We should monitor the Lorentz-Fitzgerald Contraction effect of Special Relativity rather than Time Dilation. It is the most obvious result of Special Relativity. Because both forms of Relativity are dependent on gravitation, which is a Vector process, they are both actually based on Vector (directional) effects. It is less obvious that time effects are directional (as Time Dilation certainly must be) where the directional effects of the Contraction (physical) effect is more obvious.
Time Dilation is the most popular aspect of Einstein's Special Relativity. The effect is easily seen, which certainly appears in a telescope but it does not actually have any real effects on what (or who) is being observed. In that, it is similar to the fact that all receding galaxies appear red to us on Earth, due to the Doppler Red Shift Effect, even though none of those galaxies is actually red color!
If we had telescopes that were a lot more powerful, we would immediately see that the current understanding of Time Dilation is totally wrong! Say you had a really powerful telescope where you could constantly watch your good friend (Ogg) on a distant rapidly receding (at 0.6c) planet of Siri. You would watch a Special Relativity effect which we call the Lorentz-FitzGerald Contraction.
|Just after Earth-rise, when the Earth is low in the Siri sky to the left, he appears (naturally) 6 feet tall but very skinny, as the SR LF Contraction makes him look to us on Earth as only 80% as wide. You would watch him accelerate and see his mass was 200 lbs||A few hours later, when you are looking at him from a location which is directly overhead of him, due to the SR LF Contraction effect, he appears to you to be much shorter (now 4'10" tall) but naturally pudgy. You would now weigh him at a mass of only 160 pounds. You also see his clock as only ticking 4/5 as fast as earlier|
As Siri daily rotates, when you watch him near the moment of Earth-rise, you would see him as (his true) 6 feet tall, and skinny-looking (due to that Vector direction effect). A few hours later when Siri has rotated part of a day, you are overhead of him, and you see that (obvious) Lorentz-FitzGerald Contraction in his body, where you see that he now appears to be only 4 foot 10 inches tall, and (his true) pudgy-looking. A few hours later, late in his Siri day near the moment of Earth-set for him, you again see that he appears to be 6 feet tall (and very skinny)!
You clearly see these (obvious) effects on your friend's body. Since you Saw it, do you really think that he actually started the day out tall and skinny, and became very short and pudgy before your very eyes, and he started out the day at 200 pounds mass but rapidly dropped down to 160 pounds and then back, and he started out seeming to move fast and then slow (due to Time Dilation) and then fast, twice every day? No, in actuality, he does not actually experience any of these things!
|Morning - Same Guy
looks tall and skinny
|Four Hours Later
looks short and pudgy
As a real being on Siri, he remains 6 feet tall and somewhat pudgy, at all times. The perceptions of Special Relativity are only true for you watching him from Earth, while nothing actually changes at all in his life on Siri. Special Relativity generates interesting perceptions, while his reality is not affected, whether in physical dimensions or regarding time rate or mass. From Earth, you would watch your friend moving around and accelerating as having mass of 200 pounds (during the first picture above, when he appeared 6 feet tall), but a few hours later when we are overhead for him, you would see that his weight (mass) now appeared to be 40 pounds less, at 160 pounds (while he appeared to be only 4 foot ten inches tall to you). But then, a few hours later, you again would see him as apparently having mass of 200 pounds again! His actual mass on Siri would not change for him, as always being 200 pounds. If you could watch his clock ticking, you would see that at Earth-rise, his clock appeared to run about as you might expect, while when you are overhead of him, you would clearly and obviously see that his clock then seemed to be running really slow, due to Time Dilation, at 4/5 as fast, but then as with these other Special Relativity (apparent) effects, you would watch as his clock speed up to its much faster speed like before. Each of these effects are due to the Vector nature of gravitation and Relativity, which is only seen along one direction (along our line of sight). The result, as seen by us here on Earth, is that, while Siri was doing its daily rotation, in the intervening hours, Vector Addition must be used to watch the smooth transitions of each of these effects, so none of these are "sudden". So you watch as he smoothly goes back and forth between appearing 6 feet tall (and skinny) and 4 foot ten tall (and pudgy), and between appearing to gradually change from 200 pounds down to 160 pounds and then back up to 200 pounds (and skinny again). You would also watch as his clock (and his motions) are fast and then slow down and then speed back up again, all in the course of watching him every day!
By the way, he sees the exact same effects on you here on Earth!He watches you gradually appear to change from 6 feet tall down to your mid-day height of 4'10" and you first appear to be skinny and then get pudgy and then get skinny again, and he watches your (apparent) weight (mass) change from 200 pounds down to 160 pounds and then back up to 200 pounds again. He also watches the second hand on your clock seriously slow down to 4/5 rate and then speed back up to full rate again. (due to the Time Dilation effect) as he watches you. None of those effects Actually happen to you in your Earth life! But he could go into a Siri Court and Swear that he saw those odd things happen to you, while he assured the Judge that he didn't even blink while watching you!
Consider an extremely simple Universe, in which there are only two planets which exist in the entire Universe, our Earth and a planet which I will call Siri. Since there is nothing else to look at, we would (both) spend all of our time looking at each other!
There are actually three different primary effects which we definitely see for this Special Relativity situation. The most famous one is an apparent slowing of the rate at which time seems to be passing on Siri, which we call Time Dilation. Everything we see on the planet Siri seems to be happening at a rate which we see, by our clocks on Earth, at exactly 4/5 as fast as what we might expect to see. People's movements and even heartbeats, and the rate at which chemical reactions and nuclear processes occur, and everything else on Siri appears to us to be happening at that 4/5 of the expected rate.
So, by relying on our clocks here on Earth (whether a School clock or a Cesium clock or a pendulum clock), there is no doubt at all that we see everything occurring on Siri to be occurring in very slow motion, at exactly 4/5 as fast as we might expect. If we watched long enough, even the aging and birthdays.
We also definitely see another effect of the Lorentz factor, often called the Lorentz-Fitzgerald Contraction, where everything we see along our direction of viewing appears to be shrunk (contracted) by that same factor of 0.8. It is a weird effect because it does not act in either of the two other directions. So, for example, we would see the entire planet Siri look as if it was not round (as it has to be due to how gravitation works), but sort of pumpkin-shaped, severely flattened in the direction toward us. Their planet is not actually pumpkin-shaped, and that appearance only exists from our perspective through our telescope here on Earth.
Finally, the third major effect: if we had a scale or some way to monitor acceleration to measure mass we would see that all forces and accelerations are also affected, including weight (which are all Vectors and have a specific direction) appear to be 0.8 times what we think it should be, but again, only along one direction, toward us. Again, this does not really occur, and scales on Siri would not measure anything odd; it is only an effect which we can see, from Earth, along one specific Vector direction.
Einstein showed that these three effects are necessary and consistent to ensure the Conservation Laws of the Universe, from any Relativistic perspective. We see a shorter distance which something would need to accelerate (along our direction of view) so the object must act as though it has different effective mass so the equations solve correctly. This is for both us calculating on Earth and for the people on Siri with their pencils.
Everything described above is exactly as the Earth-bound description of Special Relativity as it has long been assumed to occur, and what we see is then perfectly logical (to us on Earth).
However, all of those effects are not actually real, but they are instead just apparent effects. Why? For many logical reasons.
A really obvious logically impossible one has never been mentioned by anyone. Imagine an even faster recessional velocity between the only two planets which exist in the Universe, nearly at the speed of light, where the Lorentz Factor was 0.01. Yeah, we definitely would see everyone on that planet appear to be aging and moving at 1/100 as fast as we might expect (and we would actually see that through our telescope). By the way, they, through their excellent telescope would see all of us on Earth (obviously) moving at 1/100 as fast as they might expect us to move. We on Earth, through our wonderful telescope, would also see the Lorentz-Fitzgerald Contraction effect as well, where we would see their entire planet appears to look like a very thin pancake! And through their telescope, they also see the same Lorentz-Fitzgerald Contraction of you and me and the Earth. They would measure that the Earth appears to be 7913 miles wide and high, but only appears to be about 79 miles thick (along their line of sight). We would certainly look like a very thin pancake! But that is impossible. We know how gravitation works, and every massive object (including stars and large planets) in the Universe has to essentially be spherical shaped, in order to comply with Isaac Newton's Laws of Motion. In other words, what we would see, of a very thin pancake-shaped (massive) planet, is impossible, in this situation really close to a recessional velocity of the speed of light. The really interesting thing, due to Relativity, is that the scientists on that planet would see the exact same Lorentz-Fitzgerald Contraction of you and me and the Earth. The viewers on that planet would measure the Earth to be 7913 miles in diameter (wide and high), but they would also measure that the Earth is only 79 miles thick. According to Einstein, then, we must be on a planet, Earth, which is obviously a really thin pancake, like "Flat Earthers" claim! Which is totally impossible!
