It's about time.
Posted: Tue Aug 11, 2020 12:33 pm
As most of you know, I write the occasional article for Philosophy Now. I might have mentioned it, once or twice. Anyway, I sent them another one the other day, so perhaps in a year or so it might get published. In the meantime, here's a preview of the draft I sent in. Even if it is accepted, it's unlikely to go out without a few changes, so feel free to comment/criticise.
It’s about time.
In 1905, Albert Einstein published 4 papers so groundbreaking that 1905 is known as his annus mirabilis; or in English, his miracle year. It was in the third of those papers, which has the unpromising title "On the Electrodynamics of Moving Bodies”, that Einstein introduced the idea for which he is best known - Relativity.
In this article I’m going to concentrate on one of the most famous and most misunderstood predictions of relativity. You might have heard that according to relativity the faster you are going, the slower time passes for you.
So there’s a few elements to that claim which it would help to clarify. There’s the idea that motion affects time and then right at the end there’s the ‘for you’ bit. It’s that last bit which is the essence of relativity, but since it’s the last bit, I want to deal with the time and motion bit first.
On the face of it, it sounds ridiculous; why should the speed you are going at make any difference to how much time passes? Surely time and motion are two completely different things, so how on earth could one affect the other? Weird as it seems though, experiments show that Einstein was right, and the key to making sense of this weirdness is to understand that time and motion aren’t as different as they seem.
Think about a unit of time, a year for example. Because of the way that we use language, we say that the time it takes for the Earth to go around the Sun is one year. That way of saying it tricks us into thinking that there is an amount of time called ‘a year’ and by coincidence, it also happens to be the amount of time that it takes the earth to go around the Sun. But the idea that a year is unit of time that exists independently of the Sun and Earth is misleading, because the Earth going around the Sun is a year. If the earth went round the sun faster or slower, then a year would be different. It might have had fewer or more days in it; but then a day is just the earth spinning once on its axis.
So now we have two units of time to compare: a year and a day. We can say that a year is 365 times longer than a day. Which again reinforces this idea that time is something other than motion, but all we are actually measuring at this scale is the Earth spinning slightly more than 365 times as it makes one orbit of the sun - there’s nothing abstract there at all; no universal or objective ‘time’.
Now, that’s the sort of time we measure on a calendar. But of course there is also the sort of time we measure on a clock. Hours, minutes and seconds. None of these units correspond to any particular natural event that happens regularly in the way that days and years do. Hours, minutes and seconds are simply a day divided into smaller and smaller units, so they’re basically mathematical things; fractions of a day.
In order for a clock to work, it has to be able to count regular events which only take a small fraction of a day. A major breakthrough happened when Galileo Galilei noticed that if the chandelier in the Cathedral of Padua was swinging a lot it moved fast, and if it was only swinging a little bit, then it moved slowly. What Galileo discovered was that no matter how much the chandelier swung, it always took the same time. The story is that Galileo used his own heartbeat to time the chandelier, but as with days and years, it’s not directly time that is being measured, Galileo was counting the number of heartbeats per swing.
Using his discovery, Galileo designed a pendulum clock. In fact, being old and blind he had to describe the design to his son Vincenzo, who did the actual drawing. They even started to make a clock, but they both died before it was completed. Even so, clocks based on the same principle were the most accurate clocks until electronic clocks were invented in the 1930’s. These days atomic clocks are accurate to within a second every few hundred million years. So no excuses for being late.
In effect an atomic clock works by shining light on an atom and counting the number of times it absorbs and emits photons; which are little bundles of light. Time is defined by this effect. A second is, and I quote: "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom”
So when you are doing something like boiling an egg you do so for about the duration of 300 billion periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom, depending on how you like your eggs. Or about 5 minutes, which is a lot easier to say, but however you time your egg, you will be counting things that are moving.
To return to the point: clocks don’t directly measure any such thing as time, fundamentally they are counting devices and to all intents and purposes the practical definition of time is ‘what clocks measure’.
That’s time and motion; onto the ‘for you’ bit. As I said, that is the basis of relativity and, wouldn’t you know it, it’s Galileo again.
