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From my very limited understanding of relativity, as a person or an object travels closer to the speed of light, more and more time dilation is experienced. An object of positive mass can never reach the speed of light as it require infinite energy, and if somehow you can travel faster than time, you would actually travel back in time.
Even in fictions, we are familiar with stories of young astronauts returning from space after traveling close to the speed of light for a year, only to step out of their spaceships to be confronted by their great-great-grand children.
Superficially simple stuff right? I thought so too for 20 or so years. Then yesterday during a bout of insomnia, I imagined a scenario that was impossible to reconcile with my current understanding.
Scenario:
Flash (the super fast superhero, aka the cyborg BW God) challenges you to a 100m sprint. For some arrogant or academic reason, you glad accept.
Assumptions:
1. You run at a humanly feasible speed of 35km/h, or about 10m/s.
2. Flash runs at 299 792 457.9999999999...m/s, or roughly 0.000000000...1m/s slower than the speed of light which is theoretically perfectly achievable. Let's say that he is so fast that he experiences such massive time dilation that 1 second he experiences at his high velocity would equal 1 trillion years you would experience relatively.
3. You and Flash are somehow able to start moving at the exact same time, and Flash accelerates to his top speed so fast that it can be safely neglected as an variable.
Result (common sense):
Common sense tells us that just like shining a flashlight at a wall 100m away, from your point of view Flash should cross 100m pretty much instantly (should take him ~ 0.00000003 seconds). From Flash's point of view, he cross the finish line almost instantly and then waits for you for ~10 seconds as you sprint. Just like turning on a flashlight and running after it, so far so good.
Result (according to relativity and fiction):
This is where things get a little murky. From Flash's own perspective, he still reaches the finish line in 0.0000003 seconds. Nothing changes for himself, time dilation is only relative to another reference object. However, the question is how would YOU perceive him?
1. Is your perception of Flash the same as in the case of common sense (you see him reach the finish line in 0.0000003 seconds)?
2. Or because 1 second of Flash's time equals 1 trillion years of your time relatively, would you witness a Flash that crosses the finish line 30000 years later (1 trillion * 0.00000003 = 30000)?
The common sense scenario #1 holds value in my mind because of what I know happens when I race with a light source.
However, scenario #2 should happen according to what happens in fiction and relativity.
What are the objects of reference here? What would really happen? How is this "as you approach the speed of light you actually 'slow down'" paradox reconciled?
Man wish I had some DMT right now.
 
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I'm pretty sure the relevant detail is that Flash Decelerates at the end of the dash. If he kept going at those relativistic speeds, he wouldn't see you move until EONS later.
Disclaimer: not a physics major.
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I have very limited understanding also....
1 second of flash's time equals 1 trillion years your time from flash's perspective only when viewing the other runner. If flash kept running until you finished, to him it would be 1 trillion years. He stops though after 0.0000003 seconds and goes back to seeing you just take the 10 seconds.
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TLADT24920 Posts
"Flash that crosses the finish line 30000 years later (1 trillion * 0.00000003 = 30000)?". I think you meant Flash sees him cross the finish line that much later or did I misread? lol.
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Why would him stopping at the finish line have an effect on what happens during those 0.00000003 seconds? Analogous to the astronaut from space fiction example, the astronaut too "stops" after a traveling at high speeds for a year, but bam, 150 years have passed on earth.
Similarly, because Flash is traveling a LOT faster than the spaceship (pretty much just below the speed of light at 299 792 457.9999999999...m/s), the 0.00000003 seconds he experiences is a FUCKTON of time in relative terms. I already made the assumption that accleration and deceleration can be safely ignored as variables, so at t = 0.000000015 seconds, Flash is at the midpoint or the 50m mark of the racetrack. At this point in time, Flash is still traveling at insane relativistic speeds, while you have barely moved at all, so relatively when viewing the runner Flash is experiencing time dilation just as the astronaut on the spaceship was experiencing, albeit on a much larger scale.
TL;DR: I don't see how stopping/deceleration is relevant to what happens DURING the 0.00000003 seconds of traveling time for Flash.
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Or it could be that you see Flash cross the finish line in 30 nanoseconds (or whatever it is in scenario 1), but to Flash the time is 1 trillion times shorter because of distance contraction (your 100m is tiny in his reference frame).
I don't know what is the right answer, but one thing I remember from my relativity lectures is that simultaneity is also relative.
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On May 18 2014 01:32 BigFan wrote:
"Flash that crosses the finish line 30000 years later (1 trillion * 0.00000003 = 30000)?". I think you meant Flash sees him cross the finish line that much later or did I misread? lol.
You didn't misread.