Since we on Siri see the Earth receding at 0.6c, then, due to Time Dilation, we see that everything on Earth appears to be moving in slow motion, at 0.8 as fast as our (Siri) clocks show things should be happening. We also see the Lorentz-Fitzgerald Contraction and the change of mass described above, regarding anything we see anyone on that Earth doing. Any experiment, any acceleration. But we know that our (Siri) clocks are always precisely correct and so "we know" that the Time Dilation and the Lorentz-Fitzgerald Contraction that we see regarding Earth must be true.
But they are not, they are apparent effects. So when we here on Siri see all the people on Earth to be "obviously" aging only 4/5 as fast as our Siri clocks show they should be aging, it is not a real effect but instead it is an apparent effect. We also see the really obvious Lorentz-Fitzgerald Contraction effect where the Earth is "obviously" really seriously oval-shaped, only about 6300 miles along our (Vector) line-of-sight while 7913 miles in each of the other directions. By the way, by his (Siri) view of the Earth, this weird "bulge" constantly changes (due to the existence of some guy on a tiny and distant planet that we cannot even see! When you happen to be at a location on Earth where it is Siri-rise, he sees that you are six feet tall (but then really skinny), while six hours later, he sees that you are then 4 foot 10 inches tall and rather pudgy looking? And another six hours later when you are at Siri-set, you appear again at 6 feet tall and skinny. Please note that you do not actually experience such constant changes! Please also note that you constantly watch all these peculiar effects of your friend on Siri!
See the problem in real and apparent?
Rather than the "Earth-only" view that Earthers have always accepted as fine, Einstein taught us that all locations in the Universe have logically equivalent Relativity, and now we see that the people on Siri have come to the exact same conclusions regarding Earth. The fact that we do not (yet) have telescopes powerful enough for you to actually be able to watch your friend on Siri, you cannot (yet) see these very odd (apparent) effects on his body (apparently) getting very tall and short twice every Siri day, or him (apparently) getting skinny and pudgy twice every Siri day.
Oh, did you feel that your personal life suddenly slowed down (entirely because some very distant guy on a distant planet aimed his telescope at you?) Do you now feel that your birthdays are now much less often (again, entirely because that guy had aimed a telescope at you). Otherwise, how do you explain his (proven???) slow motion view of everything he sees on Earth?
Do you feel that you get several inches skinnier in one direction as you turn around (like when the Earth daily rotates)? Do you weigh a lot differently depending on whether a very distant telescope is turned on and depending on what direction your scale happens to be facing? In other words, does your scale weight rise and fall by 40 pounds, twice every day, just due to a distant observation of you through a telescope? If his telescope was really good, he could watch the actual scale readings of your bathroom scale while you stood on your scale all day, would he see the scale readings constantly be wildly changing? (actually, no).
Do you see that the only possible (correct) logical explanation for all this is the way that Einstein had described it to us, that of Relativity? The real Siri (and therefore, you personally) is not actually affected by the Time Dilation effects that the guy on Earth absolutely sees through his telescope as true about you and Siri?
Want to make this even weirder? Now say that the Universe only has three planets and not two, and that the third one is roaring away in some different direction. Depending on which of the other two happen to have their telescope aimed at Earth, two entirely different Special Relativity and Time Dilation and Lorentz-Fitzgerald Contraction effects would be seen from that planet. If these were real effects, then Earth and Siri (and you) would constantly be twisted and distorted, where your height and weight is constantly changing all day, every day!! But, fortunately, these various Special Relativity and Time Dilation effects are not real and they are instead just perceptions.
Each of the three planets has the Lorentz-Fitzgerald equation. So, on each planet, the scientists calculate the "Time Dilation" factor. On each planet, they calculate two different SR formulas for each of the two other planets (and its scientists) appear to be aging more slowly and changing in height and weight (mass) than himself.
See the problem?
We on Earth think that everything on Siri is "actually moving in slow motion", which we call "Time Dilation". But everybody on Siri also is certain that you and me and everything else on Earth is "moving in slow motion".
Do you feel that you (suddenly?) live your life in slow motion, entirely because some distant guy on an invisibly distant planet aimed a telescope at you? No. Neither does he. Your life, and his, passes exactly as it has for millions of previous years.
In other words, neither you nor he can actually sense any effect of "Time Dilation". As oddly as it might seem, you both OBSERVE a Time Dilation effect through your telescopes, without either of you ever feeling any such sensation. Both of your birthdays will still be exactly when you expect them to be (although the other guy observing you would see you apparently having a "slowed down life.") And it does not matter if you are the observer or the one being observed, your actual life is totally unaffected.
Do you see the "obvious reason" why Time Dilation is "only an appearance" and not a "reality?". You both cannot be seeing the other guy aging slower than yourself, and wildly also changing in height and weight and skininess, constantly and forever.
The Time Dilation effect of Special Relativity is certainly an "easily demonstrated appearance" but it is not a "real" phenomenon to either one of you.
If we see some apparent change of rate of time in some distant chemical or nuclear process or in some distant person's life, the "reality" is that the alleged "target" does not experience any "real" changes at all. The absolute proof of this is actually obvious.
The first experimental proof of Special Relativity and Time Dilation was that laboratories on the surface of the Earth, many miles below Muons that were created high in our atmosphere, were detecting those Muons! In 1941, the Rossi-Hall experiment first demonstrated the situation. That should have been impossible! Prior to that experiment, we had learned in our laboratories on Earth that the average lifetime of a Muon was 0.000 002 197 second. Even if they moved at nearly the speed of light, they must decay within about 0.41 mile of where they were created. However, scientists had discovered that Cosmic Rays (which are actually very fast moving protons at near the speed of light) from outer space were shattering atoms high in our atmosphere. Those Cosmic Rays were causing the creation of Muons around 50 miles high in our atmosphere. It was obvious to everyone that no Muon could possibly travel the 50 miles down to the surface of the earth. However, research labs on the surface of the Earth, many miles below, easily detect most of those Muons.
The only possible explanation of this is due to the Time Dilation effect of Special Relativity. This was actually the first strict experimental confirmation of Einstein's Special Relativity.
The immense energy in a Cosmic Ray (a very fast moving proton) very rapidly accelerates the relatively stationary Muon in the atmosphere up to an amazing enormous constant velocity (around 0.9954c). This is now an immense amount of Kinetic Energy in the Muon. This causes the nearly instant acceleration up to the 0.9954c velocity. We see that the appearance of time passage for the now constant-velocity-cruising Muon seems to only be passing at about 1/100th as fast as the normal time we otherwise experience. This is due to the Lorentz factor of Time Dilation of Special Relativity. Do you see why this is?
