I'm so fervently opposed to this notion of "relative to spacetime" that I absolutely insist on references. Your claims of "absolute rest" seem to violate the very foundational postulates of relativity theory.That said, I never claimed that the Earth would go faster than the speed of light relative to anything. The entire gist of my post was to reproduce a proof that a constant acceleration (and linearly increasing velocity) in one frame of reference translates to asympotitic acceleration (and asymptotic velocity with asymptote at v = c) in any inertial frame of reference. Which part of that do you disagree with?
I disagree with your notion that the earth could travel at 9.8m/s/s forever through spacetime. It would eventually hit the light-speed barrier. Unless the earth has no mass, it cannot cross into this velocity.
QuoteI disagree with your notion that the earth could travel at 9.8m/s/s forever through spacetime. It would eventually hit the light-speed barrier. Unless the earth has no mass, it cannot cross into this velocity....There is no light-speed barrier...From reading your posts on the speed of light in the thread "faster than light", your notion of "absolute spacetime" seems to be rooted in the fact tht something always has a velocity of 300,000 m/s in space and time, and thus, logically, can not surpass said velocity. This seems to be a simple misunderstanding, though. You see, in reality, people will always measure their velocity through spacetime to be the speed of light. An object, that, in its own frame of reference, is at rest, will meaure it's velocity through space to be 0 m/s and through time, be 300,000 m/s, whereas an observer from an outside frame of reference will measure it differently, in the manner described by Erasmus, in the case of an accelerating object.Of course, I'm merely basing this off your posts in another thread, and what I believe to be your position, feel free to tell my if I've constructed a strawman.
I am ignoring the effects of time when travelling through spacetime
The people in spaceship 2 will also be experiencing earthlike pull to the floor as they will be accellerating at 9.8m/s/s. But, to spaceship 1, spaceship 2 is accellerating away at 19.6m/s/s.
c as Speed LimitThe speed of light c is said to be the speed limit of the universe because nothing can be accelerated to the speed of light with respect to you. A common way of describing this situation is to say that as an object approaches the speed of light, its mass increases and more force must be exerted to produce a given acceleration. There are difficulties with the "changing mass" perspective, and it is generally preferrable to say that the relativistic momentum and relativistic energy approach infinity at the speed of light. Since the net applied force is equal to the rate of change of momentum and the work done is equal to the change in energy, it would take an infinite time and an infinite amount of work to accelerate an object to the speed of light. (Sorry, Captain Kirk. We can't give you warp speed!)A common resistance to the speed limit is to suggest that you just accelerate two different objects to more than half of the speed of light and point them toward each other, giving a relative speed greater than c. But that doesn't work! Time and space are interwoven in such a way that no one observer ever sees another object moving toward them at greater than c. The Einstein velocity addition deals with the transformation of velocities, always yielding a relative velocity less than c. It doesn't agree with your common sense, but it appears to be the way the universe works.
For the speeds and velocities I am talking about, there is no need to bother with the Lorentz transformations.
The speed of light c is said to be the speed limit of the universe because nothing can be accelerated to the speed of light with respect to you.
it would take an infinite time and an infinite amount of work to accelerate an object to the speed of light.
A common resistance to the speed limit is to suggest that you just accelerate two different objects to more than half of the speed of light and point them toward each other, giving a relative speed greater than c. But that doesn't work!
Matter cannot move faster then the speed of light through spacetime. The point at which I've been trying to get at this entire time.
... meaning it would not be able to maintain a 9.8m/s/s accelleration as it got closer and closer to the speed of like. It would start slowing it's decelleration.
It could keep doing this for infinity if you like, getting closer and closer to the speed of light, but never quite reaching it. But it would not be able to travel as fast as light itself(or faster). This means it could not maintain a 9.8m/s/s accelleration needed to simulate gravity for very long.
Again, exactly what I stated above. If you tried this two-buildings-accelerating thing, neither of them would observe the other to be moving faster than light, ever.
According to the classical newton universe, the object will accellerate forever as long as no other forces act upon it. So your friend would be correct if this was the way the universe worked. But lucky for you it is not.Taking General Relativity into account, nothing can travel faster then c, or the speed of light in a vacuum. We have to ignore the source of the accelleration for the object because to propel even single particles to near the speed of light requires an incredible amount of energy. But ignoring that no, in General Relativity you could not exceed c, nor could you maintain a 9.8m/s accelleration forever. As the object approaches c, the accelleration would decrease exponentially. The object will never reach c, but it will get closer and closer to it. As the accelleration decreased, so would the effects of the push to anything on the surface of the object. You can tell your friend that he is incorrect.
