When EACH looks at the other, from their own inertial rest-frame, they each have no sensation of motion. Therefore, they see the expected 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 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 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. 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!
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.
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!
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:
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 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 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, 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.
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 later writes 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.
| (His) Date | Dist. to go | Dist. Done | Week Avg. Speed |
|---|---|---|---|
| Start on Earth | 4.30 ly | 0.00 ly | - |
| Week One | 3.87 ly | 0.43 ly | 23 * c |
| Week Two | 3.44 ly | 0.86 ly | 23 * c |
| Week Three | 3.01 ly | 1.29 ly | 23 * c |
| Week Four | 2.58 ly | 1.72 ly | 23 * c |
| Week Five | 2.15 ly | 2.15 ly | 23 * c |
| Week Six | 1.72 ly | 2.58 ly | 23 * c |
| Week Seven | 1.29 ly | 3.01 ly | 23 * c |
| Week Eight | 0.86 ly | 3.44 ly | 23 * c |
| Week Nine | 0.43 ly | 3.87 ly | 23 * c |
| Week Ten | 0.00 ly | 4.30 ly | 23 * c |
|
Notice that EVERY week in this Log Book, his average speed is seen (by him) as being 23 times the speed of light! (He measures a movement of 0.43 ly/week, or about 23 light-weeks/week) | |||
Not even considering any Physics yet, try writing ANY Log Book entries, going from 4.3 ly 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 ly (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!
| (His) Date | Dist. to go | Dist. Done | Week Avg. Speed |
|---|---|---|---|
| Start on Earth | 4.30 ly | 0.00 ly | - |
| Week One Acceleration | 2.23 ly | 2.07 ly | 115 * c |
| Week Two | 2.21 ly | 2.09 ly | ~ c |
| Week Three | 2.19 ly | 2.11 ly | ~ c |
| Week Four | 2.17 ly | 2.13 ly | ~ c |
| Week Five | 2.15 ly | 2.15 ly | ~ c |
| Week Six | 2.13 ly | 2.17 ly | ~ c |
| Week Seven | 2.11 ly | 2.19 ly | ~ c |
| Week Eight | 2.09 ly | 2.21 ly | ~ c |
| Week Nine | 2.07 ly | 2.23 ly | ~ c |
| Week Ten Deceleration | 0.00 ly | 4.30 ly | 115 * c |
|
Notice that during the SR weeks in this Log Book, his average speed is seen as being essentially the speed of light (due to time dilation effects).
THAT would make sense to him.
Notice also that he would NOT
Obviously, something VERY strange | |||
| (His) Date | Dist. to go | Dist. Done | Week Avg. Speed |
|---|---|---|---|
| Start on Earth | 4.30 ly | 0.00 ly | - |
| He records 115 weeks of acceleration | |||
| Week 115 Acceleration | 2.23 ly | 2.07 ly | rise to ~ c |
| Week 116 | 2.21 ly | 2.09 ly | ~ c |
| Week 117 | 2.19 ly | 2.11 ly | ~ c |
| Week 118 | 2.17 ly | 2.13 ly | ~ c |
| Week 119 | 2.15 ly | 2.15 ly | ~ c |
| Week 120 | 2.13 ly | 2.17 ly | ~ c |
| Week 121 | 2.11 ly | 2.19 ly | ~ c |
| Week 122 | 2.09 ly | 2.21 ly | ~ c |
| Week 123 | 2.07 ly | 2.23 ly | ~ c |
| He records 115 weeks of deceleration | |||
| Week 238 Deceleration | 0.00 ly | 4.30 ly | ~ c |
|
Notice that during the SR weeks in this Log Book, his average speed is seen as being essentially the speed of light (due to time dilation effects). THAT would make sense to him. (He measures a movement of 0.02 ly/week, or about 1 light-week/week) Notice also that we have LOGICAL experiences for him during the MANY acceleration and deceleration weeks, when he would see his speed increase from zero to nearly the speed of light and then drop back down to zero.
Notice also that he would NOT see
| |||
THIS LogBook is the actual one that would present HIS real experiences, all of which comply with Relativity and Special Relativity. At NO point does he ever believe that he has exceeded the speed of light, so there is no violation there. It is important to note that HE has to have the sensation of accelerating for over two years (115 weeks), then 8 weeks of well-known Special Relativity constant velocity, and then another 115 weeks of deceleration. HE would therefore not experience any discontinuities of space or time or any other violations of Relativity, and he would record taking 238 weeks to get from Earth to AC.
From Earth, the perception would be rather different. If the Earth brother had kept a LogBook of his observations, it would be as follows: One ferocious week of acceleration would be recorded, then 236 weeks of constant velocity (SR) travel, followed by one week of rapid deceleration. The total trip would therefore be seen as taking a total of 238 weeks.
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 is! 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.
We might also consider what the traveling twin would see regarding his brother on Earth. During the acceleration, he would not notice much different, but the Earth twin would seem to him to be aging VERY slightly FASTER than he did. (This is while the Earth twin sees HIM apparently aging VERY fast, around 115 times normal aging rate!) 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. During the next eight weeks of his time, he travels at constant velocity, in SR conditions. So, he sees the same Time Dilation effect occurring to his brother on Earth as his brother sees of him! During those 8 weeks of his time, he would watch his brother only age about two days. (THIS is the explanation of how both brothers could see each other as aging more slowly than themselves, during the entire SR portion of the trip). Note that he, too, sees his brother as being older than he is at the start of the cruising (SR) portion of the trip; that at the halfway point of the trip, he also sees that they are momentarily the same age; and that he sees the Earth brother as having become about 4 weeks younger than he is just prior to the deceleration. During his deceleration, he would again see his Earth brother age just shy of 119 weeks. As he measures it, once he is at AC and in a rest-frame with us, his Earth brother will appear to him to have aged 238 weeks, just like all other perceptions will give.