You may know that Galileo was involved in a controversy about whether the Earth is moving or not. The fact that he refused to say the Earth is motionless got him into trouble with the Vatican. Leaving aside the politics and theology, the scientific argument for a stationary earth went back almost 2000 years to Aristotle in Ancient Greece. Aristotle pointed out that if you drop a stone, it lands at your feet and he reasoned that if the earth were moving, then if you dropped a stone, it would land as far from your feet as the earth had moved in the time it took the stone to fall. Now intuitively that makes a lot of sense.
Since Galileo was convinced the Earth is moving, he had to demonstrate that stones would nevertheless fall straight down. What he did was point out that if you are on a ship that is moving smoothly, it feels exactly the same as if it were docked and in fact everything happens exactly as if the ship were stationary. Everyone is familiar with this effect. Whether you are in a car doing 50mph, a train doing a 100mph or an aeroplane doing 500mph, if you drop a stone it falls at your feet. For you, the stone falls straight down.
However, someone watching you go past sees something different. Suppose I’m on the platform as you drop a stone on a moving train. We both agree that the stone falls a certain height, but while as far as you are concerned the stone falls vertically, to me on the platform, it has also moved horizontally. How the train is moving relative to the person watching the stone drop, changes what they see.
So, you might ask, how is the stone really moving? Fair enough. Well, the stone is on a moving train, but the train is on Earth, and Earth is spinning as it orbits the sun, and the sun is in a galaxy that is cartwheeling through the universe, and that universe is expanding. All of that movement makes it impossible to work out how the stone is actually moving - there is no absolute measure, no signpost relative to which everything else is moving. All you can do is pick a point and say how the stone is moving relative to that point.
No matter how fast you are going, so long as it smoothly: no accelerating, no braking and no going around bends, if you drop a stone, it will fall at your feet. Inside your bubble, be it a car, train or plane, absolutely everything looks exactly the same whether you are moving or not. And that is Galileo’s Principle of Relativity.
In the late 19th century, it was thought there might be an exception to this rule; and it is a possibility that intrigued a certain Albert Einstein. Earlier in the century, the Scottish physicist James Clark Maxwell had shown that the speed of light is roughly 186 000 miles per second. Which is fast enough to go round the world more than 7 times - in one second.
But suppose for the sake of argument you have a spaceship that can travel at the speed of light. You also have a mirror that you hold in front you, in the direction the spaceship is moving. The question is what would happen to your reflection? What normally happens is that light is reflected off your face, onto the mirror which then reflects the light back into your eyes and you see your image in the mirror.
Now light, not surprisingly, travels at the speed of light. So if your spaceship is travelling at the speed of light, the light reflected off your face would have to travel faster than the speed of light to reach the mirror. But it is light, and it travels at the speed of light, so it’s not going to reach the mirror, and in theory, the image, your reflection, should disappear.
So what? Well, it means that there is an instance of smooth travelling in which things look different, so Galileo’s principle of relativity would be broken. Most people would think, ‘Hm, so there’s an exception. Oh well.’ Einstein however, wondered what you would have to do to preserve the Principle of Relativity. The obvious suggestion is to say that the speed of light isn’t fixed, but one of the premises of Special Relativity is that the speed of light is as fast as anything can go. So, another approach is to say what if the reflection does disappear, but you don't notice?
Well, your not going to miss something like your reflection disappearing, except perhaps if you are frozen in time. Which sounds like gobbledygook. But Einstein did the maths and it all added up. Fortunately for those of us who aren’t great at maths, he also explained how it could be demonstrated using a thought experiment.
To do that, he came up with the idea of a light clock. Like all clocks, Einstein’s light clock counts things which are moving. What he imagined were two mirrors one above the other, arranged so that a pulse of light would bounce up and down between them and those bounces could be counted.
Just as with dropping a stone, if you have a light clock with you in your car, on a train or aeroplane, as far as you are concerned, the pulse of light bounces vertically up and down. But to someone watching you go past, the pulse of light travels a bit horizontally as well, so the overall path is diagonal. In other words, the pulse of light has to travel further between the mirrors. And the faster the vehicle is going, the further the light has to travel, which means the longer it takes to bounce between the mirrors.
The result is that the light clock ticks slower and slower as you accelerate, until in your hypothetical light speed spaceship the pulse of light stops bouncing between the mirrors altogether, because the light is going as fast as it can in the same direction as the spaceship. As far as a clock on the space ship is concerned, time has stopped.
