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Author Topic: More relativity  (Read 5121 times)

Offline syhprum

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More relativity
« on: 26/08/2006 14:03:52 »
If I accelerate a body to near c velocity it flies away from me loops round a black hole and returns.
It is well estabished that it will have aged less that a similar body that has remained with me, now the question is the energy balance how many joules are reqired to make 1kg of matter one second younger and does this imply that the mere passing of time creates energy/mass

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Offline lightarrow

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Re: More relativity
« Reply #1 on: 26/08/2006 14:38:59 »
quote:
Originally posted by syhprum

...how many joules are reqired to make 1kg of matter one second younger and does this imply that the mere passing of time creates energy/mass
The answer depends on the speed v of the body, or on how much time you can wait here on earth:
t' = t*square(1-v^2/c^2); t-t' = t*(1-square(1-v^2/c^2)) = 1second.

From this equation, knowing t, it's possible to find v; or, knowing v, it's possible to find how much time t you have to wait. Then we can compute the energy needed for the initial acceleration of the body to the speed v:

E(acc) = (mc^2)*(1-square(1-v^2/c^2))/square(1-v^2/c^2); m = 1kg.
 

Offline syhprum

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Re: More relativity
« Reply #2 on: 27/08/2006 08:41:41 »
I am very pleased to get an answer so quickly, I wonder if you could clarify one or two points.
1, am I right in assuming that the amount of time dilation (younging!) depends only on how closely I approach c.
2, as it is required for the object to be decelerated to zero velocity when it returns should there be a factor of two in the energy equation.
3, I looped my object around a black hole to get it to return this would seem to take one from special relativity general relativity or is it of no consequence.
4, my arithmetic is very weak could you please give a worked example of a body acquiring a time dilation of one second in 1000 seconds to give some idea of the magnitudes involved.

Many thanks for solutions of a very intriguing problem

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Offline lightarrow

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Re: More relativity
« Reply #3 on: 27/08/2006 16:19:26 »
quote:
Originally posted by syhprum

I am very pleased to get an answer so quickly, I wonder if you could clarify one or two points.
1, am I right in assuming that the amount of time dilation (younging!) depends only on how closely I approach c.
2, as it is required for the object to be decelerated to zero velocity when it returns should there be a factor of two in the energy equation.
3, I looped my object around a black hole to get it to return this would seem to take one from special relativity general relativity or is it of no consequence.
4, my arithmetic is very weak could you please give a worked example of a body acquiring a time dilation of one second in 1000 seconds to give some idea of the magnitudes involved.

Many thanks for solutions of a very intriguing problem

1. Depends on how closely you approach c AND on how long is your trip.
2. Yes, if you mean that the work you have to do to the body to accelerate it is the same you have to do to decelerate it.
3. General relativity.
4. If you wait here on earth for 1000 seconds and you want your 1Kg body to be 1 second younger than you after its trip, then its average speed should be 13404 Km/s ( = 0.0447c).

This implies a kinetic energy of 9*10^13Joule (since v/c is very low in this case, to obtain this value you can use the non relativistic formula as well: E = (1/2)*m*v^2).

So the total work you have to do on it is 2*9*10^13 = 1.8*10^14Joule.
« Last Edit: 27/08/2006 16:21:35 by lightarrow »
 

Offline syhprum

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Re: More relativity
« Reply #4 on: 27/08/2006 17:36:58 »
I am very gratful this question has long intrigued me, When I start up my age reducing business I will know how much to charge!, I guess it will be quite a lot.

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Offline Soul Surfer

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Re: More relativity
« Reply #5 on: 29/08/2006 10:04:49 »
The answer is zero because the body starts at rest near you gains lots of energy accelerating down the gravitational well to get up to a high speed and make the orbit and then looses it all in climbing back out to end up at rest near you.

If you are going to perform the experiment and keep a similar comparison mass with you while you stay in a circular orbit around the object  you will need to give the object a bit of a push to get it going down the well.

If you push it a bit to get it started you must take off the push you will receive back when you stop it as it flies by on the return trip.

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Offline syhprum

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Re: More relativity
« Reply #6 on: 29/08/2006 19:38:56 »
I was assuming that I expended a lot of energy accelerating it up to near c then it coasted to the region of the black hole and looped around it to get it returning, of course when falling into this gravity well it would gain additional velocity but would lose it on the way out.
It is difficult to set up this experiment even in theory as the loop around the black hole must cause some time dilation effects but I was hoping they could be ignored.
As my body is returning with the same velocity as it left a second amount of energy must be expended to recover it for examination

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Offline Soul Surfer

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Re: More relativity
« Reply #7 on: 30/08/2006 08:16:25 »
The two accelerations are in opposing directions and will cancel out. you give the particle energy to send it on its way and recover this energy when you catch it.

Also note that assuming most of the acceleration is gravitational you do not have to accelerate the body very fast yourself  just by enough to change its orbit from a distant circular orbit (which is the orbit that I assume that you are following)  to on that passes close to the black hole.

It is also interesting to note that most materials do not have any "age" associated with them so I ssume thet the object you are sending includes one of a pair of very accurate clocks.  The only natural process that determines the age of a lump of marterial is radioactivity.

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Offline syhprum

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Re: More relativity
« Reply #8 on: 31/08/2006 08:45:21 »
I made a mistake using a black hole, next time I will place my clock on a rocket with enough fuel to accelerate it up to near c then brake it ,reverse its travel, accelerate up to the same velocity in the reverse direction, brake it down to zero velocity and land it for inspection.
this will of course use more energy but should simplify the calculation of the amount of energy required.
As no external gravitational fields are involved I take it only special relativity will be required

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Offline Soul Surfer

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Re: More relativity
« Reply #9 on: 30/08/2006 08:16:25 »
The two accelerations are in opposing directions and will cancel out. you give the particle energy to send it on its way and recover this energy when you catch it.

Also note that assuming most of the acceleration is gravitational you do not have to accelerate the body very fast yourself  just by enough to change its orbit from a distant circular orbit (which is the orbit that I assume that you are following)  to on that passes close to the black hole.

It is also interesting to note that most materials do not have any "age" associated with them so I ssume thet the object you are sending includes one of a pair of very accurate clocks.  The only natural process that determines the age of a lump of marterial is radioactivity.

Learn, create, test and tell
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Offline syhprum

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Re: More relativity
« Reply #10 on: 31/08/2006 08:45:21 »
I made a mistake using a black hole, next time I will place my clock on a rocket with enough fuel to accelerate it up to near c then brake it ,reverse its travel, accelerate up to the same velocity in the reverse direction, brake it down to zero velocity and land it for inspection.
this will of course use more energy but should simplify the calculation of the amount of energy required.
As no external gravitational fields are involved I take it only special relativity will be required

syhprum
 

Offline Soul Surfer

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Re: More relativity
« Reply #11 on: 01/09/2006 10:55:49 »
OK  that will give you a figure of energy for doing the job but we have already demonstrated that you can in theory do it for nothing if you use a gravitiational field.  Either way that gives you no reason to suggest that the passage of time creats mass.

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Re: More relativity
« Reply #11 on: 01/09/2006 10:55:49 »

 

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