Time dilation in a gravitational field.

[blueman]

A hypothetical cosmonaut near the event horizon of a black hole ages more slowly then you do, and travels into the future faster than you do...<br /><br />Anyone care to explain this more fully to me? I guess I'm wondering what some ideas regarding spacetime curvature are.<br /><br />Also, to think micro for a second, a one-inch cube of hydrogen would cause an infinitesimally shallower curve in spacetime than a cube of lead. If you're willing to work out the math to very small decimals, isn't my hand closed on the cube of hydrogen experiencing a different clock-rate than the hand clutching the lead? (The earth's grav effects held equal, of course!)

 

[vogon13]

Yep. They are going to love this one. Clench your buttocks and strap yourself in.<br /><br /><img src="/images/icons/laugh.gif" /><img src="/images/icons/laugh.gif" /><img src="/images/icons/laugh.gif" /> <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>

 

[blueman]

Not that there's anything wrong with it, but you may be in the wrong forum...

 

[vogon13]

I'm thinking you have posed an excellent question to get a big fun thread going! <br /><br />Congratulations!<br /><br />I want you to be prepared for a data torrent. <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>

 

[najab]

><i>If you're willing to work out the math to very small decimals, isn't my hand closed on the cube of hydrogen experiencing a different clock-rate than the hand clutching the lead?</i><p>Yes. But the difference would be in the billionths of a second per century.</p>

 

[Saiph]

for the first one:<br /><br />If you age more slowly, cause time passes slower for you....then it's a direct consequence of time moving faster for everyone else. And because of the time moving faster for everyone else...you travel forward in time faster.<br /><br /><br />And as for the hands hypothetical...that's about the size of it. <div class="Discussion_UserSignature"> <p align="center"><font color="#c0c0c0"><br /></font></p><p align="center"><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">----</font></em></font><font color="#666699">SaiphMOD@gmail.com </font><font color="#999999"><em><font size="1">-------------------</font></em></font></p><p><font color="#999999"><em><font size="1">"This is my Timey Wimey Detector.  Goes "bing" when there's stuff.  It also fries eggs at 30 paces, wether you want it to or not actually.  I've learned to stay away from hens: It's not pretty when they blow" -- </font></em></font><font size="1" color="#999999">The Tenth Doctor, "Blink"</font></p> </div>

 

[vogon13]

Think it makes a difference if the cosmonaut is orbiting the black hole (circular path) or on a hyperbolic pass by it, or if he is doing 'the final plunge'? <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>

 

[main_sequence]

Hi<br /><br />I am not sure that you are thinking of the cosmonaut idea as accurately as relativity concludes for the passages of time from individual perspectives. From my understanding of it, the cosmonaut's point of view is that "time" outside of his position near the event horizon speeds up. Theoretically, if he held just the right position around the black hole he could watch the universe age and die around him as long as he didn't corss the event horizon. <br /> In the same token, you watching the cosmonaut would watch time "stop" for him. He wouldn't move or age because of the gravitational well effectively stopping his time from your point of view, but from the cosmonaut's point of view you have "sped up". He could watch you age and die within hours or minutes (of course his "hours" or "minutes" would last eons for the rest of us). <br /> As far as thinking of the effects of gravity has on time , I would think you could sort of sum it up by thinking of this - if you are trying to get to point B from point A in a car, the fastest route is a straight line right? Well that is sort of equivalent to having no strong gravitational fields nearby. But if you went to point B from A in a curved line, even going the same rate of speed as before it would still take a longer interval of time. The effects are similar (if not actually just restating the same scenario).<br /><br /> Basically, he only travels into the future faster from your point of view, but for him he is travelling in to the future at a normal rate. What boggles me is the consequences of change between the 2 perceptions -<br /><br /> like your cosmonaut seeing a star explode from his black hole perch after spending only a few of his "minutes" watching his astronomical surroundings. So for the observer outside of the black hole perch (us) we would have to wait say 10 million years to see it explode. Ergo, the cosmonaut has seen something that technically has not happened yet for the rest of the universe, yet

 

[rpmath]

…<br /><font color="yellow">like your cosmonaut seeing a star explode from his black hole perch after spending only a few of his "minutes" watching his astronomical surroundings. So for the observer outside of the black hole perch (us) we would have to wait say 10 million years to see it explode. Ergo, the cosmonaut has seen something that technically has not happened yet for the rest of the universe, yet all quantum differences that could provide different outcomes for that star must end with that star exploding. There could be no other outcome - even though our cosmonaut could never communicate to the rest of us that the star has exploded and that he has seen our "future".<br /></font><br />I think the cosmonaut has not seen nothing yet… <br />He will see the event after it happens, even if he only ages a few minutes.<br /><br />In relativity different observers can disagree on the simultaneity of two events, what one was the first and what one the later, but there is the concept of past and future cones:<br /><br />- If observer A can see a remote event B when or before a local event A happens, event B happened before event A (A is in B future cone, and B is in A past cone)<br />- If B can see event A before event B happens, event A happened before event B (A is in B past cone, and B in A future cone)<br />- If no one can see the other event before its own happened, they can disagree on what one was the first.<br />- If both can see the other event before the local one, you have a time loop, and paradoxes. This is not possible outside black hole event horizons… and I don’t believe in the event horizon inside…<br /><br />so… if the cosmonaut can see the supernova after a few of his minutes, this moment will be after the star explodes. He wont be able to return before the star explodes, because if he can see it, it have already happened.

 

[emperor_of_localgroup]

I have to agree with RPMath. The cosmonaut near an event horizon can not see an event in our world before it occurred. 10 mill years in our world may be just 1 heart beat of the cosmonaut. But he has to wait for 1 complete heart beat to see the explosion.<br />I think what i'm about to say is laughable. But my intuition tells me that all theoretical analysis of properties of a black hole beyond the event horizon may be just mathematical fairy tales. The explanations just do not seem to fit with the nature of the physical universe we observe and experience. There must be a discontinuity somewhere. Well, time to laugh. <div class="Discussion_UserSignature"> <font size="2" color="#ff0000"><strong>Earth is Boring</strong></font> </div>