Why is faster-than-light travel 'impossible'?

[Hielor]

Not quite correct - an inertial frame is free of proper acceleration.

Also, about reference frames in general relativity (not just inertial ones):

There is no experiment observers can perform to distinguish whether an acceleration arises because of a gravitational force or because their reference frame is accelerating. —Douglas C. Giancoli, Physics for Scientists and Engineers with Modern Physics, p. 155.

I don't see what that quote has to do with anything. If a vessel is accelerating under its own thrust, we don't need to do any experiments to know whether the acceleration felt by the occupants inside is from gravity, because we know where it's coming from--their reference frame (the spacecraft) is accelerating.

The occupants of the spacecraft feel the effect of 10g acceleration. The occupants of Earth do not. Ergo, the spacecraft is accelerating, and the Earth is not--it is not equally valid to say that the Earth is accelerating away from the spacecraft.

 

[Urwumpe]

Hielor: That is wrong. You can not even tell properly, if you are experiencing 1g gravity or 1g proper acceleration just in this moment.

How could you? If you sit inside an aircraft and watch the wall, can you tell if you are accelerating or experiencing gravity? The wall could be experiencing just the same.

 

[Stoat]

Hi Jarvita, how do you get square roots and stuff to appear on the board?

 

[Urwumpe]

Hi Jarvita, how do you get square roots and stuff to appear on the board?

Stoat: Between the [math][/math] tags, you can write laTex 2.0 math expressions.

 

[Keatah]

Navigator Trey, eh? Couldn't find his way outa paper bag with a compass!

 

[Hielor]

Hielor: That is wrong. You can not even tell properly, if you are experiencing 1g gravity or 1g proper acceleration just in this moment.

How could you? If you sit inside an aircraft and watch the wall, can you tell if you are accelerating or experiencing gravity? The wall could be experiencing just the same.

So you're saying that gravity magically appears out of nowhere and causes spacecraft to move?

It does not matter whether the acceleration comes from gravity or some other source. The fact remains that one of the two has accelerated and the other has not.

Consider a simplified case: Two hollow spheres of gravitationally insignificant mass in an empty vacuum, each of which has a smaller solid sphere inside at the exact center. One of the hollow spheres begins accelerating away from the other at a rate of 2g.

What happens to the solid spheres inside the hollow ones? One of them will bump against the side of its container, one will not. One of the two is undergoing acceleration and the other is not. You're complicating things by introducing gravity where it is irrelevant. In this case, it is quite obvious which one has accelerated, and there is no way to say that it is the other way around.

 

[Urwumpe]

What happens to the solid spheres inside the hollow ones? One of them will bump against the side of its container, one will not. One of the two is undergoing acceleration and the other is not. You're complicating things by introducing gravity where it is irrelevant. In this case, it is quite obvious which one has accelerated, and there is no way to say that it is the other way around.

It is not. what would happen if you put such a sphere pair on the ground on Earth? would the small sphere magically float around as long as you don't accelerate it?

 

[Hielor]

It is not. what would happen if you put such a sphere pair on the ground on Earth? would the small sphere magically float around as long as you don't accelerate it?

Uh, what? I never claimed they would, and you're complicating things by adding gravity again. Okay, I can do that:

Two boxes sitting in a warehouse. Inside each box is sitting a cube which experiences no friction with the inner walls of the box. A forklift begins pushing one of the boxes away from the other at a constant acceleration of .5g. What happens to the cubes?

The cube in the box being accelerated will slide to the side of its box. The cube in the untouched box will not move. Again, we have detected unequivocably which box is accelerating, and we cannot claim that the untouched box was accelerating away from the one that was pushed.

 

[Urwumpe]

The cube in the box being accelerated will slide to the side of its box. The cube in the untouched box will not move. Again, we have detected unequivocably which box is accelerating, and we cannot claim that the untouched box was accelerating away from the one that was pushed.

Don't you notice that it is you, who removes one important factor of relativity (space-time and distortion of it) from the equation. You accuse me of introducing something, while it is actually you who introduces the opposite (a lack of space-time and gravity) for the sake of getting your desired results. And that is the problem. Again: There is no, never, not at all, a difference between gravitation and inertia in relativity. It doesn't matter if you want to talk only about acceleration, because you are then equally also talking about gravitation. you can't tell.

What if your two boxes had been accelerating a constant rate since you constructed them and one of these actually stopped? Could you tell?

 

[Hielor]

Don't you notice that it is you, who removes one important factor of relativity (space-time and distortion of it) from the equation. You accuse me of introducing something, while it is actually you who introduces the opposite (a lack of space-time and gravity) for the sake of getting your desired results. And that is the problem. Again: There is no, never, not at all, a difference between gravitation and inertia in relativity. It doesn't matter if you want to talk only about acceleration, because you are then equally also talking about gravitation. you can't tell.

Space-time distortion is insignificant at the speeds I'm talking about. Note also that I've never claimed that there is any difference between gravity and acceleration...you're the one going on about gravity. I'm just pointing out that acceleration, regardless of what causes it, is not relative or symmetric, because you will always be able to tell the difference between the object that accelerated and the object that didn't.

What if your two boxes had been accelerating a constant rate since you constructed them and one of these actually stopped? Could you tell?

