Ridiculous Time Dialation Question

[astralimage]

NASA has invented a near light speed spacecraft and an astronaut flies it to Alpha Centauri. When he gets there he meets a magic snail. The magic snail can live in space and move about in it, but only at the same pace a snail can move on Earth. (He's also covered in purple poka-dots and wearing a beanie cap). <br /><br />Anyway, the magic snail challenges the astronaut to a race back to Earth. The astronaut laughs and accepts. And off they go. The astronaut takes the early lead as he accellerates to 99.99whatever C. But at near C, time slows to almost nothing for the astronaut, so the magic snail eventually passes him like he's standing still and wins the race to Earth -by like a gazillion years. <br /><br />Right?

 

[yevaud]

No. Seperate frames of reference. To the Astronaut, time slows to a crawl. However, to the outside observer, he's zipping along at a significant fraction of C.<br /><br />Quite simple. <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[astralimage]

Ok, maybe my understanding is backwards, so let's have a second race, this one from Earth to Alpha Centauri round trip -judged by the time frame of Earthlings.<br /><br />The astronaut completes the circuit in 9 years (relative to himself). But when he gets back, eons have passed on Earth and the snail is waiting for him, laughing his snail butt off. <br /><br />This also means the snail MUST have passed him at some point in the race!

 

[yevaud]

See, while the metaphor of the Snail may hold up on a sheerly intellectual level, in reality it isn't so.<br /><br />Unless the Snail is moving at some significant percentage of C, there is no way he will reach Earth before the Astronaut.<br /><br />Snail travels 6 Cm.<br />Astronaut travels 100,000 km.<br /><br />Repeat iteration. <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[astralimage]

<blockquote><font class="small">In reply to:</font><hr /><p> See, while the metaphor of the Snail may hold up on a sheerly intellectual level, in reality it isn't so. <p><hr /></p></p></blockquote><br /><br />Ok, then my question becomes: Why does it hold up on the intellectual level but not in reality?<br /><br />I mean, obviously if two objects move towards the same point from the same starting position at the same time, the faster one should get there first.<br /><br />But then again, time dilation is also a completely real and proven phenomena, right?<br /><br />

 

[yevaud]

It's a sort of mathematical trick. If you think about it, it's an example of continuous but slow motion as opposed to fast, but stop and start motion.<br /><br />It's technically possible yes, but in reality look at the actual situation/ Take a vehicle and an immortal snail in a planet's orbit. They both move away from the planet:<br /><br />A vehicle leaves at 700 kps (just picking a figure out of the air).<br /><br />A Snail departs at 6 cmps.<br /><br />The next second, the vehicle is now moving at 700 kps + A (Acceleration).<br /><br />The Snail is moving at 6 cmps + A (Acceleration).<br /><br />As long as the vehicle does not pause (and for a significant length of time too), the Snail will never catch up to it. <br /><br />Since the original question involves time-dilation, consider that this is an effect involving the observed and the observer, but it does not regardless does not alter the velocity of the vehicle in our frame of reference.<br /><br />It is moving at X% velocity; the Snail is moving at 0.00000009%X velocity. Which, under continuous acceleration, achieve it's target soonest? <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[astralimage]

You know, I do agree with you. And I appreciate you taking the time to address my question. But I just can't over this time dilation thing. <br /><br />Since I'm not that good at math, let's say in the third race (again Earth to Alpha Centauri and back -judged from Earth's perspective) the astronaut takes it up a notch, hits "overdrive" and accellerates to full C. Time ceases. Relative to Earth the snail doesn't have any time dilation cuz he's just putting along at 6 cm an hour, and he completes the circuit in exactly one gazillion years. The astronaut, by his own perspective, completes the trip in under nine years. But when he gets back, the snail and Buddha and Jesus and everybody are just looking at him shaking their heads, cuz he's been gone for an infinite amount of time!

 

[dlee0708]

<i><br />You know, I do agree with you. And I appreciate you taking the time to address my question. But I just can't over this time dilation thing. <br /><br />Since I'm not that good at math, let's say in the third race (again Earth to Alpha Centauri and back -judged from Earth's perspective) the astronaut takes it up a notch, hits "overdrive" and accellerates to full C. Time ceases. Relative to Earth the snail doesn't have any time dilation cuz he's just putting along at 6 cm an hour, and he completes the circuit in exactly one gazillion years. The astronaut, by his own perspective, completes the trip in under nine years. But when he gets back, the snail and Buddha and Jesus and everybody are just looking at him shaking their heads, cuz he's been gone for an infinite amount of time! </i><br /><br />If the astronaut goes exactly C, when he gets to Alpha Centauri the people back on earth will have aged 4 years, but the astronaut will have aged 0 seconds (this is based on Alpha Centauri being 4 light years from earth). On the trip back (again at C) the people on earth will have aged another 4 years and the astronaut will have aged 0 seconds. So for the total trip the astronaut took the people on earth will have aged 8 years and the astronaut will have aged 0 seconds.<br /><br />The snail will have gone however far he can go at 6cm/hr for 8 years (which won't be very far).<br />

