Question about General Relativity Theory

[Johnny5]

This thread is for any experts in the general theory of relativity.

 

 

Suppose that it is possible to accelerate like the starship enterprise does, where its going at warp 1, and then jumps to warp 7, but the inhabitants aren't tossed about, because they cannot feel any forces due to changes in their speed.

 

Suppose that is possible, and has been done by mankind in the future.

 

Would that existence of that kind of ship be experimental proof of the falsity of the principle of equivalence?

 

A simple yes or no will do.

 

Thank you in advance

[Janus]

That's like asking:

If Unicorns really existed, would their horns actually be an aphrodisiac?

[ydoaPs]

they wouldn't be accelerating. they would be going the same speed. do you know how WARP speed is supposed to work?

 

edit:even if they were accelerating, they have "inertial dampers."

[Johnny5]

The question has nothing to do with star trek, its about physics.

 

In fact, its about the principle of equivalence.

 

I can rephrase the question...

 

Suppose in the future mankind builds a spaceship which can do the following...

 

It can be at rest in an inertial reference frame in space, with the occupants floating.

 

Then they can be gently pressed to the floor, once the engines are on so that their weight is Mg, what it is here on earth.

 

Now, let F denote the frame in which they were originally at rest in.

 

Right now, their acceleration a in this frame is equal to 9.8 m/s^2

 

SO HERE IS THE QUESTION...

 

Suppose that a second propulsion system is now turned on, and their acceleration jumps to 1000g in frame F, but they still feel a weight W of Mg.

 

Would the existence of such a ship invalidate the general theory of relativity?

 

Yes OR No?

 

If I am not being clear enough, I can improve on that.

[swansont]

That's like asking:

If Unicorns really existed' date=' would their horns actually be an aphrodisiac?[/quote']

 

I prefer "If you built a perpetual motion machine, what color would the physics require it to be?"

[Johnny5]

I prefer "If you built a perpetual motion machine, what color would the physics require it to be?"

 

Just yes or no please. Depending on the answer, I may rapidly learn GR or not.

[swansont]

Just yes or no please. Depending on the answer, I may rapidly learn GR or not.

 

Answer me this: Have you stopped beating your wife? yes or no, please.

[Johnny5]

Answer me this: Have you stopped beating your wife? yes or no, please.

 

She used to beat me, you have it backwards.

[[Tycho?]]

That's like asking:

If Unicorns really existed' date=' would their horns actually be an aphrodisiac?[/quote']

 

Well of course.

[J.C.MacSwell]

I prefer "If you built a perpetual motion machine, what color would the physics require it to be?"

 

"Isentropic Red"

[Johnny5]

I prefer "If you built a perpetual motion machine, what color would the physics require it to be?"

 

Swansont, you have just demonstrated that you understand a very important logical principle. Can you explain that principle?

[swansont]

Swansont, you have just demonstrated that you understand a very important logical principle.

 

Oh, goody. Do I get a gold star?

 

 

Can you explain that principle?

 

Why, so you can once again change the subject? Your question was nonsense, and you were called on it. End of story.

[Johnny5]

Oh' date=' goody. Do I get a gold star?

 

 

 

 

Why, so you can once again change the subject? Your question was nonsense, and you were called on it. End of story.[/quote']

 

It's not supposed to be nonsense. I need to try harder. Give me a moment.

 

Ok first consider an Einstein elevator.

 

A man is standing in an elevator, which is accelerating uniformly through interstellar space.

 

The man is holding an apple in his hand, which to his sensory perception appears to weigh exactly what it did when he was on earth.

 

But his elevator has no windows. And the man is forgetful, he doesn't remember how his trip began. He is no longer sure whether his elevator is at rest on the surface of the earth, or not. He thinks maybe, he is in a starship, accelerating through interstellar space, on some kind of star voyage.

 

But the fact that the apple weighs the same as it did on earth, is throwing him.

 

He also thinks he knows the laws of physics, specifically...

 

Principle of equivalence: Gravitational mass and inertial mass are equivalent. In other words, there is no need to differentiate between them.

 

His understanding of gravitational mass comes from the following formula:

 

[math] \vec F = -GU_1U_2 \frac{\hat r}{r^2} [/math]

 

In the formula above, U1 denotes the gravitational mass of some object like a planet, and U2 denotes the gravitational mass of some other object like a human being, who is standing on the surface of the planet. The symbol r denotes the distance between the centers of inertia of the two gravitating bodies. The negative sign indicates that gravity is a strictly attractive force, there is no such thing as repulsive gravity. G is just a temporal constant of nature, which has been measured by experiment, and has the appropriate units so that the LHS of the equation has units of force. The letter r with the little hat on it, called appropriately r-hat, is a unit vector which points from the center of inertia of one of the objects, right towards the center of inertia of the other object.

