Science Forums 2

[AnssiH]

Originally Posted by Doctordick

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).

Yeah, and what bothers me is that they talk about relativity and the relativistic speed limit as if it was some sort of speed limit against some metaphysical space, and back that idea up with a computer animation which gives everyone exactly the idea of racing through space really fast alongside a beam of light (i.e. they give the idea that at light speed, light is at rest with you). Certainly someone might argue that they were talking about the travel taking this and this long in earth's frame, just to simplify things or whatever, but I really don't think that sort of simplification helps in communicating what relativistic speed limit means. It only serves to confuse people.

I don't mind them talking about special relativistic view only, i.e. ignoring gravitational effects or energy questions for simplicity, as you can just imagine that you shift the perspective between different space ships as they pass each others (they can certainly communicate when they pass, so this just serves as a means to discuss our ideas of relativistic ontologies).

So, for all casual lurkers who have fell prey to exactly these sorts of assertions about relativistic speed limit, let it be said that relativity certainly allows for a spaceship to get from Earth to Alpha Centauri in any arbitrarily short period of time, even in 1 second (we can allow them to gain speed before passing the start line on earth) according to its own perspective (its own clocks and its own idea about the distance of the travel)

What the relativistic speed limit more properly means, is that no given object can move faster than C in terms of any inertial frame. That is a consequence of Lorentz transformation being valid (which is a scale-like procedure to the apparent speeds, as oppose to a velocity addition procedure). I.e. in terms of Earth's frame, the clocks on space ship would be said to be at almost standstill. In ship's frame, the distance between Earth and Alpha Centauri would be said to be shrunk into some tiny distance)

The point is, it is not a speed limit against any "space", it is a speed limit against any chosen coordinate system. For anyone who has followed this analysis, that should ring some bells...

The macroscopic dynamics that we are expressing in any given coordinate system, must transform in a very specific manner (for self-coherence reasons) when we choose to express them from a different coordinate system. Quote from my previous post: "it is shown, that the dynamic behaviour of the clock absolutely must be plotted in a way where the supposed geometry and the dynamics of the construction must exhibit relativistic behaviour as a function of the chosen coordinate system."

You could say that it is simply consequential to how persistent objects have been defined, that they exhibit such relationships. It doesn't matter what coordinate system you choose to describe those objects, but as long as they appear in speeds less than C in one coordinate system, they must appear in speeds less than C after transformation to any coordinate system.

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.

Hmmm, yeah that is interesting idea.

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).

My brain went all twisty and it's late so I can't figure this out; would the ships acceleration in the mixed coordinate system show up as constant if it shows up as constant in the ships own measurement?

But one interesting thought that popped to my mind while thinking about this was that all the massive things in the universe appear to be quite close to being rest against each others... I mean, shouldn't we expect massive things to form quite uniformly across "all the inertial frames" so to speak. And if they were spread across all inertial frames in somewhat uniform manner, then from our perspective, most galaxies etc, should appear to be moving at very near the speed of light, so close that they would be almost indistinguishable as galaxies... Hmmmmm, my brain went all twisty again.

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.

Seems like a fairly simple way to figure out these things.

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.
We started with the expression

Yeah it's a bit mixed up concept because people usually keep talking about tachyon's "motion" and "speed", but really the only coherent way to incorporate the idea of tachyons into the picture is just to take something in the past as being affected by something that "happened in the future", i.e. think of it in terms of static spacetime... No matter which way you discuss that concept, it makes zero sense to talk about their motion. I think the idea they have in their head is literally a spacetime changing as a function of another time over and beyond spacetime. I would advise a person to take a deep breath and start over at that point :I

subtracting from both sides, we obtain

and then dividing by one obtains

And that should take you to the end of the OP.

Okay, that's pretty clear now, it was just a procedure I had never seen before and didn't pop into my mind. I'll try and walk through the rest of the OP soon...

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.

Heh, "slightly" out of my depth to work that out, and certainly things get complicated when you start taking all things into consideration... I was intentionally just thinking about it in terms of special relativity and with the idea of changing continuously from one inertial frame to another when you are accelerating, where you'd just assume the simultaneity of that frame (and if you are a party-loving hippie, that's probably the interpretation you want to use

But yeah, even then you couldn't keep it up absolutely forever no matter how far from earth you started :I Well, pretty long party anyway!

At any rate, one more comment to all the lurkers. I'd think anyone can understand, that it makes very little sense to suppose that reality is affected by whichever coordinate system you choose to describe it. Reality probably is whatever it is no matter how you plot it in your spacetime diagram, unless you want to go with some sort of idealistic philosophy.

Yet, the relativistic transformation between coordinate systems is valid. So, shouldn't one be interested to understand why?

At least I've been interested to find an answer to that question, therefore it is pretty hard for me to understand the reluctance to look at work which explains exactly that conundrum...

Maybe part of the problem is that people are drawn to mysterious views of the ontological reality... Look at almost any mainstream presentation of relativity / QM, it's always bunch of way too enthusiastic physicists talking about modern physics in ways that suggest very mysterious ontology to nature. They ALWAYS imply that this is the ontology that scientists have somehow practically proven to be true.

I guess, the more mysterious the presentation makes things sound, the more it sparks the interest of general public, and therefore those descriptions gain the most attention. Everybody loves the possibility of "Many-Worlds" and relativistic time and length contraction and 11 dimensions without understanding where those concepts are coming from...

-Anssi