So why wouldn't you notice? How is Galileo’s Principle of Relativity preserved? Well, the speed of light is as fast as anything can go. And just as the light in the light clock is going as fast as it can in the same direction as the spaceship, every atom in your body is doing the same, so there’s no interaction between the atoms and molecules in your body - no biological processes, no mental processes - your body doesn’t age and your brain doesn’t think. There’s no image of you in the mirror, and you don’t even know it. For you time stops.
What about for everyone else though? Well, time passes for them at a rate that is dependent on how fast they are moving compared to the speed of light. But remember, however fast you are moving, it feels the same as if you were standing still. Stones fall at your feet and the pulse of light in your light clock bounces straight up and down. It is everyone else who, relative to you, is moving. And that has an apparently paradoxical consequence.
Suppose when you dropped a stone as I watched from the platform that I too had dropped a stone. Now we intuitively feel that it is you on the train that is moving, but imagine your train is heading off into the sunset. So relative to me stuck on the platform, you are moving due west. But as you rattle along, the Sun is still going down and that’s because the Earth is spinning eastwards faster than you are moving westwards, so relative to the Sun, you are moving eastwards. Just not quite as fast as me.
Back in the railway station, how we are moving relative to the sun has no effect on how we see each other’s stone falling, we both see the other’s stone move horizontally by exactly the same amount. And the same is true about our light clocks, we both see each others pulse of light move horizontally, and therefore, weirdly, we both see each others clock tick more slowly. If we never get to compare our clocks, we would never know who had been travelling the faster; and if the train carries on in a straight line, it will never get back to the station. But, you might say, if the train keeps heading west, it will eventually get back to where it started. True, but it will have gone around the world. In other words, not in a straight line
So Imagine that your train is going round in a circle, in the middle of which is me with my light clock. In that case you would see my pulse of light bounce straight up and down. I on the other hand would still see your pulse of light move horizontally, so I would see your clock ticking slower than my clock, which means you would see my clock tick faster than yours. But going round in circles isn’t the smooth motion of special relativity, so no rules are broken; and in fact experiments confirm that time does slow down the faster you are going, although to be clear, we should remember that strictly speaking, clocks tick fewer times the faster they are going.
In 1971, scientists Joseph Hafele and Richard Keating, conducted a simple demonstration. They got some atomic clocks, put them on a commercial jet liner, and flew them round the world twice. Once heading eastwards and once westwards. When they compared their clocks with a clock that stayed on the ground, they showed different times. When the clocks flew eastwards, they lost time compared to the clock on the ground, whereas when they flew westwards they gained time. Which sounds crazy, but it’s the same effect as when you are riding into the sunset.
In the Hafele-Keating experiment, when the clocks flew westwards, they were still moving east relative to the sun, but not as much as the clock on the ground, and even less compared to when the clocks flew eastwards. So rather than thinking that the clocks flying westwards gained time and those flying east lost time, it’s slightly less mind bending to think that compared to when the clocks flew westwards the clock on the ground lost time, and that when they flew eastwards, they lost even more time.
So it has been shown that clocks really do slow down the faster they are moving. So do all the processes that give rise to life and consciousness which, somewhat metaphorically, we can describe as time slowing down. Why then did it take until 1971 for someone to prove it? Well, even at 500mph, about the speed of a commercial jet, the effect is tiny. Think about that stone falling. Suppose it falls for half a second. At 500mph in half a second the plane will have flown a little over a hundred metres, so to someone watching from outside the plane, the diagonal path of the falling stone is very clear. However, in that same half a second, the light pulse will have travelled 93 thousand miles, so instead of there being one very obviously diagonal path, as for the stone, the beam of light will have bounced up and down hundreds of millions of times, so the amount the plane has moved forward for each bounce is a fraction of a millimetre; so the extra distance the pulse of light has to travel is tiny, hence the slowing of the clock is tiny. Despite flying all the way round the world, the results of the Hafele-Keating experiment were measured in nanoseconds, billionths of a second. But when you have clocks which are accurate to within a second every few hundred million years, that’s not a problem.