 

Now, his understanding of inertial mass comes from the following formula:

 

[math] \vec F = \frac {d(Mv)}{dt} [/math]

 

The symbol M in the formula above, is called inertial mass. Now comes an important question, which is this, "how do you measure the inertial mass of something?" Here is how the man answers this question:

 

 

You give the object a push.

 

You give it a shove in some chosen direction, and then the center of inertia of the object accelerates in a reference frame in which the center of inertia used to be at rest. So the center of inertia accelerated in that frame, and the accelerating is easily measurable using clocks at rest in the frame, and rulers at rest in the frame. So that you can compute the acceleration a of the object in the frame. The symbol a is a vector quantity, which means that it has both magnitude and direction.

 

Now, you assume that inertial mass M is a property of the object, and doesn't change because you pushed the object. Using calculus, the man also knows this:

 

[math] \vec F = M\frac {d\vec v}{dt} +\vec v \frac {dM}{dt} [/math]

 

Since he assumes that the inertia of the object doesn't vary when he pushes it, it follows that dM=0, whence this formula can be used in the appropriate circumstances:

 

 

[math] \vec F = M\frac {d\vec v}{dt} = M \vec a [/math]

 

As you can see, the man understands that acceleration is the derivative with respect to time of velocity.

 

Since the gravity formula has the same units as the formula known as Newton's second law of motion, he can equate the two formulas as follows:

 

[math] -GU_1U_2 \frac{\hat r}{r^2} = M \vec a [/math]

 

He then invokes the principle of equivalence, which is that gravitational mass and inertial mass are absolutely equivalent, and so he can write this:

 

[math] -GM_e M \frac{\hat r}{r^2} = M \vec a [/math]

 

Where M_e is the mass of earth, and M is his mass. For you see, he isn't sure about whether or not his elevator is on the surface of the earth.

 

Now, there is a scale inside the elevator, which measures his weight W. He feels like he usually feels when he is on earth, and he knows that the rate of acceleration due to gravity is 9.8 m/s^2 = g, so that W=Mg, so he writes:

 

[math] -GM_e M \frac{\hat r}{r^2} = M \vec g [/math]

 

He then divides both sides of the equation above by M, since he knows that his inertial mass is nonzero, so he obtains the following formula:

 

[math] -GM_e \frac{\hat r}{r^2} = \vec g [/math]

 

So now, he thinks that it might be possible that his rate of acceleration through interstellar space is equivalent to the LHS of the above formula.

 

And this possibility has occurred to him, because he assumes that the principle of equivalence is true.

 

But then he wonders for a moment. What if the principle of equivalence isn't true? He never had any reason to doubt it before, he previously believed it. But the man is being honest with himself, and says, "you know what, I really am not sure whether or not gravitational mass and inertial mass are equivalent."

 

He then wonders what could falsify the principle of equivalence, and he comes up with the following idea...

 

He thinks back to Newton's second law for a moment...

 

[math] \vec F = M\frac {d\vec v}{dt} +\vec v \frac {dM}{dt} [/math]

 

If his elevator is using a conventional propulsion system, then it is not the case that dM is zero. The system mass is varying in time, matter is being ejected from the elevator, in order to make F be nonzero.

 

He rewrites Newton's second law as follows:

 

[math] \vec F = M\vec a +\vec v \frac {dM}{dt} [/math]

 

He can feel that his weight is W, what it normally is on earth, and so he writes:

 

[math] W = M\vec g = M \vec a +\vec v \frac {dM}{dt} [/math]

 

He then writes:

 

[math] \vec g = \vec a +\vec v \frac{1}{M} \frac {dM}{dt} [/math]

 

He then writes:

 

[math] 9.8 = \frac{dv}{dt} + v \frac{1}{M} \frac {dM}{dt} [/math]

 

He now realizes, that he is uncertain which frame his speed v was defined in.

 

He then wonders this, what if his propulsion system doesn't work by ejecting material from the ship... and writes this...

 

[math] 9.8 = \frac{dv}{dt} [/math]

 

He stares long and hard at that formula for a moment. He then thinks, what if there are two propulsion systems which are accelerating my ship through interstellar space, after all I didn't build the elevator.

 

What if propulsion system one works by ejecting material from the elevator, and propulsion system two works in another way which I don't understand, without ejecting material so that dM=0. Then, the following would be the case:

 

When propulsion system one is on, there is a force on the ship, but when propulsion system one is off, there is no force on the ship and I will float weightless.

 

When propulsion system two is on, and propulsion system one is on, propulsion system two will accelerate the ship, in absense of an external force. This would make any additional change in speed of the elevator undetectable by my sensory perception, in other words my weight inside the ship wouldn't change, even though the speed of the ship is changing.