Even if the Muon was traveling downward at essentially the speed of light, we Earthers see that it could only go around 0.41 mile before decaying into an electron and some radiation. However, it has 50 miles to go (in our perspective) and so the Muon has to have Time Dilation by a factor of about a hundred, entirely because of what we see, that it gets all the way through the atmosphere. We say that time appears "normal" to us but we see the very high velocity Muon appears to age only around 1/100th as fast as everything else we experience. Since we Earth scientists see the Muon to appear to be aging at only about 1/100th of its actual half-life age, we see nothing weird in that the Muon is able to travel around a hundred times as far. There is plenty of time for the Muon to proceed through the entire atmosphere which we have measured as 50 miles thick, and down into a laboratory on Earth. When the extremely fast moving Muon impacts some atom in the laboratory, it suddenly extremely decelerates and it then always gives off a bright flash of Bremsstrahlung Radiation (as it decelerates in the lab). That phrase is a German phrase that means "braking radiation". The entire trip we see shows the Muon first accelerating, getting an enormous amount of Kinetic Energy from the Cosmic Ray. Then we see it travel at constant velocity downward through our atmosphere, where we see the effect of Time Dilation so the Muon can last long enough to get completely through our very thick atmosphere, and finally it collides with something in the Lab, where it suddenly decelerates and gives off all that Kinetic Energy in a different form in the Lab, as Bremsstrahlung Radiation. We see that energy is Conserved during the entire trip.Actually, we don't have good enough equipment (yet) to monitor two very brief moments of this trip. The Muon is a real object, and so by Newton's Laws of Motion, it must make a "complete trip" which involves (a) acceleration, then (b) constant velocity cruising and finally (c) deceleration to eventually stop in the (original) Inertial Rest Frame of Motion, The initial acceleration of the Muon from some of the Kinetic Energy of the Cosmic Ray occurs faster than we can photograph it. That acceleration may occur in just 10-16 second, around a million times faster than we have any equipment to monitor. We do know how much Kinetic Energy that the Muon would have to absorb from the Cosmic Ray, for that amount of mass to achieve that amazing velocity of 0.9954c . We just don't know how long it would take to transfer that amount of Kinetic Energy to it from a Cosmic Ray. The other situation is similar. We don't have any equipment that can monitor a racing Muon (at 0.9954c) very suddenly decelerating and stopping, to give up all that Kinetic Energy it had been carrying. But, experimentally, we know that the event causes a unique flash of radiation, which was given the name Bremsstrahlung radiation long ago (braking radiation). Some day, after we develop faster test equipment (by a million times) we may then be able to watch a Bremsstrahlung event occur, and maybe figure out the details. For now, our knowledge of that portion of the Muon adventure is only described in one word, Bremsstrahlung. We can only now watch the Muon during its constant velocity portion of its trip. I personally suspect that we have wonderful lessons ahead of us when we will some day be able to carefully monitor the acceleration and the deceleration portions of the trip. I think I know what we may then find, but the world may have to wait for now.
A tiny scientist on a Muon would see a very different trip. He would see the entire Earth as appearing to move and age very slowly. The very same Lorentz formula applies as discussed before, where the Muon scientist would see all Earth people moving at only 1/100th as fast as he was normally familiar with. Another effect of Special Relativity is that (vertical) Distance appears to be reduced (Lorentz-Fitzgerald Contraction), so he sees the entire Earth's atmosphere as appearing to only be about half a mile thick. Interestingly, he also sees all those humans down below him as looking like weird pancakes, with heights that are less than one inch tall, but with the width and thickness dimensions you are familiar with.
The Muon scientist sees nothing odd in his lasting long enough to travel entirely through the half-mile-thick atmosphere to get all the way down to the (pancake) laboratory. It is absolutely logical to a Muon scientist that he makes it all the way down to a lab on Earth. He only sees the Earth's atmosphere as half a mile thick so he sees no problem with his 0.9954c velocity easily getting him entirely through it all. Of course, that Lorentz apparent Contraction, given that he sees the entire Earth rushing upward at him at 0.9954c, he sees that the entire atmosphere looks to be half a mile thick to him (as well as the "pancake" references to the humans down there and the laboratory target down there.
Notice something very important. The Earth observer sees the Muon to appear to be aging and moving at 1/100th as fast as he otherwise expects. At the same time, the Muon observer also sees the Earth to appear to be aging and moving at 1/100th as fast as he otherwise expects. See how weird this seems? BOTH of them SEE that the "other guy" appears to only be aging 1/100th as fast as himself. Neither of them experiences anything unusual at all. This is an odd characteristic of Special Relativity that others do not seem to realize.
Notice something else that is very important: You (and everyone else on Earth) are not actually living at 1/100th as fast. Your life is absolutely unaffected by this situation. It turns out that the Muon scientist also is not affected from his standard life.
The result of this is that our lives are not remotely actually altered by any Special Relativity situation. All the effects that we see are also not actually affecting the Muon at all. It is just a perception, where both sides see that the other guy appears to have the different time and velocity and mass effects that we think we see of the "other guy". There is no disobeying the speed of light as being the fastest possible.
To a Muon scientist (while roaring down at 0.9954c), you appear to be a pancake, to be less than one-inch-tall, but in our reality, you are five or six feet tall. Do you feel that you are actually only an inch tall? No. In other words, within the Special Relativity effect in a Muon environment, all of us humans down below look like peculiar very-slow-moving pancakes! But, within our perspective, we are the same as we ever have been.
Therefore, neither side experiences any quirky effects, just stuff that appears "normal". Whether it is an Earth scientist or a Muon scientist, time passes exactly as it is expected, but when they look at the situation in the different (non-accelerating) location, the effects of Time Dilation are clearly observed.
This is even more obvious to us if some distant observer aims a powerful telescope at us. Just because he clearly sees us through his telescope to be moving and aging slowly does not cause our lives to suddenly slow down per the equation of Special Relativity and Time Dilation! In fact, we would not and could not (ever) "experience" any of the various "observed" processes of Special Relativity. Our body weight (mass) would not suddenly change just because someone on a rapidly moving planet happened to aim a telescope toward us. We would not age more slowly or move more slowly. We would not feel any sensations whatever of what the distant observer clearly witnesses as Time Dilation effects of Earth and us. Indeed, if two different people observed us from different directions, from different planets, which are traveling at different velocities from or toward us, our lives would not have any "confusion" as to which Special Relativity we were to comply with. We would not change at all. It is not a "real" process. Albert Einstein certainly understood, and he certainly tried to help other scientists to better understand, but we fellow humans seemed to not really grasp much of what Einstein tried to teach us. Nearly everyone today is excited about the idea of "time travel" and "wormholes" but such ideas are actually not remotely possible.
Maybe a different approach might improve our understanding of Special Relativity.
Imagine that, in your backyard, you have a world-class telescope, and you pointed it at a distant planet (which we will call Siri) that is moving away from us at ferocious velocity, at 0.6c (more than half the speed of light) but not accelerating. You, on Earth, feel that you are not moving and also not accelerating. Through your telescope, (correctly, according to Einstein's Special Relativity and Lorentz' Time Dilation), you definitely see that a guy on that planet seems to be moving in slow motion, at exactly 0.8 times as fast as you might expect him to be moving. You know this by using a very precise clock on your wall.
However, that guy has his own "universe-class" telescope (exactly like yours) which he has constantly pointed right at you, here on Earth. He sees no acceleration by you or the Earth, but he sees that you and the Earth are receding from him at that same ferocious velocity, 0.6c. He, on his planet Siri, does not feel any movement or acceleration at all. Einstein explained to us that we (here on Earth) are not in any "preferred Inertial Reference Frame". Now, think of yourself as that guy. Through his excellent telescope, he sees you (on Earth) seeming to be "moving in slow motion", at exactly 0.8 times as fast as he might expect you to be moving (by his Siri clock).
See the weird part? You see him to seem to be moving and aging slowly, and at the same time, he sees you to seem to be moving and aging slowly. Where Physicists and the world have believed that Special Relativity lets us absolutely see him actually moving and living more slowly (since around 1960, shortly after Einstein had died), that guy on Siri also sees the exact same effect occurring to you here on Earth! Both of these scientists are smart and they know what they see. And if you are willing to only consider one-side of this situation, from Earth, you might easily think what has always been assumed, that the Siri guy is actually living more slowly than we are. The problem is that he, on Siri, truly would see the same effect is constantly occurring to you and the entire Earth.
There is an alternate way we can analyze this situation. You don't really think that all the people on the entire planet Siri are living in slow-motion just because some distant planet (Earth) happens to be moving away from Siri at a ferocious velocity (for billions of years?) Do you actually assume that the Time Dilation effect that you definitely see, only occurs while you are looking toward Siri? In other words, that assumption can be seen as very wrong because you believe that his life jumps back and forth between full-speed time and 80% time, every time you aim your telescope (or binoculars) at Siri. Do you really think that his life physically slows down and speeds up every time you aim your binoculars at Siri? No. Same deal the other way. If his binoculars can change the rate of time passing on the entire Earth, then do you feel your car suddenly slows down from 70 mph to 56 mph and then just as suddenly speeds back up to 70 mph again? When you throw a baseball at 70 mph, does it get part way to the Catcher and suddenly slows down to 56 mph before he catches it. I must admit that the game of baseball might be much more entertaining with such effects in it.