One of the things that is most often misunderstood about Special Relativity is that it is about what you see, rather than what really is the case. Remember that no one can tell how things are actually moving, all that anyone can say is how much something is moving relative to a point of their choosing. And while it is only relative to that point that we can tell that time is moving faster or slower, it is a demonstrable fact that time really is affected by speed. Just as Einstein predicted
It’s about time.
In 1905, Albert Einstein published 4 papers so groundbreaking that 1905 is known as his annus mirabilis; or in English, his miracle year. It was in the third of those papers, which has the unpromising title "On the Electrodynamics of Moving Bodies”, that Einstein introduced the idea for which he is best known - Relativity.
In this article I’m going to concentrate on one of the most famous and most misunderstood predictions of relativity. You might have heard that according to relativity the faster you are going, the slower time passes for you.
So there’s a few elements to that claim which it would help to clarify. There’s the idea that motion affects time and then right at the end there’s the ‘for you’ bit. It’s that last bit which is the essence of relativity, but since it’s the last bit, I want to deal with the time and motion bit first.
On the face of it, it sounds ridiculous; why should the speed you are going at make any difference to how much time passes? Surely time and motion are two completely different things, so how on earth could one affect the other? Weird as it seems though, experiments show that Einstein was right, and the key to making sense of this weirdness is to understand that time and motion aren’t as different as they seem.
Think about a unit of time, a year for example. Because of the way that we use language, we say that the time it takes for the Earth to go around the Sun is one year. That way of saying it tricks us into thinking that there is an amount of time called ‘a year’ and by coincidence, it also happens to be the amount of time that it takes the earth to go around the Sun. But the idea that a year is unit of time that exists independently of the Sun and Earth is misleading, because the Earth going around the Sun is a year. If the earth went round the sun faster or slower, then a year would be different. It might have had fewer or more days in it; but then a day is just the earth spinning once on its axis.
So now we have two units of time to compare: a year and a day. We can say that a year is 365 times longer than a day. Which again reinforces this idea that time is something other than motion, but all we are actually measuring at this scale is the Earth spinning slightly more than 365 times as it makes one orbit of the sun - there’s nothing abstract there at all; no universal or objective ‘time’.
Now, that’s the sort of time we measure on a calendar. But of course there is also the sort of time we measure on a clock. Hours, minutes and seconds. None of these units correspond to any particular natural event that happens regularly in the way that days and years do. Hours, minutes and seconds are simply a day divided into smaller and smaller units, so they’re basically mathematical things; fractions of a day.
In order for a clock to work, it has to be able to count regular events which only take a small fraction of a day. A major breakthrough happened when Galileo Galilei noticed that if the chandelier in the Cathedral of Padua was swinging a lot it moved fast, and if it was only swinging a little bit, then it moved slowly. What Galileo discovered was that no matter how much the chandelier swung, it always took the same time. The story is that Galileo used his own heartbeat to time the chandelier, but as with days and years, it’s not directly time that is being measured, Galileo was counting the number of heartbeats per swing.
Using his discovery, Galileo designed a pendulum clock. In fact, being old and blind he had to describe the design to his son Vincenzo, who did the actual drawing. They even started to make a clock, but they both died before it was completed. Even so, clocks based on the same principle were the most accurate clocks until electronic clocks were invented in the 1930’s. These days atomic clocks are accurate to within a second every few hundred million years. So no excuses for being late.
In effect an atomic clock works by shining light on an atom and counting the number of times it absorbs and emits photons; which are little bundles of light. Time is defined by this effect. A second is, and I quote: "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom”
So when you are doing something like boiling an egg you do so for about the duration of 300 billion periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom, depending on how you like your eggs. Or about 5 minutes, which is a lot easier to say, but however you time your egg, you will be counting things that are moving.
To return to the point: clocks don’t directly measure any such thing as time, fundamentally they are counting devices and to all intents and purposes the practical definition of time is ‘what clocks measure’.
That’s time and motion; onto the ‘for you’ bit. As I said, that is the basis of relativity and, wouldn’t you know it, it’s Galileo again.
You may know that Galileo was involved in a controversy about whether the Earth is moving or not. The fact that he refused to say the Earth is motionless got him into trouble with the Vatican. Leaving aside the politics and theology, the scientific argument for a stationary earth went back almost 2000 years to Aristotle in Ancient Greece. Aristotle pointed out that if you drop a stone, it lands at your feet and he reasoned that if the earth were moving, then if you dropped a stone, it would land as far from your feet as the earth had moved in the time it took the stone to fall. Now intuitively that makes a lot of sense.