 

And it is this idea which finally makes him wonder whether or not the principle of equivalence is true. He thinks back to Einstein, who he knows formulated the principle. The idea behind the work of the general theory of relativity, is that being at rest on the surface of a planet with acceleration due to gravity g, is completely equivalent to uniform acceleration through deep space at a rate dv/dt = g.

 

So he finally realizes that if propulsion system number two is possible, then his elevator could be accelerating at some rate far greater than g, but his weight would still be what it is on earth. So he now questions whether or not the existence of such a propulsion system would all by itself invalidate the principle of equivalence.

 

So now comes a question for those who consider themselves experts in the general theory of relativity.

 

Suppose that propulsion system number two, has been built. Would that mean that the principle of equivalence is false?

 

 

Yes or no?

 

 

 

PS: If you answer the question properly for me, you can have all the stars you want. Kind Regards

[Johnny5]

Here is perhaps the simplest way to explain my question...

 

What IF

 

Your weight inside a spaceship is not necessarily directly proportional to it's acceleration as defined in some inertial reference frame?

 

Would that mean that the principle of equivalence is false?

 

Or to phrase my question still another way,

 

what if it were possible to go from rest to 4000 miles per hour in just a few seconds, but never know (from inside the Elevator), that you changed speeds. Would that mean that the propulsion system used, demonstrates that the principle of equivalence is false?

[swansont]

In the middle there it looks like you changed m from being the mass of the man to being the mass of the elevator/spaceship, and then they are both in the same equation.

[ydoaPs]

The question has nothing to do with star trek' date=' its about physics.

 

In fact, its about the principle of equivalence.

 

I can rephrase the question...

 

Suppose in the future mankind builds a spaceship which can do the following...

 

It can be at rest in an inertial reference frame in space, with the occupants floating.

 

Then they can be gently pressed to the floor, once the engines are on so that their weight is Mg, what it is here on earth.

 

Now, let F denote the frame in which they were originally at rest in.

 

Right now, their acceleration a in this frame is equal to 9.8 m/s^2

 

SO HERE IS THE QUESTION...

 

Suppose that a second propulsion system is now turned on, and their acceleration jumps to 1000g in frame F, but they still feel a weight W of Mg.

 

Would the existence of such a ship invalidate the general theory of relativity?

 

Yes OR No?

 

If I am not being clear enough, I can improve on that.[/quote']

THEY DO NOT ACCELERATE. go to sayo's site and look up warp drive. the name somewhat tells you how it is supposed to work.

[Johnny5]

In the middle there it looks like you changed m from being the mass of the man to being the mass of the elevator/spaceship, and then they are both in the same equation.

 

yes... that was wrong indeed.

 

 

He then wonders what could falsify the principle of equivalence' date=' and he comes up with the following idea...

 

He thinks back to Newton's second law for a moment...

 

[math'] \vec F = M\frac {d\vec v}{dt} +\vec v \frac {dM}{dt} [/math]

 

If his elevator is using a conventional propulsion system, then it is not the case that dM is zero. The system mass is varying in time, matter is being ejected from the elevator, in order to make F be nonzero.

 

He rewrites Newton's second law as follows:

 

[math] \vec F = M\vec a +\vec v \frac {dM}{dt} [/math]

 

He can feel that his weight is W, what it normally is on earth, and so he writes:

 

[math] W = M\vec g = M \vec a +\vec v \frac {dM}{dt} [/math]

 

 

You mean in there dont you?

[Johnny5]

THEY DO NOT ACCELERATE. go to sayo's site and look up warp drive. the name somewhat tells you how it is supposed to work.

 

Where is Sayo's site? I am interested in real physics you know, but I will have a look.

[swansont]

You mean in there dont you?

 

Yes.

[atinymonkey]

I am interested in real physics you know, but I will have a look.

 

'Real' physics?

[ydoaPs]

Where is Sayo's site? I am interested in real physics you know, but I will have a look.

wait, aren't you Mr. SR is BullS*** ? anyway, his site is on his sig. i think

[Johnny5]

...his site is on his sig. i think

 

I looked at his signature, and saw something about squirrels. No website.

[swansont]

'Real' physics?

 

Gotta love the irony, don't you?

[ydoaPs]

http://www.starfleetarchive.com/

[Johnny5]

You guys are not answering my question here...

 

I want to know if...

 

I have said it 10 different ways so far...

 

I want to know if... force and acceleration can be decoupled???

 

Yes I think that is what I am asking.

 

For the nth time...

 

If force and acceleration can be decoupled, would that mean that the principle of equivalence is false?

 

I am trying to ask it the best way I know how...

 

If it is possible to change speeds, without having your weight altered, is the principle of equivalence false?

 

There try answering one of them.