Yes, absolutely, because one of the cubes would no longer be pressed against the side of the box by the acceleration.

 

[Stoat]

I'll have to have a bit play with that, bear in mind that I'm pretty thick :huh:

A few words on the "superlens," create a grid of nano wires which have a negative permeability. Then nano split rings, tank circuits in effect, which have a negative permittivity. (On first reading about this, I thought neg times neg, equals a positive but no, you get a + bi type expressions)

These lenses have some pretty wild properties. Light bends around them, and we can have anti parallel wave forms. One to try out is the cos of the natural log of the Lorentzian. We have an f.m wave that scoots off with some group velocity, to the right, and another wave which travels to the left at a much lower group velocity.

I suppose that if we live in a Bose Einstein condensate, then we live in a tiny very "cold" bit of a huge universe. That has to be a bit of a bummer for the old ego, don't ya know

 

[Urwumpe]

Yes, absolutely, because one of the cubes would no longer be pressed against the side of the box by the acceleration.

But it would not be absolute as you claim it. You just have a difference between two references. But unless you measure the velocity change between the two, you can't even tell if the difference is change in speed or change in gravity.

 

[Hielor]

But it would not be absolute as you claim it. You just have a difference between two references. But unless you measure the velocity change between the two, you can't even tell if the difference is change in speed or change in gravity.

It doesn't matter what caused the difference, didn't you just get done saying that inertia and gravitation are the same? The fact remains that one is no longer being accelerated, one is still being accelerated, and you can tell which is which.

 

[Fizyk]

Hielor: imagine you were in a coma, you wake up and you find yourself in a closed room without windows. You feel the normal 1g gravity. The point of the gravity-acceleration equivalence is that you might as well be on a rocket which accelerates at 1g, and you have no way to tell (without looking outside) which possibility is true.

Urwumpe: it is true, that gravity and acceleration are equivalent, but the twin paradox doesn't need gravity. The same thinking applies to the situation of two rockets:

Let's imagine two twins floating in empty space in their rockets. One of the twins (let's say it's twin 2) starts the engines, accelerates to a near-c velocity relative to the other one, turns around and goes back. Which one is older when they meet again?

The naive thinking, which leads to the paradox says: twin 2 was going fast, so he should be younger. But relative to the twin 2, it was twin 1 who was accelerating and going fast, so he should be younger. Paradox - both should be younger.

The point is, acceleration is not relative, as Hielor said. Twin 2 can tell he was accelerating, whether it was by gravity or by the engines of his rocket, but his experience was different from twin 1's experience, who was floating freely all the time. The reference frame of twin 1 was inertial, but the frame of twin 2 was not.

Another good way to look at this, valid in curved space-time too: first twin's world line was a straight line (or, more generally, a geodesic), while the world line of twin 2 was curved. Their world lines meet at two events - the event where twin 2 starts his rocket and the event where the twins meet again. The time that passed for each of the twins is equal to the length of their world lines. Straight lines are the longest paths between two points in space-time, so the one that was using his engines will be younger when they meet again.

 

[Artlav]

imagine you were in a coma, you wake up and you find yourself in a closed room without windows. You feel the normal 1g gravity. The point of the gravity-acceleration equivalence is that you might as well be on a rocket which accelerates at 1g, and you have no way to tell (without looking outside) which possibility is true.

What about tides?
The rocket would not produce a tidal difference, but a planet's gravity would be a little less at the ceiling than at the floor.

 

[Fizyk]

What about tides?
The rocket would not produce a tidal difference, but a planet's gravity would be a little less at the ceiling than at the floor.

It's funny, but actually the rocket would produce a tidal difference too. Simply put, because the front of the rocket is in a bit different place than the back of the rocket, the acceleration causes the time to flow a bit differently in the front than in the back (just like gravity does), which in turn means that the front must accelerate a bit slower than the back for the rocket to stay the same size.

The only difference between an accelerating rocket and the gravity of a planet would be in the lateral directions. The gravitational field of a planet has spherical symmetry, and the "gravity" produced by accelerating rocket doesn't. A planet with an infinite radius would produce the same results, though (but I'm not 100% sure about that).

 

[Artlav]

It's funny, but actually the rocket would produce a tidal difference too. Simply put, because the front of the rocket is in a bit different place than the back of the rocket, the acceleration causes the time to flow a bit differently in the front than in the back (just like gravity does), which in turn means that the front must accelerate a bit slower than the back for the rocket to stay the same size.

That's interesting, how does it work?
Tentatively, the front should accelerate a little slower than the back, or there would be no forces and perceived gravity, but what is the exact reasoning and explanation?

 

[Fizyk]

The simplest reasoning involves the Lorentz contraction.

If the front and the back of the rocket had the same acceleration (let's say it's relative to Earth), the length of the rocket would be constant relative to Earth. But, because the rocket goes faster and faster, its length must decrease (relative to Earth) due to Lorentz contraction. So, in the Earth's frame of reference, the front of the rocket accelerates a bit slower than the back, so that the rocket contracts as it has to. This translates to different accelerations perceived by people in different places in the rocket.

 

[Stoat]

The principle moment of the rocket would change, or then again perhaps not :lol:

 

[ZombiezuRFER]

isn't acceleration all relative? ie, one object is accelerating when compared to another, but the same can be applied to the other?