@"gordi", @"Bally002", and @"Sol" have the right answers, from the viewpoint of Relativity. If we assume Relativity to be a correct theory, and we assume time dilation to be a real thing, then the results are different relative to the observer's viewpoint. If we change observers, then we also change the viewpoint, and by extension the results.
From our viewpoint, as Observer 1, 2.5 billion years pass, the photon is travelling for that 2.5 billion years, and is no longer "there" if it is "here".
From the viewpoint of the photon, as Observer 2, no time passes, and it is neither "there" nor "here", is simply "is", location is irrelevant, as it does not experience any time passing, so it cannot have moved at all. Velocity is change of position over time. If you take time out of the equation, then a change of position is irrelevant.
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Einstein's so called "Twins paradox" has never been a paradox to me, and I don't understand why it is to anyone. It was a "thought experiment" that seems to me to not have been thought through to it's logical conclusion.
If we take two twins, and launch one into space at light speed, but leave the other on Earth, then the one moving away at light speed APPEARS, from the Earth bound observer's viewpoint, not to be aging as he moves away. That is because the light reaching the observer is moving toward the observer at the same sped that the other twin is moving AWAY from him. So the Earth observer sees the same image continually, which is not aging.
The same is true of the twin moving at light speed - Earth seems to not be aging even though he IS, because he is riding the same light wave he was riding when he left Earth, and that image, for him, will not change. If he were to surpass the speed of light, he could then see his launch, and eventually his own birth as he successively passed the light from those events. Earth would appear to be going backwards in time, from his viewpoint.
So far so good, but the "paradox" comes in when they say that the traveling twin would return to an Earth many centuries in his future, and that's where it goes off the rails. If the traveling twin reverses course and starts back to Earth, then he will be passing outbound light from Earth as he travels inward at the speed of light, so everything will appear to him to be moving at an accelerated pace, faster than it is actually happening. In other words, what appeared to him on the outbound trip to be frozen in time, will be made up for by accelerated observation on the way back. It does not follow that time is actually changing, only that what he SEES is accelerated. he would arrive back in proper time factoring in his travel time, rather than the rate light travels at. The light travel only affects his observation, NOT his actual chronology.
Both twins would age at the same rate. The only difference would be in their perception of the light.
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E=MC^2 is a formula for energy, not time. What it means is that as your velocity increases, your apparent mass also increases to the point that you can no longer pack enough energy in to accelerate any further. As you apparent mass increases towards infinity, so does the amount of energy required to accelerate you, and you eventually reach a point where there is not enough energy in the universe to accelerate you any further, and velocity levels out with no further acceleration. That speed is supposed to be the speed of light, which is why light speed is considered to be the universal speed limit.
That's why FTL travel would have to find a loophole, like bending space so that less space is crossed in a given time frame, thereby giving only the appearance of FTL travel without having to use up all of the energy in the universe to actually try to do it. From the traveler's viewpoint, less space is being crossed to get to the destination, so that he's not violating that physical law - space is being "compressed", which makes it appear that the traveler is moving faster than he really is traveling to an observer on the outside of his system.
Space can be manipulated like that at the quantum level. It's complicated, and involves "quantum entanglement", but it's the reason "spooky action at a distance" is a thing.
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From our viewpoint, as Observer 1, 2.5 billion years pass, the photon is travelling for that 2.5 billion years, and is no longer "there" if it is "here".
From the viewpoint of the photon, as Observer 2, no time passes, and it is neither "there" nor "here", is simply "is", location is irrelevant, as it does not experience any time passing, so it cannot have moved at all. Velocity is change of position over time. If you take time out of the equation, then a change of position is irrelevant.
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Einstein's so called "Twins paradox" has never been a paradox to me, and I don't understand why it is to anyone. It was a "thought experiment" that seems to me to not have been thought through to it's logical conclusion.
If we take two twins, and launch one into space at light speed, but leave the other on Earth, then the one moving away at light speed APPEARS, from the Earth bound observer's viewpoint, not to be aging as he moves away. That is because the light reaching the observer is moving toward the observer at the same sped that the other twin is moving AWAY from him. So the Earth observer sees the same image continually, which is not aging.
The same is true of the twin moving at light speed - Earth seems to not be aging even though he IS, because he is riding the same light wave he was riding when he left Earth, and that image, for him, will not change. If he were to surpass the speed of light, he could then see his launch, and eventually his own birth as he successively passed the light from those events. Earth would appear to be going backwards in time, from his viewpoint.
So far so good, but the "paradox" comes in when they say that the traveling twin would return to an Earth many centuries in his future, and that's where it goes off the rails. If the traveling twin reverses course and starts back to Earth, then he will be passing outbound light from Earth as he travels inward at the speed of light, so everything will appear to him to be moving at an accelerated pace, faster than it is actually happening. In other words, what appeared to him on the outbound trip to be frozen in time, will be made up for by accelerated observation on the way back. It does not follow that time is actually changing, only that what he SEES is accelerated. he would arrive back in proper time factoring in his travel time, rather than the rate light travels at. The light travel only affects his observation, NOT his actual chronology.
Both twins would age at the same rate. The only difference would be in their perception of the light.
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E=MC^2 is a formula for energy, not time. What it means is that as your velocity increases, your apparent mass also increases to the point that you can no longer pack enough energy in to accelerate any further. As you apparent mass increases towards infinity, so does the amount of energy required to accelerate you, and you eventually reach a point where there is not enough energy in the universe to accelerate you any further, and velocity levels out with no further acceleration. That speed is supposed to be the speed of light, which is why light speed is considered to be the universal speed limit.
That's why FTL travel would have to find a loophole, like bending space so that less space is crossed in a given time frame, thereby giving only the appearance of FTL travel without having to use up all of the energy in the universe to actually try to do it. From the traveler's viewpoint, less space is being crossed to get to the destination, so that he's not violating that physical law - space is being "compressed", which makes it appear that the traveler is moving faster than he really is traveling to an observer on the outside of his system.
Space can be manipulated like that at the quantum level. It's complicated, and involves "quantum entanglement", but it's the reason "spooky action at a distance" is a thing.
.
Diogenes was eating bread and lentils for supper. He was seen by the philosopher Aristippus, who lived comfortably by flattering the king.
Said Aristippus, ‘If you would learn to be subservient to the king you would not have to live on lentils.’ Said Diogenes, ‘Learn to live on lentils and you will not have to be subservient to the king.’
Said Aristippus, ‘If you would learn to be subservient to the king you would not have to live on lentils.’ Said Diogenes, ‘Learn to live on lentils and you will not have to be subservient to the king.’