Well, the same way that our lives do not fluctuate in such ways due to each time anybody on any other planet points a telescope or binoculars at the Earth, the same is true the other way. We might think that all the people on Siri are actually having their rate of time changing due to the Time Dilation effect of Special Relativity, as we definitely can see it have effect (not yet for people out there but definitely for the rates that we can watch chemical reactions occur or the rate at which we can see nuclear reactions occur), but what we see is not actually happening. It just appears to be happening. We think we see several effects, such as a Lorentz-FitzGerald Contraction of (only radial) distances, and a Lorentz change of mass and a Lorentz slowing in the rate of time passage, but these are all inter-related apparent effects. When he tries to run (radially regarding Earth) we see that his acceleration seems to have changed, which is due to the "changed mass" and the "lesser distance" and the "slowing in the rate of time". What we see appears to be perfectly logical and compatible. And no such effects are seen when he turns and tries to run "laterally" (in the x or y direction), but only for his motions in the direction of our line of sight (the z direction). He does not experience it harder to run in the z direction (due to the apparent changed mass) than in any other direction. We see all those effects, only because we have a perception of Lorentz' effects of Special Relativity, and those effects seem to exist along only one direction.
So, neither way, as seen from Earth or from Siri, time travel is not remotely possible (in reality).
We did make an assumption in this reasoning. To simplify this concept, we had assumed that both of our planets rotate at the exact same rate, where both of our clocks (actually) run at the same rate. We will discuss this factor later.
Maybe you are both better scientists than that, and you don't want to try to judge such Time Dilation observations based on biological processes of each other or of effects of the gravitational field strength of each other's planets. So you do other experiments, such as timing how long a chemical reaction or a nuclear reaction like a Cesium clock takes to occur to determine that 0.8 observed time difference. The 0.8 factor is valid, but only when one is exclusively using his own planetary spinning and so his own clocks. (Our initial, simplified observation of "moving in slow motion" might be dependent on our species being exactly identical, and possibly on planets which were identical with identical gravitational field strengths.)
See the problem? You both see the appearance of each other "moving very slowly", due to what we each call Time Dilation. However, think of this more analytically. Are you ACTUALLY "moving slowly", just because he pointed his telescope at you? No. Your life is exactly as you have always known it, with birthdays at the right times, etc. AND SO DOES HE.
The Perception of "Time Dilation" is not an actual phenomenon, but only a perception of something that you both can absolutely see through your telescopes. You will both think you see the other guy "moving and aging in very slow motion", but neither of your lives actually experience any such things.
If there had been "reality", then all the very logical questions would be appropriate, especially in trying to explain "which of the two of you actually saw the other one aging more slowly than himself", and all sorts of other weird questions. But the life of that guy you were looking at did not suddenly change just because some distant guy, you, pointed a telescope at him.
It is frustrating that even my fellow physicists seem to totally misunderstand this issue. They only think that the Earth is in a Preferred Reference Frame of Reference so that they only need to examine everything from only our perspective. It seems really pretty obvious to me, as it did to Einstein, who had tried to explain it to the rest of us.
As a Theoretical Physicist, and one who has spent much of his career in studying both forms of Relativity, I find it frustrating that virtually everyone has such wrong ideas regarding Special Relativity. What Einstein had tried to teach us is that Special Relativity can cause the perception of rather odd aspects of how time seems to pass. But the reality does not get altered for the people or events we are observing. We see popular media promote science-fiction ideas that include things like time passing at unexpected rates (which we call Time Dilation, and which has gotten huge publicity). If that experience were actually true, yes, some of the popular speculations regarding time (including ideas of the speed of light being able to change) might be true. But it is not.
Think about this. If your life could actually experience such Time Dilation, and if the Universe actually has millions or billions of inhabited planets out there, then you would (logically) have your daily life speeding up and slowing down, every time that anyone on any of those planets happened to point a telescope toward where the Earth happened to be. Do you experience such bizarre effects in your daily life? No. Would it apply every time someone with a pair of binoculars pointed them upward toward us? Or would there be some dependence where only expensive telescopes have this effect (on all of the inhabited planets in the Universe?) No, that would be illogical and silly.
There is a complication in this logic that we also need to consider. For us on Earth, the basis of all of our time systems and clocks is the rate of our Earth spinning. A similar situation is obviously true on that other planet we are considering, which is not likely to be spinning in exactly 23h 56m. So when we say that that guy "seems to be moving slowly", we make that statement based on Earth clocks. We would think we saw that to be true, but actually only based on our clocks. We would need to do some additional analysis to determine a "time conversion factor" between the two planets and their laboratories. For example, we might use some process that we believe to be known throughout the Universe, such as the rate at which Cesium atomic clocks vibrate. Once we have applied this correction factor, then all the logic described in this Paper can be seen as true and accurate.
For fifty years, I have tried to explain this to the public, and to my fellow Physicists but they instead seem to prefer the "sexiness" of the many goofy science fiction speculations that various people have dreamed up, like "time travel" and "wormholes" and "faster than the speed of light". Maybe it is just because I am a Theoretical Physicist that this seems really "obvious" to me. But many of the things that are popularly promoted as being "consequences of Special Relativity" are simply "perceptions" and not actually "reality". I use some examples below which I think shows why this is the case.
In the first graphic below, consider us on Earth looking through our powerful telescope at a scientist on a rapidly receding planet Siri, while the second graphic shows a Siri scientist who is also looking through his (identical) powerful telescope at the rapidly receding Earth scientist. Einstein explained that all (non-accelerating) locations in the Universe are equal, or actually, Equivalent, so that both Observers regarding Time Dilation must witness similar, logical, views, that is, both would see the other as appearing to age more slowly than himself. Both would see Time Dilation as a reality, but only as applying to the other guy. We on Earth seem to insist that we have some sort of "special environment", where only our view matters.
There is surprising misunderstanding regarding the exact correct truth and logic of what Time Dilation is. Or, more specifically, of what Special Relativity is. I am a Theoretical Physicist who has spent much of my career studying subjects associated with Einstein's Relativity. Two basic facts are clear and unavoidable. First, the person who Observes any of the events of Relativity does not and cannot Experience any of them. That includes Time Dilation and an assortment of speculated issues such as "time travel" and "wormholes" and many other speculative assumptions. The only effect which can be detected is for that (Earth) Observer to look (usually through a telescope) at someone or something which is either wildly accelerating (GR) or traveling at extreme velocity toward or away from the observer (SR). Oddly, even then, Second, the person being Observed does not experience anything unusual! He lives a very mundane life, where he thinks time is moving at the same rate that he has always experienced during his life.
So neither the Observer nor the person or event being observed actually experiences any alteration of the rate of time passing (or a variety of other things like the apparent inertial mass that an observed person or object seems to have or distances or velocities which objects seem to move at). Even though the Observer sees an effect such as Time Dilation, it is actually a "perceptional" phenomenon and not anything which is actually "real". People are surprised that this is equally true for both of the scientists who are observing each other.
This statement has to be true! Otherwise, the (wrong) assumption that one or the other of "identical twins" would have to age faster or slower than his identical twin sibling. That does not and cannot happen.
The following discussion and graphics is a decently clear example of the real situation, essentially directly from Albert Einstein's thought experiments. The following animated graphics present two separate views. First is a view of Earth here. An Earth scientist has an accurate school-style wall clock and a very powerful telescope, which he carefully aims exactly at a distant planet, Siri, which he has measured to be receding away from Earth at extreme velocity, that of 0.6 of the speed of light. Neither the Earth nor Siri is accelerating, so there is only a constant velocity detected between them. After we have examined the situation for the Earth scientist (and the Earth in general), we will travel to the observed planet Siri to see what everything looks like from there.
