, but when we see it have brightness variations on the period of months, we see a great dilemma because that implies that it is small. If the actual object was actually only 1/100,000 as bright as we perceive it to be AND if the months we see during a variation are actually many years, many of the serious problems of Astrophysics might find some fairly simple resolutions.

But, of course, that would depend on whether GR effects actually apply for Relativistic radial acceleration. It is merely mentioned here as one of many possible implications of this new perspective.

Imagine that there were two planets near opposite sides of the Universe, each headed toward the other at extremely high CONSTANT speed. That means that Special Relativity should apply and therefore Time Dilation. Say within two meters per second of the speed of light, where the Time Compression effect would be more than a thousand trillion to one IN BOTH DIRECTIONS. There is an accurate atomic clock on both planets and they each have amazing telescopes to be able to see the clock on the other planet at any time. See the problem? While planet 1 SEES exactly one year pass on planet 2, planet 1 actually would experience a thousand trillion years, longer than anything has ever existed. THIS then requires that planet 1 is immensely old. Now look from planet 2, and see the similar situation, where only one year on planet 1 would pass while planet 2 experiences a thousand trillion years, but we just saw that planet 1 necessarily existed a thousand trillion years, EACH of which would have to match up with a thousand trillion years on planet 2. As Special Relativity and Time Dilation is currently understood, BOTH planets would have to exist for impossible periods of time. That indicates that the current theory must somehow be wrong. But Time Dilation is considered to be a simple and obvious consequence of Special Relativity.

The explanation of this bizarre situation is equally bizarre! In order that two objects GET to a relative CONSTANT velocity of just two m/s less than the velocity of light REQUIRES the one which had done all that accelerating to have "aged" astoundingly fast, due to the Time Compression effect of acceleration (in General Relativity). In other words, the one that did the acceleration would have to have ALREADY experienced those thousands of trillions of years of acceleration, BEFORE the situation that we now are considering. The point being made here is that, since the Universe appears to be about 13 billion years old, NEITHER object had enough time to accelerate to that great a relative CONSTANT velocity, which means that the example we have been speculating about could NOT have been possible! Even though Relativity often seems very peculiar, it STILL has to comply with the Laws of science!

The equations above make clear that there is an intimate relationship between the Time Dilation of Special Relativity and the Time Compression of General Relativity. A trip can only make sense once it is completed, that is that the observer and traveler are both again in the same inertial reference frame.

That indicates that acceleration is a necessary PRE-CONDITION for Time Dilation as an EARLIER Time Compression due to acceleration, at least for any Static Reference Frame. More, whatever the total cumulative effect of that (previous) Time Compression might then become available for a later Time Dilation effect being witnessed. Actually, BOTH the Time Compression of the ACCELERATION and then the later DECELERATION, must necessarily EXACTLY MATCH the total observed Time Dilation. The final result is that the trip ALWAYS takes the "correct" amount of total time, from BOTH of their perspectives as well as from the perspective of ANY other observer of their interactions. No matter who is watching, when they get back to the SAME Static Reference Frame, they WILL be exactly the same total age (and will again appear as Twins!)

Advanced Physics-related presentations in this Domain:

Conservation of Angular Momentum A Violation of the Conservation of Angular Momentum(Sept 2006)
Galaxy Spiral Arms Stability and Dynamics A purely Newtonian gravitational explanation (Nov 1997, Aug 1998)
Twins Paradox. The Twins Paradox of Relativity is Certainly and Obviously Wrong (research 1997-2004, published Aug 2004)
Perturbation Theory. Gravitational Theory and Resonance (Aug 2001, Dec 2001)
Origin of the Earth. Planetary Gravitational Resonances (Dec 2001)
Rotation of the Sun (Jan 2000)
Origin of the Universe. Cosmogony - Cosmology (more logical than the Big Bang) (devised 1960, internet 1998)
Time Passes Faster Here on Earth than on the Moon! (but only a fraction of a second per year!) (Jan 2009)