Since Galileo was convinced the Earth is moving, he had to demonstrate that stones would nevertheless fall straight down. What he did was point out that if you are on a ship that is moving smoothly, it feels exactly the same as if it were docked and in fact everything happens exactly as if the ship were stationary. Everyone is familiar with this effect. Whether you are in a car doing 50mph, a train doing a 100mph or an aeroplane doing 500mph, if you drop a stone it falls at your feet. For you, the stone falls straight down.
However, someone watching you go past sees something different. Suppose I’m on the platform as you drop a stone on a moving train. We both agree that the stone falls a certain height, but while as far as you are concerned the stone falls vertically, to me on the platform, it has also moved horizontally. How the train is moving relative to the person watching the stone drop, changes what they see.
So, you might ask, how is the stone really moving? Fair enough. Well, the stone is on a moving train, but the train is on Earth, and Earth is spinning as it orbits the sun, and the sun is in a galaxy that is cartwheeling through the universe, and that universe is expanding. All of that movement makes it impossible to work out how the stone is actually moving - there is no absolute measure, no signpost relative to which everything else is moving. All you can do is pick a point and say how the stone is moving relative to that point.
No matter how fast you are going, so long as it smoothly: no accelerating, no braking and no going around bends, if you drop a stone, it will fall at your feet. Inside your bubble, be it a car, train or plane, absolutely everything looks exactly the same whether you are moving or not. And that is Galileo’s Principle of Relativity.
In the late 19th century, it was thought there might be an exception to this rule; and it is a possibility that intrigued a certain Albert Einstein. Earlier in the century, the Scottish physicist James Clark Maxwell had shown that the speed of light is roughly 186 000 miles per second. Which is fast enough to go round the world more than 7 times - in one second.
But suppose for the sake of argument you have a spaceship that can travel at the speed of light. You also have a mirror that you hold in front you, in the direction the spaceship is moving. The question is what would happen to your reflection? What normally happens is that light is reflected off your face, onto the mirror which then reflects the light back into your eyes and you see your image in the mirror.
Now light, not surprisingly, travels at the speed of light. So if your spaceship is travelling at the speed of light, the light reflected off your face would have to travel faster than the speed of light to reach the mirror. But it is light, and it travels at the speed of light, so it’s not going to reach the mirror, and in theory, the image, your reflection, should disappear.
So what? Well, it means that there is an instance of smooth travelling in which things look different, so Galileo’s principle of relativity would be broken. Most people would think, ‘Hm, so there’s an exception. Oh well.’ Einstein however, wondered what you would have to do to preserve the Principle of Relativity. The obvious suggestion is to say that the speed of light isn’t fixed, but one of the premises of Special Relativity is that the speed of light is as fast as anything can go. So, another approach is to say what if the reflection does disappear, but you don't notice?
Well, your not going to miss something like your reflection disappearing, except perhaps if you are frozen in time. Which sounds like gobbledygook. But Einstein did the maths and it all added up. Fortunately for those of us who aren’t great at maths, he also explained how it could be demonstrated using a thought experiment.
To do that, he came up with the idea of a light clock. Like all clocks, Einstein’s light clock counts things which are moving. What he imagined were two mirrors one above the other, arranged so that a pulse of light would bounce up and down between them and those bounces could be counted.
Just as with dropping a stone, if you have a light clock with you in your car, on a train or aeroplane, as far as you are concerned, the pulse of light bounces vertically up and down. But to someone watching you go past, the pulse of light travels a bit horizontally as well, so the overall path is diagonal. In other words, the pulse of light has to travel further between the mirrors. And the faster the vehicle is going, the further the light has to travel, which means the longer it takes to bounce between the mirrors.
The result is that the light clock ticks slower and slower as you accelerate, until in your hypothetical light speed spaceship the pulse of light stops bouncing between the mirrors altogether, because the light is going as fast as it can in the same direction as the spaceship. As far as a clock on the space ship is concerned, time has stopped.