If Flash kept going at his speeds then yes, he would see you cross the finish line 30000 years later.
BUT... he stops at the finish line. What happens DURING the 0.00000003 seconds it takes Flash to travel to the finish line?
Remember, since Flash is so close to the speed of light, that even 0.00000003 seconds is a very long time. Just as the fiction spaceship example, after 0.00000001 second Flash is the 33.33m of the racetrack, or that 10000 years have passed on earth when he "returns" to earth (stops at the finish line).
What am I missing here?
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Stopping only matters because a year going near light speed is going to produce a lot more time dialation then 0.00000003 seconds of it. I think? haha
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On May 18 2014 01:45 calh wrote:
Or it could be that you see Flash cross the finish line in 30 nanoseconds (or whatever it is in scenario 1), but to Flash the time is 1 trillion times shorter because of distance contraction (your 100m is tiny in his reference frame).
I don't know what is the right answer, but one thing I remember from my relativity lectures is that simultaneity is also relative.
Could you elaborate on that please, especially the distance contraction part?
so are you saying to Flash it would seem that he actually crosses 100m in 30/1 trillion nanoseconds? I can't seem to wrap my head around that concept, especially since speed is constant? Or is it?
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Netherlands6188 Posts
10m/s is only humanly feasible if you're Usain Bolt. Just sayin'.
+ Show Spoiler +I'm also just kidding, we had two guys in highschool who were only a few fractions of a second slower than him. Pretty sure there are many more people out there that fast.
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I think because of distance contraction at that speed the 100m is like calh said, looks 1 trillion times shorter to Flash. To him he would be barley taking a step forward to cross the finish line.
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On May 18 2014 01:54 Dizmaul wrote:
Stopping only matters because a year going near light speed is going to produce a lot more time dialation then 0.00000003 seconds of it. I think? haha
See that was my point; of course that would be true if speed is constant in both cases, but it is not. Flash is experiencing a LOT more time dilation than the astronaut on the spaceship, because he is traveling at speeds so much closer to light than the spaceship, so even 0.00000003 seconds of Flash traveling at his insane speeds produces MORE time dilation.
Remember we're working with infinity here; the spaceship is travel really fast at 299 792 457m/s, or just 1 m/s under the speed of light, producing time dilation of 1 year = 150 years, BUT for Flash, he is traveling at 299 792 457.9999999999...m/s (there is no limit as to how CLOSE Flash can get to the speed of light, implying there is no limit as to the amount of time dilation he would experience.
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I think you need to think about it the other way around. When the people on earth have waited 150 years for the astronaut, They would tell you they have only been in there ship 1 year because of there speed. So if you "wait" for flash to cross the finish line it was 0.00000003 seconds for you. For him it would be even less time.
The more I think about it when you say it took Flash 0.00000003 seconds to cross the finish line that's what you would say. Flash because he is going so fast he would tell you it was a fraction of that time. If you did a race where, to us it took Flash 30000 years to cross the finish line. (1 trillion * 0.00000003 = 30000). To him it would of only been 0.00000003 seconds, what we see him do in the 100m.
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On May 18 2014 02:11 Dizmaul wrote:
I think you need to think about it the other way around. When the people on earth have waited 150 years for the astronaut, They would tell you they have only been in there ship 1 year because of there speed. So if you "wait" for flash to cross the finish line it was 0.00000003 seconds for you. For him it would be even less time.
Wait if it's 0.00000003 seconds for me, then it would be only 0.00000003/1 trillion seconds for Flash, and since distance is constant at 100m, somehow flash was able to travel at 1 trillion times the speed of light? I mean Distance / time = speed, so if distance doesn't change, and time is shortened to 1/1 trillionth, the only thing left is speed right? Which has increased by 1 trillion times?
Also, since we always talk about the speed of light and not velocity, let's say that a tiny person traveling in a ship close to the speed of light is doing so in a circular direction around you, and camera technology (unthinkably high frames) has advanced so much that you can fully capture the motion of the tiny person and see him clearly in a video as he revolves around you. What would you see here? A tiny person that is traveling at a high speed, but is moving (breathing, turning, etc.) at an excruciatingly slow speed?
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I don't think there would be such extreme effects, partly because we can actually do this experiment by using something even faster than flash; i.e. a flashlight.
So if you actually did that experiment you could easily observe the result which is intuitively obvious to everyone. After you turn on the flashlight, a few nanoseconds later or so the light is observed to hit a barrier at the end of a 100 m distance (of course you have to subtract the time it takes for the light to bounce off and reach your eye, but its clearly implied to be a very small amount of time in terms of how long it takes to reach the barrier).