Note that BOTH of them see a "fast aging" effect during the GR accelerations and the TD "slowing" during the SR constant-velocity cruising.
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.
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. 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 seems to be harder than I had expected! But the reasoning above makes clear that it has to be the case.
An interesting consequence of this is that there must therefore be some identifiable relationship between rate of acceleration and relative velocity, where an SR effect of Time Dilation is exactly canceled out by an equal and opposite GR effect of "Time Compression". A strict mathematical treatment should identify exactly what that relationship between SR velocity and GR acceleration is. I have a nagging suspicion that g will turn out to be significant in it, as somehow CAUSING the rate that we see time pass!
| Trip to Alpha Centauri, in Days, maximum velocity 0.6c | |||
|---|---|---|---|
| Acceleration is constant at 6.4 m/s2 | |||
| Phase | Traveler's Days | Days Seen from Earth | Time Ratio |
| Acceleration | 327 | 523 | 1.60 |
| Cruising | 1960 | 1568 | 0.80 |
| Deceleration | 327 | 523 | 1.60 |
| Total Trip | 2612 | 2612 | 1.00 |
We can see during the long Cruising phase, that we on Earth would see him appear to age noticeably slower than we were (more than a year gain!) However, we see that during both the acceleration and deceleration, we would see him age faster by around half a year each. The result is that the number of total number of days that we saw the trip take (2612) is exactly the same as the number of days that he personally experienced on board the spaceship. This is true since Alpha Centauri and its planet are not moving at any significant velocity from us on Earth. We can also see that we arrive at Alpha Centauri 2612 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 2612 days for the trip.
| Trip to Alpha Centauri, in Days, maximum velocity 0.6c | |||
|---|---|---|---|
| Acceleration is constant at 3.2 m/s2 | |||
| Phase | Traveler's Days | Days Seen from Earth | Time Ratio |
| Acceleration | 653 | 784 | 1.20 |
| Cruising | 1306 | 1045 | 0.80 |
| Deceleration | 653 | 784 | 1.20 |
| Total Trip | 2612 | 2612 | 1.00 |
Here we have used an acceleration rate half as great, a smaller rocket engine. It results in the Cruising period being shorter, but the entire trip is exactly the same length! Notice that with the smaller acceleration rate, we have a much smaller time ratio effect during the acceleration, only a factor of 1.20 instead of the 1.60 in the example above.
| Trip to Alpha Centauri, in Days, maximum velocity 0.6c | |||
|---|---|---|---|
| Acceleration is constant at 1.6 m/s2 | |||
| Phase | Traveler's Days | Days Seen from Earth | Time Ratio |
| Acceleration | 1306 | 1306 | 1.00 |
| Cruising | 0 | 0 | 0.80 |
| Deceleration | 1306 | 1306 | 1.00 |
| Total Trip | 2612 | 2612 | 1.00 |
Here we have used an acceleration rate half again as great, the lowest possible acceleration which just barely gets us to the maximum velocity by the centerpoint of the trip, so there is NO Cruising phase and we immediately turn the rocket engine around and decelerate for the entire second half of the trip. Notice that the Time ratio during the acceleration is exactly 1.0, meaning that there would be no noticeable time speeding effect during this trip.
Here are the same three trips, but with a higher maximum velocity, of 0.8c. This results in the entire trip taking fewer days, 1960 instead of the 2612 of the examples above. The accelerations required are greater to get up to the higher maximum speed.
| Trip to Alpha Centauri, in Days, maximum velocity 0.8c | |||
|---|---|---|---|
| Acceleration is constant at 11.2 m/s2 | |||
| Phase | Traveler's Days | Days Seen from Earth | Time Ratio |
| Acceleration | 245 | 539 | 2.20 |
| Cruising | 1470 | 882 | 0.60 |
| Deceleration | 245 | 539 | 2.20 |
| Total Trip | 1960 | 1960 | 1.00 |
Here he gains nearly two years during the Cruising phase, but loses nearly a year each during the acceleration and deceleration phases of the trip.
| Trip to Alpha Centauri, in Days, maximum velocity 0.8c | |||
|---|---|---|---|
| Acceleration is constant at 5.6 m/s2 | |||
| Phase | Traveler's Days | Days Seen from Earth | Time Ratio |
| Acceleration | 490 | 686 | 1.40 |
| Cruising | 980 | 588 | 0.60 |
| Deceleration | 490 | 686 | 1.40 |
| Total Trip | 1960 | 1960 | 1.00 |
Smaller rocket engine with half the acceleration.
| Trip to Alpha Centauri, in Days, maximum velocity 0.8c | |||
|---|---|---|---|
| Acceleration is constant at 2.8 m/s2 | |||
| Phase | Traveler's Days | Days Seen from Earth | Time Ratio |
| Acceleration | 980 | 980 | 1.00 |
| Cruising | 0 | 0 | 0.60 |
| Deceleration | 980 | 980 | 1.00 |
| Total Trip | 1960 | 1960 | 1.00 |
And half again of the acceleration, again to exactly get to the desired maximum velocity at the halfway point, with no Cruising time and immediate conversion to deceleration. These three trips are also all of exactly the same total length, both as experienced by the traveler and as witnessed from the Earth, although in each case, the proportions are different as seen from the two perspectives.
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!
That, 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!
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 travel where the initial and final velocities are identical, the "Time Compression Factor" of General Relativity is given by the following equations:
TCFactor = vmax / c + 4.42968 * (vmax / c)2
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.
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