Request for Help re the Notion of Potential Infinity
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Request for Help re the Notion of Potential Infinity
I think to myself that if I were to build a special rocket and fire it vertically up from Earth into the heavens above me, that this rocket, once it had escaped the Earth's atmosphere and entered into space proper, would continue to travel forward in a straight line for ever. This is because , as I say , it is a special rocket that has been fitted with sophisticated technology that alerts it to the looming presence of any object in its flight path that it might crash into like an asteroid or a planet or a star, or any other phenomenon in space that might destroy it should it fly too close toward it, like a black hole, for example. This technology automatically instructs my rocket to swerve around any such space- hazards at a safe distance and then, once it has past by them safely, to re-orient itself back into flying forward along the straight linear path that it was taking before the hazard/s were sensed by the technical devices on-board and the diversionary action ( of flying around them) was taken.
So, in sum, this rocket is travelling forward/ahead in a straight line through space just like the Apollo 11's module ("Eagle") as it flew through space towards the moon, only my rocket would swerves around the moon or anything else blocking its way or threatening to somehow stop it or destroy it. My rocket, that is, ultimately just keeps on flying forward along its original linear trajectory deeper and deeper and deeper into space...
My question is this... Am I right in thinking that this special rocket of mine will never stop flying ,that it will literally continue to track forward along its line of flight for ever ( for eternity) as there is nothing to stop it? Its mission , that is, is called "Potential Infinity", for no matter how many space miles it puts behind it there will always be another one ahead to traverse, then after that another one, and then another one and so on and on . Is there anything wrong with my presuming that this is, in fact, what will actually happen ?
Regards
Dachshund
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Re: Request for Help re the Notion of Potential Infinity
My personal take on this would be that there are a number of options.
1. As you describe it simply keeps going.
2. Forces such as gravity eventually cause the rocket to stop. There is finite energy in the universe so this is inevitable no matter how well designed the rocket.
3. The universe crashes due to an exception caused by a rocket being over bounds.
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Re: Request for Help re the Notion of Potential Infinity
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Re: Request for Help re the Notion of Potential Infinity
Personally I have no idea what time is, what space is or how it is possible to move. I only know that I am able to move and meet people at set times.
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Re: Request for Help re the Notion of Potential Infinity
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Re: Request for Help re the Notion of Potential Infinity
3. Is a joke on my part. Sometimes a computer game will crash if you go to an area of the game which is unexpected by the programmer. Although I doubt we something as simple as a computer game we could be some kind of a program.
- Halc
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Re: Request for Help re the Notion of Potential Infinity
This is plausible to imagine. A real rocket would run out of fuel quickly, but could continue to accelerate using a technology like a Bussard ramjet.Dachshund wrote: ↑May 29th, 2018, 9:25 am I think to myself that if I were to build a special rocket and fire it vertically up from Earth into the heavens above me, that this rocket, once it had escaped the Earth's atmosphere and entered into space proper, would continue to travel forward in a straight line for ever.
Without acceleration, we could fire the ship out of a cannon at near lightspeed, or you could just consider Earth already traveling at that speed in a different intertial reference frame, although the trip would be less sexy since it would be a lot like staying home and not really going anywhere. So let's go with the Bussard rocket. Perfectly reasonable to imagine it avoiding obstacles.
Option 2 is to shine light in some direction without obstacles. How far will that light get? OK, you don't get to look out the window if you consider this option, but the mathematics is not a whole lot different. There is no need to accelerate it since light always travels at lightspeed while the rocket is always less than that.
The rocket (or the supply of fuel through which it flies) will eventually decay/be consumed by entropy. Not so much the light photons which don't die the entropy death so long as they don't hit anything.My question is this... Am I right in thinking that this special rocket of mine will never stop flying ,that it will literally continue to track forward along its line of flight for ever ( for eternity) as there is nothing to stop it?
The only mathematical limit is the event horizon. The ship cannot get to it, and neither can the light we projected. If it can be said that there is anything beyond that event horizon, it is inaccessible from Earth by any means. That doesn't mean the ship will not travel infinitely far. That event horizon recedes (in proper distance) over time, so your ship continues to move so long as it exists, and there will continue to be 'stuff'' in front of the ship. But if there are two alien ships way out there in reasonable proximity to each other, but one just inside and the other just outside of Earth's event horizon, your ship/light could only ever reach the former alien ship or its light, and then only if the alien ship is coming towards us as much as much as your ship is attempting to reach it. The other alien ship is utterly inaccessible to your ship and thus effectively exists as much as unicorns.