I can only assume that objects/people moving slower than the speed of light would operate in the same way. So therefore it must be option #1
As for the explanation as to how this meshes with special relativity, I think that if you had placed a clock on flash as he was running, and you observed this clock, it would appear to be moving extremely slowly. So the fact is that the faster Flash runs, the less he ages. But because the time spent under this time dilation effect is so small the age reduction is negligible.
I think the issue is that Flash would have to travel for a very, very long distance (and then come back) in order for these time dilation effects to be significant. That's why if you read about the "Twin Paradox" on Wikipedia, they talk about how one twin waits until one year has passed while travelling near the speed of light. In that case, two centuries pass on Earth for the other twin. But here Flash is just travelling 100 m, which is a very small fraction of a second so nothing is really noticeable.
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lol what is this? There is no paradox. Flash's perception does not change your perception. You would percieve him move and cross the line at near lightspeed, just as he percieves near 0 time change.
Scenario #2 is not what happens with relativity. At all.
"This is where things get a little murky. From Flash's own perspective, he still reaches the finish line in 0.0000003 seconds. "
This makes no sense. Did someone tell you this, or did you actually try to understand the theory of relativity?
Heck, the fact that you acquaint scenario #2 with fiction says it all.
There is no paradox to reconcile.
Edit: the twin paradox is not a paradox either.
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On May 18 2014 02:27 EngrishTeacher wrote:Show nested quote +On May 18 2014 02:11 Dizmaul wrote:
I think you need to think about it the other way around. When the people on earth have waited 150 years for the astronaut, They would tell you they have only been in there ship 1 year because of there speed. So if you "wait" for flash to cross the finish line it was 0.00000003 seconds for you. For him it would be even less time. Wait if it's 0.00000003 seconds for me, then it would be only 0.00000003/1 trillion seconds for Flash, and since distance is constant at 100m, somehow flash was able to travel at 1 trillion times the speed of light? I mean Distance / time = speed, so if distance doesn't change, and time is shortened to 1/1 trillionth, the only thing left is speed right? Which has increased by 1 trillion times? Also, since we always talk about the speed of light and not velocity, let's say that a tiny person traveling in a ship close to the speed of light is doing so in a circular direction around you, and camera technology (unthinkably high frames) has advanced so much that you can fully capture the motion of the tiny person and see him clearly in a video as he revolves around you. What would you see here? A tiny person that is traveling at a high speed, but is moving (breathing, turning, etc.) at an excruciatingly slow speed?
The Distance to flash would be 1 Trillion times shorter also that's what distance contraction is doing.
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On May 18 2014 02:34 Dizmaul wrote:Show nested quote +On May 18 2014 02:27 EngrishTeacher wrote:On May 18 2014 02:11 Dizmaul wrote:
I think you need to think about it the other way around. When the people on earth have waited 150 years for the astronaut, They would tell you they have only been in there ship 1 year because of there speed. So if you "wait" for flash to cross the finish line it was 0.00000003 seconds for you. For him it would be even less time. Wait if it's 0.00000003 seconds for me, then it would be only 0.00000003/1 trillion seconds for Flash, and since distance is constant at 100m, somehow flash was able to travel at 1 trillion times the speed of light? I mean Distance / time = speed, so if distance doesn't change, and time is shortened to 1/1 trillionth, the only thing left is speed right? Which has increased by 1 trillion times? Also, since we always talk about the speed of light and not velocity, let's say that a tiny person traveling in a ship close to the speed of light is doing so in a circular direction around you, and camera technology (unthinkably high frames) has advanced so much that you can fully capture the motion of the tiny person and see him clearly in a video as he revolves around you. What would you see here? A tiny person that is traveling at a high speed, but is moving (breathing, turning, etc.) at an excruciatingly slow speed? The Distance to flash would be 1 Trillion times shorter also that's what distance contraction is doing.
There's actually a pretty well-known example that helps explain that, and that's muon decay. Instead of trying to do it myself, I'll let Wikipedia explain this for me 
When a cosmic ray proton impacts atomic nuclei in the upper atmosphere, pions are created. These decay within a relatively short distance (meters) into muons (their preferred decay product), and muon neutrinos. The muons from these high energy cosmic rays generally continue in about the same direction as the original proton, at a velocity near the speed of light.
Although their lifetime without relativistic effects would allow a half-survival distance of only about 0.66 km (660 meters) at most (as seen from Earth) the time dilation effect of special relativity (from the viewpoint of the Earth) allows cosmic ray secondary muons to survive the flight to the Earth's surface, since in the Earth frame, the muons have a longer half life due to their velocity.
From the viewpoint (inertial frame) of the muon, on the other hand, it is the length contraction effect of special relativity which allows this penetration, since in the muon frame, its lifetime is unaffected, but the length contraction causes distances through the atmosphere and Earth to be far shorter than these distances in the Earth rest-frame.