So why wouldn't you notice? How is Galileo’s Principle of Relativity preserved? Well, the speed of light is as fast as anything can go. And just as the light in the light clock is going as fast as it can in the same direction as the spaceship, every atom in your body is doing the same, so there’s no interaction between the atoms and molecules in your body - no biological processes, no mental processes - your body doesn’t age and your brain doesn’t think. There’s no image of you in the mirror, and you don’t even know it. For you time stops.
What about for everyone else though? Well, time passes for them at a rate that is dependent on how fast they are moving compared to the speed of light. But remember, however fast you are moving, it feels the same as if you were standing still. Stones fall at your feet and the pulse of light in your light clock bounces straight up and down. It is everyone else who, relative to you, is moving. And that has an apparently paradoxical consequence.
Suppose when you dropped a stone as I watched from the platform that I too had dropped a stone. Now we intuitively feel that it is you on the train that is moving, but imagine your train is heading off into the sunset. So relative to me stuck on the platform, you are moving due west. But as you rattle along, the Sun is still going down and that’s because the Earth is spinning eastwards faster than you are moving westwards, so relative to the Sun, you are moving eastwards. Just not quite as fast as me.
Back in the railway station, how we are moving relative to the sun has no effect on how we see each other’s stone falling, we both see the other’s stone move horizontally by exactly the same amount. And the same is true about our light clocks, we both see each others pulse of light move horizontally, and therefore, weirdly, we both see each others clock tick more slowly. If we never get to compare our clocks, we would never know who had been travelling the faster; and if the train carries on in a straight line, it will never get back to the station. But, you might say, if the train keeps heading west, it will eventually get back to where it started. True, but it will have gone around the world. In other words, not in a straight line
So Imagine that your train is going round in a circle, in the middle of which is me with my light clock. In that case you would see my pulse of light bounce straight up and down. I on the other hand would still see your pulse of light move horizontally, so I would see your clock ticking slower than my clock, which means you would see my clock tick faster than yours. But going round in circles isn’t the smooth motion of special relativity, so no rules are broken; and in fact experiments confirm that time does slow down the faster you are going, although to be clear, we should remember that strictly speaking, clocks tick fewer times the faster they are going.
In 1971, scientists Joseph Hafele and Richard Keating, conducted a simple demonstration. They got some atomic clocks, put them on a commercial jet liner, and flew them round the world twice. Once heading eastwards and once westwards. When they compared their clocks with a clock that stayed on the ground, they showed different times. When the clocks flew eastwards, they lost time compared to the clock on the ground, whereas when they flew westwards they gained time. Which sounds crazy, but it’s the same effect as when you are riding into the sunset.
In the Hafele-Keating experiment, when the clocks flew westwards, they were still moving east relative to the sun, but not as much as the clock on the ground, and even less compared to when the clocks flew eastwards. So rather than thinking that the clocks flying westwards gained time and those flying east lost time, it’s slightly less mind bending to think that compared to when the clocks flew westwards the clock on the ground lost time, and that when they flew eastwards, they lost even more time.
So it has been shown that clocks really do slow down the faster they are moving. So do all the processes that give rise to life and consciousness which, somewhat metaphorically, we can describe as time slowing down. Why then did it take until 1971 for someone to prove it? Well, even at 500mph, about the speed of a commercial jet, the effect is tiny. Think about that stone falling. Suppose it falls for half a second. At 500mph in half a second the plane will have flown a little over a hundred metres, so to someone watching from outside the plane, the diagonal path of the falling stone is very clear. However, in that same half a second, the light pulse will have travelled 93 thousand miles, so instead of there being one very obviously diagonal path, as for the stone, the beam of light will have bounced up and down hundreds of millions of times, so the amount the plane has moved forward for each bounce is a fraction of a millimetre; so the extra distance the pulse of light has to travel is tiny, hence the slowing of the clock is tiny. Despite flying all the way round the world, the results of the Hafele-Keating experiment were measured in nanoseconds, billionths of a second. But when you have clocks which are accurate to within a second every few hundred million years, that’s not a problem.
One of the things that is most often misunderstood about Special Relativity is that it is about what you see, rather than what really is the case. Remember that no one can tell how things are actually moving, all that anyone can say is how much something is moving relative to a point of their choosing. And while it is only relative to that point that we can tell that time is moving faster or slower, it is a demonstrable fact that time really is affected by speed. Just as Einstein predicted
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