There will always be more space and matter in front of it, unless space itself collapses in a big crunch, which appears to not be the case. It is expanding, and the expansion is accelerating, not slowing down. It is unlikely to ever turn around. Without accelerating expansion, there would be no event horizon.Its mission , that is, is called "Potential Infinity", for no matter how many space miles it puts behind it there will always be another one ahead to traverse, then after that another one, and then another one and so on and on . Is there anything wrong with my presuming that this is, in fact, what will actually happen ?
- Halc
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Re: Request for Help re the Notion of Potential Infinity
Matter is evenly distributed on average, so gravity is not going to slow anything down in the long run. It pulls as often as it pushes. If energy runs out, the ship simply keeps going at whatever velocity it has achieved but it ceases to accelerate further.
This makes it sound like the universe cares about the rocket. I mentioned the big crunch (big bang in reverse, implying a finite limit to time), but the rocket doesn't have any effect on that if it is the eventual fate. Big rip is also a limit to time. That happens if the event horizon ever shrinks to size zero, after which the universe ends just as much as the crunch scenario.3. The universe crashes due to an exception caused by a rocket being over bounds.
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Re: Request for Help re the Notion of Potential Infinity
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Re: Request for Help re the Notion of Potential Infinity
Regards
Dachshund
- ThomasHobbes
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Re: Request for Help re the Notion of Potential Infinity
(A) The size of the universe is defined by the relation between its parts.Dachshund wrote: ↑May 29th, 2018, 9:25 am Like the Irish-born British political philosopher Edmund Burke I am fascinated by the night sky. When I gaze into the starry heavens I feel the sense of a strangely delightful reverential awe at my own subordination before the terrifying boundlessness of the infinite night sky.
I think to myself that if I were to build a special rocket and fire it vertically up from Earth into the heavens above me, that this rocket, once it had escaped the Earth's atmosphere and entered into space proper, would continue to travel forward in a straight line for ever. This is because , as I say , it is a special rocket that has been fitted with sophisticated technology that alerts it to the looming presence of any object in its flight path that it might crash into like an asteroid or a planet or a star, or any other phenomenon in space that might destroy it should it fly too close toward it, like a black hole, for example. This technology automatically instructs my rocket to swerve around any such space- hazards at a safe distance and then, once it has past by them safely, to re-orient itself back into flying forward along the straight linear path that it was taking before the hazard/s were sensed by the technical devices on-board and the diversionary action ( of flying around them) was taken.
So, in sum, this rocket is travelling forward/ahead in a straight line through space just like the Apollo 11's module ("Eagle") as it flew through space towards the moon, only my rocket would swerves around the moon or anything else blocking its way or threatening to somehow stop it or destroy it. My rocket, that is, ultimately just keeps on flying forward along its original linear trajectory deeper and deeper and deeper into space...
My question is this... Am I right in thinking that this special rocket of mine will never stop flying ,that it will literally continue to track forward along its line of flight for ever ( for eternity) as there is nothing to stop it? Its mission , that is, is called "Potential Infinity", for no matter how many space miles it puts behind it there will always be another one ahead to traverse, then after that another one, and then another one and so on and on . Is there anything wrong with my presuming that this is, in fact, what will actually happen ?
Regards
Dachshund
Two things.
1 yes you shall continue for ever but the universe is expanding faster than your ship is travelling. So there would be no problem to continue for eternity.
2 In the unlikely event that you could go faster than the universe is expanding, your own expansion beyond the 'edge' would simply increase the dimension of the universe along your path. (See A)
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Re: Request for Help re the Notion of Potential Infinity
Halc my point 3 is not supposed to be serious. And my point 2 was not supposed to be accepted as fact, it's just a possibility. The universe is not perfectly homogeneous.
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Re: Request for Help re the Notion of Potential Infinity
- ThomasHobbes
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Re: Request for Help re the Notion of Potential Infinity
You do not need any energy to keep moving. You only need energy to slow down.
"TH there is one very large problem with going for eternity. It is impossible because it isnt a length of time which exists."
I do not think this makes any sense whatever.
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Re: Request for Help re the Notion of Potential Infinity
What's the confusion about eternity? Let us imagine we travel on the rocket for ten years. Obviously we could travel a day longer. Also we are no closer to having travelled for eternity than before we started ten years ago. If you replace ten years with any number all the above still holds. Any real number can't be eternity and is infinitely far away from eternity. You can't travel eternally in reality. This seems straight forward to me.
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