 

[lukman]

Time dilation is actually very very very small compare to the speed. So, if the astronaut clock is 1/10 slower than the snai, it doenst matter, he is still travelling 10quadrilliun times faster than the snail. So, actually, time dilation is relative stuff, very confusing, but you wont have chance to experience or prove such huge time dilation. I mean, even star trek uses warpspeed (subspace travel) instead of speeding in a space. <div class="Discussion_UserSignature"> </div>

 

[derekmcd]

As in any race, the one who has aged less upon reaching the finishline wins. <div class="Discussion_UserSignature"> <div> </div><br /><div><span style="color:#0000ff" class="Apple-style-span">"If something's hard to do, then it's not worth doing." - Homer Simpson</span></div> </div>

 

[weeman]

<font color="yellow"> Since I'm not that good at math, let's say in the third race (again Earth to Alpha Centauri and back -judged from Earth's perspective) the astronaut takes it up a notch, hits "overdrive" and accellerates to full C. Time ceases. Relative to Earth the snail doesn't have any time dilation cuz he's just putting along at 6 cm an hour, and he completes the circuit in exactly one gazillion years. The astronaut, by his own perspective, completes the trip in under nine years. But when he gets back, the snail and Buddha and Jesus and everybody are just looking at him shaking their heads, cuz he's been gone for an infinite amount of time! </font><br /><br />From the astronaut's perspective, the trip would be instantaneous. If he reaches full C, then time outside of his ship has come to a complete stop. This should also mean that he could circumnavigate the entire Universe instantly. <br /><br />Lets say for a second that the astronaut is at one end of the galaxy. He decides he needs to make a quick trip to the opposite end of the galaxy, some 100,000 lightyears away. He puts in the coordinates so the ship will power up to C, then power down the engines when the it reaches the other end of the galaxy. For a second the astronaut can hear the engines powering up, then suddenly the engines power down. The astronaut scratches his head thinking the ship hasn't gone anywhere. However, to his amazement, when he looks outside he realizes the ship has already reached the other end of the galaxy!!<br /><br />This is because the ship traveled at C, meaning time stopped for the astronaut, meaning the trip seemed instantaneous. Of course, if time stops, then this wouldn't be possible anyways. If time is stopped, then there is no time for the processes in the ships computer to tell the engines to power down. <br /><br />The dilemma that I often have is whether or not time actually ceases on the ship when the astronaut reaches C, or if it's time outside the ship that <div class="Discussion_UserSignature"> <p> </p><p><strong><font color="#ff0000">Techies: We do it in the dark. </font></strong></p><p><font color="#0000ff"><strong>"Put your hand on a stove for a minute and it seems like an hour. Sit with that special girl for an hour and it seems like a minute. That's relativity.</strong><strong>" -Albert Einstein </strong></font></p> </div>

 

[dragon04]

It's already been proven that the clock on board a moving object runs slower that a clock that is "stationary" relative to it.<br /><br />I can't remember the particular case, but two astronauts who were twins participated in the experiment. The twin that was travelling on a jet airliner "aged" less than his brother who was "on the ground".<br /><br />Although I understand what you're saying. From the point of reference of the brother on the ground, the flying brother was experiencing "slower" time, and the airborne brother saw his grounded sibling experiencing "accelerated" time from his frame of reference. <div class="Discussion_UserSignature"> <em>"2012.. Year of the Dragon!! Get on the Dragon Wagon!".</em> </div>

 

[SpeedFreek]

The classic answer is that the astronaut who has <i> accelerated </i> to a relativistic speed will experience time dilation, relative to another inertial frame of reference. The astronaut doesn't actually experience time any differently from normal (he can't notice that his clock is running slowly) but at the end of the journey he will have experienced <i> less time </i> than an observer in an inertial reference frame will have experienced - due to the length contraction which goes along with time dilation. He will arrive home younger than his twin brother.<br /><br />The problem is that according to special relativity, time dilation is <i> symmetrical </i> between different inertial frames of reference. So whilst the astronaut is travelling at a constant speed, an observer on Earth would see the astronaut looking slowed down, but the astronaut would also see the observer on Earth slowed down too! So if that is the case, if when both parties are in an inertial frame they see each other slowed by the same amount, when does the time dilation actually happen?<br /><br />If they could watch each other from departure to arrival, what would they see? If they see each other slowed by the same amount when the astronaut is moving at a constant speed, then they would have to see the difference happen only during the non-inertial parts of the journey (acceleration or deceleration).<br /><br />In practice, what might happen is that the astronaut would see the observer looking speeded up during the non-inertial parts of his journey, but at constant speeds he would see the observer slowed down to the same rate as the observer sees the astronaut. But to the observer, during the non-inertial parts of the journey the astronaut would look really slowed down but at constant speeds he would speed up to the same rate as he sees the observer! The net result of all this is that when they might actually see the difference happen (but the last 2 paragraphs are not part of special relativity, whi <div class="Discussion_UserSignature"> <p><font color="#ff0000">_______________________________________________<br /></font><font size="2"><em>SpeedFreek</em></font> </p> </div>