In both cases, we simplify things by focusing entirely on images of the two wall clocks which the scientists have in their Labs, one in a Lab here on Earth (which is a school-style clock) and the other in a distant Lab on a planet we are calling Siri (which has a wooden frame clock on its wall). These two planets and Laboratories are not accelerating. On Earth, we see Siri receding away from us at a tremendous velocity (at 0.6 of the speed of light).
My ultimate intention here is to present a clearer presentation of Special Relativity "for non-Physicists".
Looking at the Earth laboratory first, we see the prominent Earth wall clock at the top that is always timed exactly to GMT. Much of the rest of the image is of a giant telescope, with its eyepiece image of a large wooden frame wall clock on the other (receding) planet's wall, which we see as moving away from us at 0.6c. The Time Dilation effect we see of all of Siri therefore appears to have their time passing slowly, running at 0.8 the actual GMT time-rate he observes in his Laboratory here on Earth, due to Special Relativity and its Time Dilation.
The actual true time we ever detect and experience on Earth is always exactly what we are used to, GMT, given by our school style wall clock here on Earth. Only the image of Siri seen in the eyepiece of the telescope has the appearance of having time running much slower due to Time Dilation.
This situation is similar to what many people expect of Time Dilation and Special Relativity. A critical difference is that nothing in our Earth Laboratory gives any appearance that any time-rate is or could be any different from what we expect. The Earth scientist cannot "alter time" in any way, and his life is destined to continue as he had always experienced.
Now we look at the image of what the Siri scientist sees in his Lab. As on Earth, there is a large wooden frame wall clock in his laboratory, timed exactly to his own planetary time. The other portion of the Siri Laboratory image is the view of his giant telescope, and a scientist looking at its eyepiece. He has his telescope aimed exactly at Earth and so he sees in his eyepiece an image of the Earth school style wall clock of the Earth scientist we had just examined.
This is very important. The Siri scientist sees and has measured that the Earth is receding from him at very high (constant) velocity of 0.6c. He also has NO sensation that he is moving at all. As a result, he sees the image of the Earth clock appear to running at 0.8 the actual rate of his Siri wall clock, again due to Special Relativity and its Time Dilation.
Actually, per Einstein, no scientist could ever detect that he was on Earth or on Siri, as everything would seem exactly correct to each of them
The actual true time that the Siri scientist ever detects is what he is used to, given by his wooden frame wall clock of his Siri Lab. Only the image seen (of Earth and its clock) through the telescope's eyepiece has the appearance of running much slower due to Time Dilation.
no acceleration is present anywhere so both Laboratories are certain that their own wall clock is perfectly reliable and accurate (in the Inertial [non-Accelerating] Reference Frame) in their own labs). However they each see the "other" wall clock (as seen through their telescope's eyepiece) to be running clearly slowly.
The point is that the "Time Dilation effect" is not actually a physically true phenomenon, but each clearly sees the "moving clock in the telescope eyepiece" appear to run at 0.8 times the rate of their own clock.
This is definitely obvious to witness, for both. However, regarding any "physical sensation in the other Laboratory", no, there would be none.
The distant Siri observer might think that you are aging at 4/5 the rate which he is aging at due to his calculation of Time Dilation, but you know that your birthdays are exactly as far apart as you have always experienced. You also think that he is aging 4/5 as fast as you do. These are Observed perceptions and they are not actually real.
For the Muons, their enormous (constant) velocity (around 0.9954c) causes (Time Dilation) time to appear "normal" to us but they see us to appear to age only around 1/100th as fast for the Muons (themselves), much more slowly. Also, we Earth scientists see those Muons to appear to be aging only about 1/100th of their actual ages, and so we see those Muons actually have plenty of (Earth-) time to travel the distance of many Earth miles down to the labs.
In their environment, the Muons see it as easy to travel the entire 50 (Earth) miles down to a laboratory on Earth, and it seems very logical to them because they appear to see the entire atmosphere to only be 1/100 as thick, that is, a fraction of a mile thick. It is absolutely logical to an Muon scientist that they make it all the way down to a lab on Earth (due to Time Dilation). We Earth scientists see those Muons (and their tiny Muon scientists) to appear to be aging only about 1/100th of their actual ages, and so, to us Earthers, those Muons actually have plenty of (Earth-) time to travel the distance of many miles down to the labs.
To the Muons, everything is pretty much as expected but our atmosphere looks like it is only less than a half-mile thick. Interestingly, they see everything in the Earth environment to only have vertical dimensions of about 1/100 of what we experience. Laboratories on the ground are only 1/100 as far, in their perspective, therefore our entire atmosphere appears less than 0.28 mile thick, and so it is totally logical for some of the Muons to be able to get all the way to the surface, without disobeying the speed of light being the fastest possible.
To a Muon scientist, you appear to be a pancake, to be less than ONE INCH TALL, although your other dimensions would not seem changed. In other words, in a Muon environment, all of us humans down below look like peculiar very-slow-moving pancakes!
There have been countless other experimental confirmations of the Time Dilation effects of Special Relativity.
Therefore, no one senses any quirky effects, just stuff that is "normal". Whether it is an Earth scientist or a Siri scientist or a Muon scientist, time passes exactly as it is expected, but when they look at the situation in the different (non-accelerating) location, the effects of Time Dilation are clearly observed.
The graphics above are meant to show that "life is perfectly normal" for each of the scientists, but both see the other as being in a peculiar environment, where time seems to run slowly, that (radial) distances seem to be shorter, that the other appears to age more slowly, and where masses seem to be changed. The important point is that these observations are entirely appearances and both see the other's clock as running clearly slowly, while his own clock is behaving exactly as he expects.
All those odd Relativity effects make it so that either scientist can do or witness any experiment that the other scientist might do, and logic is never violated, as Einstein had assured us. They each could watch the other shine a flashlight "directly ahead" and everything would be fine. The "speed of light" of that flashlight beam still turns out to be exactly c to each of them. Speed still adds like we all know it does. For one of the observers, the speed he sees is not "c + c" or 2c, but rather two "Time Dilated" numbers which total exactly c. The other scientist, who actually did the experiment, simply sees that c is the speed of light. For an observer, the speed of a bullet or an accelerating rocket is also just the sum of two "Time Dilated" velocities which results in exactly the correct logical bullet or rocket speed. To that (Relativistic) Observer, the bullet or rocket appears to accelerate differently due to it having changed inertial mass (to him), and also because the distance being seen as being covered is less due to the same Dilation formula (again, to him).
A critical detail for Special Relativity is that both the observer and that person or event being observed are in what Physicists call an Inertial Rest Frame of Reference, which means that no acceleration is occurring. On Earth, we only have two locations available that precisely comply with that, the North Pole and the South Pole. So we take a scientist, give him a heavy coat, and stand him at the North Pole. We give him a really good telescope and a wall clock and a precise Cesium clock, too.
We have found him a planet, Siri, any distance away from us which we have found to be traveling exactly radially away from us, at exactly 0.6c, an enormous speed. Either that planet is not spinning at all, or if it is, a scientist has been sent so he is standing exactly at its North Pole. He also has a heavy coat and a really good telescope and a wall clock and a precise Cesium clock.
The Earth scientist and the Siri scientist are each looking through their really good telescopes toward each other. Their telescopes are far better than any telescopes we have ever made and they can see each other smiling and waving at each other. Even the hands on the clocks on their walls are visible through each of their telescopes (as the graphics above have shown)
Note that the Siri scientist does not feel any movement or acceleration (any more than we do on Earth) and he sees the Earth moving radially away from him at exactly 0.6c.
We will now visit the scientist at our North Pole. His clock and his Cesium clock are always exactly synchronized. But when he looks at the Siri clock he sees through the telescope, he sees that wall clock appears to be running much more slowly. (The Cesium clock on Siri also exactly is synchronized with that wall clock, which we see as running much more slowly than our clocks here on Earth.
An observer who is not moving at all, such as at our North Pole, would see such a rapidly moving (at 0.6c) (receding) man appear to have time pass much more slowly. Hendrik Lorentz and George FitzGerald discovered the well-known formula which is the Time Dilation time-rate factor ß (which is ) that gives us 0.800 (which is less than 1.000 so it is an observed time-slowing effect) as the Time Dilation time-rate (slowing) factor which you (at the North Pole) observe for that person rapidly receding due to Special Relativity due to recessional velocity (not "experienced" by him but only as seen by you, a motionless observer at our North Pole.)