Thanks for the reference. I'm a little worried that you may have misrepesented the hypothesis, but I'll just assume you did not. In any case, Dr. Hallock and I agree that as measured from an inertial frame, the Earth's velocity would only asymptotically approach c. We only disagree on what would happen in the frame of reference of the ship.As a thought experiment, consider what would happen if the Earth (spaceship, whatever) suddenly stopped accelerating. Now it's inertial again, meaning it's at rest again, meaning it should be able to accelerate from 0 all over again, because all inertial reference frames are equivalent. If you are right, then upon starting to accelerate again, the passengers on the ship would not feel the same artificial gravity that they felt the first time the ship starts accelerating, which would give them an experiment to test for "absolute rest", which is a glaring contradiction to the principle of relativity.
While in special relativity there is no standard of rest and no preferred reference frame, in general relativity the situation is somewhat different. A rest frame for any particular region of space can be defined as the frame which is not rotating compared to the background of distant stars and for which the cosmic microwave background radiation, CMBR, has the same spectrum in all directions and so the concept of local motion in that frame is meaningful. In another region of space, there would also be a rest frame for which the CMBR is the same in all directions, but the two rest frames are moving with respect to each other so there is no preferred frame of that type for the universe as a whole and no center of the universe. We can however, define a comoving rest frame for the universe as a whole for which the requirement of the CMBR being the same in all directions and there being a standard of rotation based on the distant stars is met at all locations.
If it stopped accellerating, it would still have it's remaining velocity.
Also, there is a state of absolute rest in any frame and can be determined. I mentioned using the background radiation as a way to find a state of rest before.
Quote from: "troubadour"Also, there is a state of absolute rest in any frame and can be determined. I mentioned using the background radiation as a way to find a state of rest before.Just out of curiosity, what's the Earth's velocity with respect to the CMBR? Also, what makes the CMBR a preferred reference frame?
Well, did any of you know that science has now proven two things: 1. That a light pulse can travel faster than light (since light is both a particle, and a wave, this might suggest that objects can too) and 2. that said light pulse actually arrived before it left when it traveled faster than light. This means, that it essentially travelled back in time. This notion may seem ridiculous, but I have provided a link to the article. This suggests that it might be possible for matter to break the light speed barrier under very specific conditions. So, let's say the earth is flat (but it's not). And then let's say that these specific conditions are met somehow, and the earth starts travelling upwards at a speed faster than the speed of light. Well, then we would all be travelling backwards in time, which we know is not true. Therefore, the earth cannot be constantly gaining speed (not only because it can't travel faster than light without travelling back in time, but also because of the obvious reason that there is nothing propelling it upwards) because, as was stated in the beginning of this thread, the earth would have broken the light speed barrier by day 354. Well, the earth has obviously been around much longer than that, so it would already be travelling faster than light, which can't be possible, or we would be moving backwards in time. Hope this settles the gravity factor once and for all, but I'm expecting a bunch of conspiracy claims, so it probably won't.
Quote from: "Erasmus"Just out of curiosity, what's the Earth's velocity with respect to the CMBR? Also, what makes the CMBR a preferred reference frame?The CMBR's source is the big bang, the beginning of space and time. If you get to the point where it is even in all directions (no red or blue shift), then you are at rest in relation to spacetime.
Just out of curiosity, what's the Earth's velocity with respect to the CMBR? Also, what makes the CMBR a preferred reference frame?
If gravity is the earth accelerating upwards, then does that mean FEers don't believe gravity has a relation to mass?
Quote from: "troubadour"Quote from: "Erasmus"Just out of curiosity, what's the Earth's velocity with respect to the CMBR? Also, what makes the CMBR a preferred reference frame?The CMBR's source is the big bang, the beginning of space and time. If you get to the point where it is even in all directions (no red or blue shift), then you are at rest in relation to spacetime.Um, obviously all that means is that you're at rest relative to the CMBR.So what about the Earth's velocity w.r.t. the CMBR?