 

[yevaud]

Of course - to re-relate all this back to the original question - it's a moot point. There would be no way for the Snail to catch up to the astronaut. Taking time dilative effects into account is irrelevant, as the velocity of the ship and that of the Snail are what we, the outside observer, sees. Whether or not the astronaut experiences time-dilation makes no difference whatsoever. <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[derekmcd]

Agreed.<br /><br />He, who has aged less, wins... Would not time dilation only emphasize the basic rule?<br /><br /> <div class="Discussion_UserSignature"> <div> </div><br /><div><span style="color:#0000ff" class="Apple-style-span">"If something's hard to do, then it's not worth doing." - Homer Simpson</span></div> </div>

 

[yevaud]

Well, true. Courtesy of the effect of time dilation, the Astronaut would arrive at Earth aged perhaps a year or some similarly small time-span. He would then live out his life and happily expire.<br /><br />The Snail, travelling at some much smaller velocity, would arrive at Earth several tens of thousands of years later.<br /><br />(Well, that's one interpretation of it all)<br /><br />Btw, the original question is flawed anyways. Because in the parable of the Tortoise and the Hare, the key event was the Hare lying down to sleep, thereby allowing the Tortoise (or Snail) to pass him by the slow and steady method.<br /><br />In the case proposed, even if the Ship stopped "moving" which I take to mean accelerating, it would still be moving at whatever velocity it had managed to acquire.<br /><br />Magnitudes harder for the Tortoise (or Snail) to catch up. <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[ianke]

So what is the snail driving?<img src="/images/icons/smile.gif" /> <div class="Discussion_UserSignature"> </div>

 

[yevaud]

Dunno. But the assumption was that the Snail and the Astronaut would try to reprise the Snail and the Hare. <br /><br />(Probably my mistake - I said Snail back when and meant Tortoise - so I'm stuck with it for this post)<br /><br />The way the Snail beats the Hare is that the Hare, though speedy, stops and naps, allowing the much slower but continually moving Snail to surpass him.<br /><br />Highly unlikely in this scenario. <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[derekmcd]

I think Astralimage's confusion lies in thinking that the astronaut's slowing down of time, means everyone around him "speeds up"... hence faster, quicker, speedier. <div class="Discussion_UserSignature"> <div> </div><br /><div><span style="color:#0000ff" class="Apple-style-span">"If something's hard to do, then it's not worth doing." - Homer Simpson</span></div> </div>

 

[yevaud]

Of course. That's why we're all trying to demonstrate examples of frames of reference, time-dilation versus none, relative motion, what have you, to show him what's possible and what isn't. <br /><br />Not to mention discussing immortal, space-propulsion equipped Snails, and the hapless Astronauts they vainly chase. <img src="/images/icons/wink.gif" /> <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[ianke]

Yeah, but if the snail has a ferrari... <br /><br /><br />Sorry, I couldn't help it. <div class="Discussion_UserSignature"> </div>

 

[derekmcd]

Or a wormhole... hmm. Now that would be quite a conundrum. The snail could arrive first, but the astronaut achieving light speed would age less. All observers, including the astronaut, would know the snail arrived before the astronaut. The astronaut, however, could make the legitimate claim that he finished the race in less time. <div class="Discussion_UserSignature"> <div> </div><br /><div><span style="color:#0000ff" class="Apple-style-span">"If something's hard to do, then it's not worth doing." - Homer Simpson</span></div> </div>

 

[ianke]

LMAO<br /><br />I hope he took his ferrari with him or he's walking when he gets there. <img src="/images/icons/laugh.gif" /> <div class="Discussion_UserSignature"> </div>

 

[astralimage]

<blockquote><font class="small">In reply to:</font><hr /><p> Of course. That's why we're all trying to demonstrate examples of frames of reference, time-dilation versus none, relative motion, what have you, to show him what's possible and what isn't. <p><hr /></p></p></blockquote><br /><br />Yeah, I had the whole time dilation thing backwards (and mispelled) but I think I've got a better grip on it now.<br /><br />I was just thinking of that old example of the two twins. The one who flies off at light speed comes back to find the Earthbound one much older than himself. So in my mind, I kind of pictured time on Earth speeding up compared to the LS or near LS traveler. But I see now there's no getting around the fact that if ship A goes round trip to Alpha Centauri at LS it will still be a 9 year journey to the observer on Earth, and ship B going half the speed light will find that 18 years have passed on Earth when he returns -and so on. It's a good thing too, cuz by my reckoning all the light in the universe would be stationary -and that would really screw up the system!<br /><br />My misunderstanding, all clarified -thanks all.