We will now visit the scientist on that other planet, Siri. His clock and his Cesium clock are always exactly synchronized, based on the spinning rate of his planet. But when he looks at the clock he sees (on Earth) through his telescope, he sees that Earth wall clock appears to be running much more slowly. (The Cesium clock there (on Earth) is also exactly is synchronized with that Earth wall clock, which he sees as running much more slowly than his clocks on his planet.
Einstein made clear that either one of our non-accelerating scientists has a perfectly logical perspective and neither is "better".
This conversation so far has entirely been about Special Relativity, mostly because the math is decently simple. It turns out that similar reasoning can be done for our two scientists if they were "Relatively Accelerating" from each other, but then General Relativity would need to be examined and the math involved needs to be the math of "curved space", that is Riemannian Non-Euclidean math and space and geometry.
When you do that Riemannian curved-space math, you find that General Relativity has exactly the opposite time-rate effect from what all Physicists believe to be true. It does not have a "time slowing effect" like Time Dilation, but instead has a "time speeding effect" which totally changes everything in many fields of modern Physics. A very precise math proof follows. All "time travel" speculations are certainly impossible. The popular Twins Paradox story is also impossible. Many entire fields of modern Physics are based on this wrong assumption. NASA has sadly tried many experiments which ignored General Relativity which turned out to be total failures, including the rather famous Hafele-Keating experiment in October 1971. That experiment was a dreadful failure. The famous Kip Thorne believes that speculative "wormholes" exist. The famous Stephen Hawking spent half an hour in his recent "Genius" TV series in trying to prove a wrong assumption of his about Cesium clocks on a mountain.
Time passes on the surface of the Moon slightly more slowly than it does here on Earth. (A Moon clock would run about one ninetieth of a second slower per year than an identical clock here on Earth). The math to prove this is quite simple, and you can even confirm that this is the truth. The following math is indisputable and precise.
We live our lives on the surface of the Earth, where we constantly daily rotate at around 1000 mph, so Einstein's Special Relativity clearly applies to us. We also "ride in a daily curved circle" (around the Earth) in that same process, which means that we also constantly accelerate (radially downward), so that Einstein's General Relativity also applies to us. (We call it centripetal acceleration!) (The Handbook of Chemistry and Physics provides the precise centripetal acceleration value for the Equator.) These effects are both easy to calculate and it turns out that mathematically their time-rate consequences are exactly opposite each other! One (SR) is a Dilation (slowing) of apparent time-rate while the other (GR) is a Speeding of apparent time-rate. They always exactly cancel each other's net effects out for us! There is and can be no net Relativistic time-rate effect on us! That is equally true for people in their homes, for Astronauts who orbit the Earth in the ISS, and even in airliners which circle the Earth. The precise math proof of this new perspective follows.
Please note one very important detail which no one seems to realize. In Relativity, the person or event being watched does not actually change in any way. No "time travel" ever occurs to him or is even possible. No goofy experiences ever occur in his life. Only the (usually distant) observer sees any appearance where the rate of time passage seems to have changed.
We place you at the North Pole, where you are neither moving nor
accelerating due to the daily spinning of the Earth. You will be our
"stationary observer" for the following analysis of the
movements of a man who is standing at the Equator of the Earth. The
factors regarding the time-rate effects of both Special and General
Relativity are extremely minimal for us on the Earth, but they are easy
to calculate. To calculate the Time Dilation Effect of Special
Relativity: A person standing at the Equator "orbits" moves
at precisely 1,674.366 102 km/hr, "orbiting" with the surface of
the Earth every sidereal day. (Equatorial circumference divided by the
seconds in a sidereal day, both precisely known measurements of the Earth).
This is the same as 0.465 101 695 km/sec (v). We know that the
speed of light (c) is 299,792.458 km/sec. Hendrik Lorentz and George
FitzGerald discovered the well-known formula which is the Time Dilation
time-rate factor ß
(which is )
that gives us 0.999 999 999 998 796 560 (which is less than 1.000 so it is a time-slowing effect ) as the Time Dilation time-rate (slowing) factor which you (at the North Pole) see for that person standing at the Equator due to Special Relativity due to the rotational speed (not "experienced" by him at the Equator but only as seen by you, a motionless observer).
For the time-rate Effect of General Relativity, for that person at the Equator of the Earth we have a 6,378,137 meter Equatorial Earth radius (d) and his radially downward centripetal acceleration (a) there is 0.033 915 785 m/sec2. This results in the Equivalency Factor ( ) being 1.000 000 000 001 203 440 , which is then the General Relativity time-rate (speeding) factor on the person standing at the Equator being 1.000 000 000 001 203 440 (which is more than 1.000 so it is a time-speeding effect) (due to acceleration).
Since both Relativistic effects constantly exist, we must multiply these two factors to determine the net Relativistic effect. That is: SR Time Dilation factor of 0.999 999 999 998 796 560 times the GR factor of 1.000 000 000 001 203 440 which results in the net Relativistic time-rate effect being exactly 1.000 000 000 000 000 000 (within experimental error). This is a precise mathematical proof that the two Relativistic time-rate effects exactly cancel each other out (for you viewing the person at the Equator).
A dreadful logical blunder occurred in Physics in the early 1960s and it was never fixed. Even NASA believed that an orbiting satellite or even a conventional airliner circling the Earth, only experienced the effect of Einstein's Special Relativity and Time Dilation. That was and is wrong. Well, misleading, because NASA did not seem to realize that both Special Relativity and General Relativity always constantly apply at the same time. NASA had neglected to consider the effects of General Relativity. NASA had (wrongly) assumed that we on Earth are in what we Physicists call an Inertial Rest Frame of Reference (that is, there is no acceleration acting on us.) It turns out easy to mathematically prove that, for an object that is circling a massive planet like Earth, as in the precise math example above, both effects exist, and that they exactly cancel each other out! One is due to the speed of the motion (SR) and the other is due to the acceleration of the motion (GR), as Einstein had clearly explained.
During the 1960s, NASA included Cesium clocks on a number of earth satellites, to try to prove that their assumption about Time Dilation applied, but all those experiments dreadfully failed. NASA even performed a rather famous (but wrong) experiment in October 1971 to try to prove that (wrong assumption) that only Time Dilation was acting, by sending sets of four identical Cesium clocks both ways around the Earth in conventional airliners, in the Hafele-Keating experiment. That experiment wound up with results which were worthless, well within the experimental margin of error.
A popular claim is that if identical twin brothers were born on Earth, and one went to the ISS (International Space Station) for ten years, the brother who remained on Earth would be able to detect a slightly slower aging of his brother on the ISS, due to Time Dilation. The calculated effect of Einstein's Time Dilation would only be a fraction of one second difference in age, but using identical Cesium (atomic) clocks, that would be easy to detect. That claim is wrongly based on the Earth twin being in an Inertial Rest Frame of Reference that was not accelerating, such that only Time Dilation would apply. That claim was also wrongly based on the ISS twin not being in such an Inertial Rest Frame of Reference.
We on Earth (incorrectly) think we are in such a non-accelerating Inertial Rest Frame of Reference! (Of course, for thousands of years we also thought we lived on a flat Earth that was not moving at all!) However, we each revolve around the Earth once every day, at high speed in a curved circular path, which means we are also each constantly accelerating (radially downward) in a circle. And so NASA and everyone else (incorrectly) assumed that such satellite and airliner Time Dilation effects would be experimentally detected.
Here is the problem!
The passengers on the ISS also think they are in a non-accelerating Inertial Rest Frame of Reference, since they also do not sense any acceleration. If we make a slight adjustment to that story of twins, we can see an obvious demonstration of the logical blunder they had done (and which everyone still accepts as correct!) Consider that a family had lived on the ISS and they had twins, and one of those sons decided to take a rocket ship trip to the surface of the Earth (for ten years). The "non-traveling" brother who stayed on the ISS would see that his brother (on Earth) was living more slowly than he was living, due to Time Dilation, which he could prove by a comparison of cesium clocks. If we looked at everything from the perspective of the ISS rather than the Earth, and the ISS twin brother compared his Cesium clock with one he could watch on Earth, Einstein's Time Dilation would (seem to) require that he would also see that the Earth clock was running slower than his own Cesium clock was running.
