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Originally Posted by AnssiH
I personally wouldn't know what to answer, as it's kind of a matter of what one supposes "being conscious" means.
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My point exactly! Primitive outlooks have almost always included dreams as being as real as what we call reality. Certainly, in my dreams, I feel as if I am conscious; how is it that I remember what happened if that were not the case? And Dennet's definition of consciousness seems to me to include dreaming. The issue is, what philosophical position is appropriate here.
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Originally Posted by AnssiH
Of course I understand some people associated "being conscious" with the everyday idea of being awake...
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The reason I brought the question up.
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Originally Posted by AnssiH
Incidentally, as I'm writing this there's a History Channel program "The Universe" on, and it's an episode about space travel. They are bringing up the speed limit of light speed as per relativity, and sure enough, they have once again dumbed it down so much as to make completely false assertions. Here's a direct 1:1 quote straight from Mr. Neil deGrasse Tyson (PhD in Astrophysics)
"Light's fast, but the universe is huge. So even if we could ride on a beam of light, if we wanted to cross the galaxy - the way they do it on the science fiction programs - it would take a hundred thousand years to do it".
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It's all in your perspective. If you could offset the effects of acceleration (some kind of internal force field local to the ships cabin which would accelerate every element in your local environment at exactly the same rate), the ship could attain astounding accelerations. Now of course that is a science fiction idea but it isn't one which violates any law of physics except perhaps the energy problem which is not trivial. Let us suppose we have some way of using the free matter in space to obtain this energy (if we are moving fast enough, the amount of material we intercept could be quite large).
So let us say any desired acceleration is possible. If that is the case, we can go anyplace in the universe in as little time as we desire (insofar as ship time is concerned). Using a “earth rest frame of reference map of the universe” together with a ship time clock for time measurements, we can achieve any velocity right up to infinity and, strange as it might seem, we can use Newtonian physics to plot our course through the universe. That is an interesting consequence of using that mixed coordinate system. I suspect, if humans ever do achieve interstellar travel, they will use my geometry for plotting their course; it is much simpler than using Einstein's picture. For any physicists reading this note that one “g” acceleration (in the mixed coordinate system) is not one “g” acceleration in the ships frame so the standard relativistic comparisons are not valid. (I just pointed that out because I know you will do the relativistic calculations and point out my answer is different).
But back to the reason I mentioned this case. It is much easier to see rapid travel as “forcing” one into the future instead of in terms of a limiting velocity. For example, Alpha-Centauri is roughly four light years away. It is somewhat surprising that one “g” (32 feet per second per second) is almost exactly equal to one light year per year per year. So if we accelerated off towards Alpha-Centauri at one “g” (as measured on our mixed coordinate system) until we got half way there (two light years)
it would take two years (ship time). We could then de-accelerate for another two years and arrive at rest at Alpha-Centauri. We could spend what time we needed there and then return to earth in another four years (ship time). So we would say the round trip was eight years long. How much time would pass on earth?
The answer is quite simple: our actual path in my space would be four segments, each two light years in the x direction plus two light years in the tau direction, c being one light year per year. Since these directions are orthogonal to each other, our actual total distance of travel would be
light years. So the earth observers would say the trip took roughly eleven years and four months. That is, we could see ourselves as being forced into the future a distance of roughly three years and four months.
Suppose we wanted to go to the other side of the galaxy, some 200,000 light years away. Half way would be 100,000 light years;
=447 years so, at one “g” it would take roughly 1,800 years ship time for the round trip. At four g's (something the crew could probably get used to) we could do the round trip in roughly a little over 900 years (ship time). But how long would we be gone, earth time?
which is roughly 410,000 years. Just a tad short (by a mere 10,000 years) of the apparent speed of light. In this case we have been pushed about 409,100 years into the future. But what will the crew say their velocity was? They went some four hundred thousand light years in a little over 900 years. That would be almost 450 light years per year.
It's all how you look at these things. And I also get annoyed with professional physicists.
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Originally Posted by AnssiH
Well, then they go on to talk about space warps in terms of static spacetime, and about tachyons in a really stupid and incoherent manner (They seem to think tachyon simply refers to an "infinitely fast" object or something). I can't go on because I'm getting too depressed over that, so back to the topic  |
You should notice that “tachyons” don't exist in my representation. “Apparent” velocities in excess of light are just plain -???- “not possible” -???- (see the above analysis). That is one reason I do not like Einstein's picture: it suggests the existence of phenomena which violate the logic of his own construct. A very poor characteristic for any theory to contain.
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Originally Posted by AnssiH
While I was able to understand that that expressions is true, I do not know what the algebraic steps are in between there. It's just once again my unfamiliarity with math, I'm sure it's something really simple :P
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We started with the expression
subtracting
from both sides, we obtain
and then dividing by
one obtains
And that should take you to the end of the OP. I just read your latest post and agree with most all of it; however, I don't think it would be possible to chart a path which would allow you to party all the time by accelerating your ship in a manner where it would be the New Year's Eve on earth all the time! The general relativistic transformation has to yield a stopped clock on the earth as seen from your ship! That, I think might require an infinite acceleration. But maybe you could get far enough away from the earth such that there was enough mass between you and the earth to yield a black hole solution.
Have fun -- Dick