Both effects are equally valid ways of explaining the fast muon's unusual survival over distances.
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On May 18 2014 02:34 Dizmaul wrote:Show nested quote +On May 18 2014 02:27 EngrishTeacher wrote:On May 18 2014 02:11 Dizmaul wrote:
I think you need to think about it the other way around. When the people on earth have waited 150 years for the astronaut, They would tell you they have only been in there ship 1 year because of there speed. So if you "wait" for flash to cross the finish line it was 0.00000003 seconds for you. For him it would be even less time. Wait if it's 0.00000003 seconds for me, then it would be only 0.00000003/1 trillion seconds for Flash, and since distance is constant at 100m, somehow flash was able to travel at 1 trillion times the speed of light? I mean Distance / time = speed, so if distance doesn't change, and time is shortened to 1/1 trillionth, the only thing left is speed right? Which has increased by 1 trillion times? Also, since we always talk about the speed of light and not velocity, let's say that a tiny person traveling in a ship close to the speed of light is doing so in a circular direction around you, and camera technology (unthinkably high frames) has advanced so much that you can fully capture the motion of the tiny person and see him clearly in a video as he revolves around you. What would you see here? A tiny person that is traveling at a high speed, but is moving (breathing, turning, etc.) at an excruciatingly slow speed? The Distance to flash would be 1 Trillion times shorter also that's what distance contraction is doing.
... Ok that just totally blew my mind.
So no, we do not need faster-than-light travel to cross galaxies. All we need to do is eventually be able to harness enough energy to accelerate a spaceship close enough to the speed of light such that galaxies could be crossed in seconds from the viewpoint of the astronaut?
The reasoning is that because of both the time dilation and length contraction effects, and the fact that speed of light is constant, so distance is shorted and time is dilated both on a massive scale. Distance / Speed = Time, so distance decreases while time dilates as well, and this phenomenon is amplified as you get closer to the speed of light. In the end, as you get so close to the speed of the light, time dilates and distance contracts so much that shouldn't you be able pretty much teleport to any point in the universe?
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On May 18 2014 02:48 EngrishTeacher wrote:Show nested quote +On May 18 2014 02:34 Dizmaul wrote:On May 18 2014 02:27 EngrishTeacher wrote:On May 18 2014 02:11 Dizmaul wrote:
I think you need to think about it the other way around. When the people on earth have waited 150 years for the astronaut, They would tell you they have only been in there ship 1 year because of there speed. So if you "wait" for flash to cross the finish line it was 0.00000003 seconds for you. For him it would be even less time. Wait if it's 0.00000003 seconds for me, then it would be only 0.00000003/1 trillion seconds for Flash, and since distance is constant at 100m, somehow flash was able to travel at 1 trillion times the speed of light? I mean Distance / time = speed, so if distance doesn't change, and time is shortened to 1/1 trillionth, the only thing left is speed right? Which has increased by 1 trillion times? Also, since we always talk about the speed of light and not velocity, let's say that a tiny person traveling in a ship close to the speed of light is doing so in a circular direction around you, and camera technology (unthinkably high frames) has advanced so much that you can fully capture the motion of the tiny person and see him clearly in a video as he revolves around you. What would you see here? A tiny person that is traveling at a high speed, but is moving (breathing, turning, etc.) at an excruciatingly slow speed? The Distance to flash would be 1 Trillion times shorter also that's what distance contraction is doing. ... Ok that just totally blew my mind. So no, we do not need faster-than-light travel to cross galaxies. All we need to do is eventually be able to harness enough energy to accelerate a spaceship close enough to the speed of light such that galaxies could be crossed in seconds from the viewpoint of the astronaut? The reasoning is that because of both the time dilation and length contraction effects, and the fact that speed of light is constant, so distance is shorted and time is dilated both on a massive scale. Distance / Speed = Time, so distance decreases while time dilates as well, and this phenomenon is amplified as you get closer to the speed of light. In the end, as you get so close to the speed of the light, time dilates and distance contracts so much that shouldn't you be able pretty much teleport to any point in the universe?
It would seem like a teleport up to a certain distance. Maybe a couple minuites pass for the people at point A and B while for the traveller its almost instant. But if you wanted to travel more then a couple light years away you might run into the problems of the people you're going to see not being there anymore. Our galaxy alone is 100k light years in diameter. While to the traveler it would be a short trip to cross the milky way, the people at point A and B would have 100k years pass.
This is why speed is not a option to getting to the rest of the universe. You need to fold space time and cut through or no one is going to be waiting for you upon arrival.
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EPT