Globular Clusters. All Globulars Must Regularly Pass Through the cluttered Galaxy Plane, which would be very disruptive to their pristine form. (Nov 1997, Aug 1998)
Existence of Photons. A Hubble Experiment to Confirm the Existence of Individual Photons (experimental proof of quanta) (Feb 2000)
The Origin of the Moon (June 2000)
Rotation of Jupiter, Saturn, and the Earth (Jupiter has a lot of gaseous turbulence which should have slowed down its rapid rotation over billions of years) (March 1998)
Cepheid Variables Velocity Graph Analysis (Feb 2003)
Compton Effect. A Possible New Compton Effect (Mar 2003)
Olbers Paradox Regarding Neutrinos (Oct 2004)
Kepler and Newton. Calculations (2006)
Pulsars. Pulsars May Be Quite Different than we have Assumed (June 2008)
How the Sun Works in Creating Light and Heat (Aug 2006)
Fusion. Lives of Stars and You (Aug 2004)
Equation of Time. Sundial to Clock-Time Correction Factor (Jan 2009)
General Relativity. Confirming General Relativity with a simple experiment. (Jan 2009)
General Relativity. Does Time Dilation Result? (Jan 2009)
Geysers on Io. Source of Driving Energy (June 1998)
Mass Extinctions. A New Explanation For Apparent Periodicity of Mass Extinctions (May 1998, August 2001)
Precession. Gyroscope Precession and Precession of the Earth's Equinoxes (Apr 1998)
Tides. Mathematical Explanation of Tides (Jan 2002)
Source of Energy Using the Moon (1990, Dec. 2009)
Earth's Magnetic Field. Complex nature of the magnetic field and its source (March 1996)
Perfect Energy Source From the Earth's Spinning (1990, Nov. 2002)

Nuclear or Atomic Physics related Subjects:

Nuclear Structure. Statistical Analysis of Same-Atomic-Weight Isotopes (research 1996-2003, published Nov 2003)
Quantum Defect The Quantum Defect is a Physical Quantity and not a Fudge Factor(July 2007)
Atomic Ionization Data Surprising Patterns in the NIST Data Regarding Atomic Ionization (June 2007)
Nuclear Physics Logical Inconsistencies in Nuclear Physics (August 2007)
Neutrinos. Where Did All the Neutrinos Come From? (August 2004)
Neutrinos. Neutrinos from Everywhere? (Oct 2004)
Quantum Nuclear Physics. A Possible Alternative (Aug 2001, Dec 2001, Jan 2004)
Quantum Physics. A Potential Improvement (2006)
Quantum Physics is Compatible with the Standard Model
Quantum Physics is Compatible with the Standard Model (2002, Sept 2006, Oct 2010)
Quantum Dynamics (March 2008)
Ionization Potential. Surprising patterns among different elements (March 2003)

Nuclear Structure. The Mass Defect Chart (calculation, formula) (research 1996-2003, published Nov 2003)
Assorted other Physics Subjects:

Precession. Gyroscope Precession and Precession of the Earth's Equinoxes (Apr 1998)
Earth's Magnetic Field. Complex nature of the magnetic field and its source (March 1996)
Perfect Energy Source From the Earth's Spinning (1990, Nov. 2002)

Earth Energy Flow Rates due to Precessional Effects (63,000 MegaWatts) (Sept 2006)
Gravitational Constant. An Important Gravitation Experiment (Feb 2004)
Tornadoes. The Physics of Tornadoes, including How they Form. Solar Energy, an Immense Source of Energy, Far Greater than all Fossil Fuels (Feb 2000, Feb 2006, May 2009)
Carbon-14. Radiometric Age Dating, Carbon-14, C-14 (Dec 1998)
Mass Extinctions. An Old Explanation For Apparent Periodicity of Mass Extinctions (Aug 2003)
Hurricanes A Credible Approach to Hurricane Reduction (Feb 2001)
Equation of Time. Sundial to Clock-Time Correction Factor (Jan 2009)

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