Because they both (incorrectly) believed they were in non-accelerating Inertial Rest Frames, this must be true, that both brothers would measure that the other one was aging more slowly than himself!
This would be an easy experiment to do, since there are lots of Cesium clocks in Earth laboratories and also several on board the ISS. And it would obviously fail. Only after each of them correctly considered his own acceleration and therefore that General Relativity was acting, would they then resolve the flawed situation.
When the traveling brother got back home, neither would be younger or older than the other! This is true for either version of the story, whether the family lived on Earth or on the ISS.
This situation is vaguely similar to the popular Twins Paradox story, which also happens to be totally wrong due to neglecting the effects of General Relativity, but for slightly different reasons, discussed below.
The logical flaw here is that both clocks and brothers are constantly and continuously accelerating, in the process of the curved paths of circling the center of the Earth.
In an accelerating (non-inertial) Rest Frame of Reference, Einstein showed that a different set of circumstances must exist, that of General Relativity. Physics even has a formula called the Equivalency Principle, which can be used to calculate the Time-rate effects of any acceleration (or "equivalently" the effect of any gravitational field such as due to the Earth).
We know the orbital speed and altitude of the ISS, and we can easily calculate the strength of the Earth's gravitational field at that orbital distance. The Time Dilation effect due to the orbital speed of the ISS is a factor of 0.999 999 999 669 (calculated below, which is only a difference of less than one part per billion of time). The time-rate effect due to the orbital acceleration of the ISS is 1.000 000 000 330 (also calculated below, which is also a difference of less than one part in a billion of time, but in the opposite direction!) We must multiply these two numbers to account for the net Relativistic effects of both speed and acceleration, and the product is amazingly close to being exactly 1.000 000 000 (actually, 0.999 999 999 998 999 999).
In other words, for an orbiting ISS satellite, the net effect of the speed and acceleration is such that there is no Relativistic time change effect! In other words, NASA in the 1960s and still, is dead wrong about expecting to see Time Dilation effects in satellites or airliners, due to a logical failure of not including the (really obvious) effects of the General Relativity of the orbital acceleration!
There are even still people today (2019) who aggressively claim that the 1971 experiment should have worked and so they present endless claims about why it didn't. But they do not seem to realize that the experiment failed because it was based on faulty logic, that of ignoring General Relativity.
Up above, we also calculated the Precise Time Dilation Effect and the Equivalency Factor for us who are orbiting on the surface of the Earth as it rotates, and that also shows that the two effects exactly counteract each other and there is no net Relativistic time difference effect due to the Earth spinning.
This mathematically proves two interesting new insights! First, that the time effect of acceleration is opposite that of speed, creating a Time Speeding General Relativity effect which opposes the well known Time Dilation effect of speed and Special Relativity. Second, for any satellite in a perfectly circular orbit around a symmetric planet (or star), the time altering effects of the two different Relativitys of speed and acceleration exactly cancel each other out!
It is sad that, today, 2015 and 2016, famous Physicists still get this wrong, and still it is because they totally ignore the consequences of General Relativity. A currently popular showboating move is to take two Cesium clocks, which are lavishly bragged about as incredibly precise and reliable, and first synchronize them. Then one of those atomic clocks is driven up a mountain, and the (allegedly smart) commentator describes how a Relativity time-rate effect causes one of the clocks to "run slower" than the other due to the difference in altitude. Even the "infallible" Stephen Hawking demonstrated sadly poor logic in promoting this claim. A recent TV series by Hawking (Genius) spent half an hour of valuable TV time in presenting this faulty logic and conclusions! There are a bunch of logical errors there! At a location which is a mile higher on a mountain, yes, the gravitational field of the Earth is a tiny bit weaker, which would have a General Relativity time-rate effect, but the person and clock is also circling the center of the Earth FASTER due to having to travel a longer circumference each day, which has a Time Dilation effect due to the higher speed. Hawking (and the others who have presented such public spectacles) never mention that there are actually two Relativistic time effects going on, due to both General and Special Relativity. Since they never even mention the fact that two effects are happening, no one ever does the math (presented here) to show that the two Relativistic time-rate effects happen to exactly counteract each other! I expected a lot more of Hawking. More than that, ALL modern Physicists (including Hawking) have never yet solved Einstein's original set of ten Tensor Riemannian Calculus Differential Equations to discover that the time-rate effects of General and Special Relativity happen to be opposite. They all (wrongly) assume they are the same, all Time Dilation effects. Why doesn't someone at least try to do the math? And so the "major conclusion" that Hawking presented in his mountain experiment is simply not true! He did a one-day experiment and his results were that the two (identical) Cesium clocks were then 20 nano-seconds different where he claimed that "the results confirmed the assumption he had started out having made. " It is a sad aspect of modern science that researchers first make an assumption and then (selectively) do some experiment which seems to confirm that they are right!
By the way, the mountain experiments of Hawking and others are essentially just variants on a theme of the failed 1971 Hafele-Keating experiment in the jet airliners. But at least then, four Cesium clocks were used instead of one. A valid such mountain experiment should run for a month or a year rather than just a single day. And it should be repeated by others who do not carry the same pre-conceived assumptions.
Since 2006, I have tried to get NASA or the ESA to include a Cesium clock in a soft-landing on the Moon. In 2018, the Japan Space Agency (JAXA) intends to launch another soft-lander. Such a simple experiment, where identical Cesium clocks on the Earth and Moon might be continuously compared, will prove once and for all whether Einstein was right about General Relativity. My calculations, based on Einstein, indicate that the Earth clock should count about 10,976 times more ticks every hour than the identical clock on the Moon, entirely due to the difference in our gravitational field strengths on the surface of the Earth and Moon, and on Einstein's General Relativity and the Equivalency Principle. Such a simple and inexpensive experiment would instantly confirm that Einstein was right and it would also demonstrate the logical flaws in the popular assumptions regarding Time Dilation, Hafele-Keating, the Twins Paradox, alleged Time Travel, and other fields of modern Physics.
Physicists use a fairly simple equation to calculate the Time Dilation effect that occurs during Special Relativity, that is, when there is no acceleration but a relatively high constant velocity. This can be due to either the observed light source moving toward the observer or away from the observer (the Time Dilation effect is the same, either way).
Here is the Time Dilation formula factor for time-rate: ß (which is ) This is the multiplying factor of the rate of time that appears to be passing to an observer. (c) represents the speed of light and (v) represents the velocity. If v is in the range of any velocity that we humans are capable of creating, this factor is extremely minimal. This factor (called ß) was discovered by Hendrik Lorentz and George FitzGerald around 130 years ago.
Consider the Earth satellite called the ISS (International Space Station) orbiting at 27,743.8 kilometers per hour, orbiting the Earth every hour and a half. This is 7.7066 kilometers per second. In this case, we would have v = 7.7066 and c = 299,792.458 kilometers per second. ß is then 0.999 999 999 669, which gives us the Time Dilation proportion effect for the ISS satellite due to Special Relativity due to the orbital speed. This is assuming a perfectly circular orbit such that the speed stayed exactly constant, and an Earth that was perfectly spherical, none of which is quite precisely true.
So for an observer on the Earth's surface the satellite might seem to show time passing slightly more slowly than we would measure with our Cesium (atomic) clocks in a lab on Earth. NASA tried to do this experiment during the 1960s by putting an identical Cesium clock inside an orbiting satellite, and compared the time with that of their "Standard" Cesium clock in Washington, DC. Those experiments were all failures, where they always showed greater variation between the various Cesium clocks than the expected Dilation effect!
You might notice that the apparent difference is really minimal! In an entire year, the two clocks (in the ISS as compared to an atomic clock in a Lab on the surface of the Earth) would only have become different by about 1/100 of a second.
The Hafele-Keating experiment, which had Cesium clocks inside conventional airliners, actually had slower speeds (around 900 kph) than our example of a person standing at the Equator, so we will pass on adding those calculations here, although any reader could easily do the math, to see why that NASA experiment failed so dreadfully.
Such experiments did seem to detect slight differences in the rate of time of the Cesium clocks, but the expected Dilation differences were so small that they never exceeded experimental errors! There were two reasons for that. One is that even though Cesium clocks are extremely accurate and reliable, trying to consistently find a difference of less than one part per billion of time is near the limit to the capability of such atomic clocks. The other reason was that NASA seemed to be ignorant of the continuous effects of General Relativity.
In October 1971, NASA installed sets of four Cesium clocks in two passenger airplanes, and sent one of the airplanes westward around the Earth while the other airplane was sent eastward. This experiment was considered very significant, and the Hafele-Keating experiment is still cited as being something important. However, that experiment was really just a sad joke, demonstrating amazing ignorance! The most prominent actual experimental result might have been the significant variation between the set of four allegedly identical Cesium clocks on each aircraft! Given the speed of passenger airliners, the (expected) effect of Time Dilation would have only been around 1/50,000 of a second in a year. And yet the experimental results of the Hafele-Keating experiment showed experimental errors between the individual Cesium clocks which were far greater than what they hoped to find. The 1971 NASA experiment was a total failure!
The other reason is actually far more important. In order for a satellite (or an airliner) to orbit, it must constantly radially accelerate due to the pull of Earth's gravity, to create the curved circular orbital path. You do this when you try to drive around a tight circle, and you feel an acceleration which seems to be pushing you sideways in the seat. We call it centripetal acceleration. Einstein had showed that an entirely different set of Relativity equations are necessary for when accelerations are present, which he called General Relativity. The Special Relativity equations are mathematically simple. The General Relativity equations are horrifically complicated. Einstein presented a set of ten complex Tensor Riemannian Calculus Differential equations, which must be simultaneously solved to get an answer. So far, in a hundred years of countless mathematicians and physicists trying to solve those Tensor Riemannian Calculus equations, no one yet has solved them!
Einstein died in 1955. Around 1960, various groups of physicists decided that they were free to apply speculative assumptions to simplify Einstein's equations, and then they could solve their simplified problem. Unfortunately, the various groups of mathematicians and physicists had made different assumptions (none of which were solidly based on logic!) and so they each got different answers! There is a strong likelihood that ALL of those resulting answers are wrong!
We want to go back to that orbiting ISS satellite and its Cesium clock, to now try to examine the time-rate effects of the centripetal orbital acceleration, which is the time-rate effect of General Relativity.
Here is the factor called the Equivalency Principle in physics. (c) represents the speed of light, 299,792.458 km/s2. (a) represents the local acceleration due to a gravitational field or other source of acceleration. And (d) represents a distance, which is the orbital radius distance in that gravitational field.
Note that the Equivalency Principle is a dimensionless parameter, [m/s2] * [m] / [m2/s2]
It is also true that both the acceleration and the distance happen to be Vector quantities, but both are always along the exact same direction, and so their Vector Product is the same as for Scalar numbers, so their Vector nature is irrelevant here.
The ISS satellite is at 342.2 km altitude plus 6378 km Earth radius or 6720.2 km from the Earth's center and the gravitational acceleration it is subjected to is around 8.827 meters/sec2. This results in the Equivalency Factor for the ISS being 1 + 0.000 000 000 330
This then results in the (perceived) General Relativity time-rate effect on the ISS (as seen from the Earth's surface as) being 1.000 000 000 330 (this is more than 1.0000 so therefore it is a time-rate speeding effect).
I find it fascinating that for the ISS in a circular orbit, the Time Dilation factor for the ISS due to the speed is 0.999 999 999 669, while the Time Speeding factor due to the acceleration, per General Relativity is 1.000 000 000 330
These two time-rate Relativistic effects are both constantly in effect so the two time-rate factors have to be multiplied and they have opposite time-rate effects to each other, where their product is incredibly close to experimentally being exactly 1.000 000 000 net time-rate effect!
Please note that this is a mathematical proof that the two Relativistic time-rate effects exactly cancel each other out (for the person on the ISS), within any conceivable error factor.
We might try to claim that the passengers on the ISS do not detect any acceleration and so we could claim that they were in an Inertial Rest Frame of Reference.
Since the ISS passengers do not feel any acceleration, and they therefore feel that they are in an Inertial Rest Frame of Reference, what do they see when they look down at Earth? They would see the surface of the Earth constantly zooming past their (apparently, to their, stationary) satellite. By all the laws of science, they would see an apparent Time Dilation effect where everyone on Earth would seem to be living and moving slower than they would in their spacecraft!
The Earthbound scientists and their Cesium clocks would detect the apparent Time Dilation time-rate effect on the ISS satellite and its occupants and its clock.
Simultaneously, the scientists on board the ISS and their Cesium clock would detect the apparent Time Dilation time-rate effect on the Earth's surface and its billions of occupants and its Cesium clocks!
If there were not any acceleration due to the orbiting or the rotation of the Earth then, yes, they actually could both see the others as apparently living more slowly than they live! That sounds impossible but it is certainly possible. Special Relativity and its effects are only for straight line flight, no acceleration, where the duration of an encounter would necessarily be rather brief.
For a satellite, which is orbiting and therefore constantly accelerating, that is not possible. In fact, this reasoning proves that the time effects of General Relativity is opposite that of Special Relativity, and the calculations done above for a man standing at the Equator and for a satellite even show that the two opposing time effects exactly cancel each other out. Because of the two time-rate effects, and the fact that they are opposite, the satellite and its passengers could orbit for as long as desired without becoming older or younger than "twin brothers left on Earth!"
That is, for the ISS, the SR Dilation time-rate effect of speed of 0.999 999 999 669 times the GR Speeding time-rate effect of acceleration of 1.000 000 000 330 is exactly unity!
We already showed the math that for a person at the Equator of the Earth, the SR Dilation time-rate effect of speed of 0.999 999 999 998 796 560 times the GR Speeding time-rate effect of acceleration of 1.000 000 000 001 203 440 is exactly 1.000 000 000 000 000 000 within experimental measurement error!
NASA has sent the ISS into a higher orbit recently, so the numbers cited here from NASA are now out-of-date.
Reference was made to the Twins Paradox story of around 1962, which is similar to the example mentioned above. The Twins Paradox is (wrongly) similar in that it assumes no acceleration and therefore, no General Relativity, in order for the Time Dilation effect to seem to be accurate and correct. There were two huge logical errors in the setup of that story. The really obvious one is that they only considered their story from the rest frame of a non-accelerating Earth. The Earth brother would see the spaceship brother appear to be aging more slowly than him. But they overlooked an important fact that Einstein made clear, that anyone in an inertial rest-frame can equally look at the Universe! They overlooked that everything can be looked at from the rest frame of the non-accelerating spaceship. Per Einstein's Special Relativity and Time Dilation, he would certainly see the earthbound brother appear to be aging more slowly than himself. Both of these situations would be occurring simultaneously! They both would see their twin brother as aging more slowly than him! Relativity has some peculiar aspects to it, and this is one of them!
The second huge logical error is that the Twins Paradox story totally ignores the fact that there has to be massive acceleration and deceleration occurring during much, most of such a trip. Given any acceleration rate that humans could survive, the process of getting up to any velocity close to the speed of light, takes a long time, many months, and then many months of deceleration to slow down to an Inertial Rest Frame of Reference on any destination planet. The analysis above shows that the effect of all that acceleration is substantial and it is opposite the Time Dilation effect which does famously appear to occur during the "coasting" (Special Relativity) part of the trip. A very thorough examination of all the true effects show that the Time Speeding effects during the acceleration and deceleration exactly cancel out the Time Dilation effects of the well known Time Dilation time-rate effect during the coasting phase. Any such entire trip (beginning from and ending in the same Inertial Rest Frame of Reference) necessarily has no time paradox at all! A thorough presentation of that analysis is at http://mb-soft.com/public2/twinspar.html The Twins Paradox is Wrong
Carl W. Johnson, Theoretical Physicist, University of Chicago, 1967