Questions deriving from the Principle of Equivalence

[Chaste]

Hi all,

There are a few doubts I hope I can get enlightened.

If we were in a lab in outer space, free of gravitational influence and the lab accelerates downwards, what will we experience? do we 'move' to the top of the lab?

What I'm confused about also is, why is that when you have an acceleration of -g, in space, the lab experiences the same thing as if it was on the surface of the earth(motionless). Therefore, you cannot distinguish blah blah blah that whether you are accelerating upwards in space or under the influence of gravity.

So abstract. argh.

 

[Fredrik]

Yes, you will move to the top, exactly as if you're being pulled by a force.

This is an example of how to use the equivalence principle: SR predicts that a clock in the ceiling will tick at a slower rate than a clock on the floor when the lab is accelerating downwards. The equivalence principle says that we can interpret this as a prediction about the behavior of clocks on the floor and in the ceiling of a lab on Earth.

 

[Naty1]

If we were in a lab in outer space, free of gravitational influence and the lab accelerates downwards, what will we experience? do we 'move' to the top of the lab?

Chaste: Suppose the lab was in a gravitational field and contents weightless? Can you then answer your question about acceleration?

A subtle distinction is that in free fall, giving into gravity, when it is present, or floating motionless in the absence of any gravity, are both inertially equivalent (locally). No forces act on either. Once you "accelerate" you feel a force exactly as Fredrick describes.

For example, Wikipedia says
http://en.wikipedia.org/wiki/Weightlessness

The sensation of weightlessness experienced by astronauts is not the result of there being zero gravitational acceleration, but of there being zero difference between the acceleration of the spacecraft and the acceleration of the astronaut.

What I'm confused about also is, why is that when you have an acceleration of -g, in space, the lab experiences the same thing as if it was on the surface of the earth(motionless). Therefore, you cannot distinguish blah blah blah that whether you are accelerating upwards in space or under the influence of gravity.

You have touched upon an aspect of Einstein's genius: it is that very fact ("equivalence")that enabled him to pick from among several theories he developed which experimentally would have been almost identical, too close to make a pick in 1915. Until, I believe, Bill Unruh uncovered a subtle distinction between gravity and acceleration, now Unruh's Law, they might have been considered "exactly" equivalent; now they are seen as "virtually" equivalent.
One answer is because math sez so; another says both curve space; neither is especially satisfying, and certainly not intuitive.
This "equivalence" is like many physical manifestations in our universe, not obvious...not any more than space contraction and time dilation with speed, nor "uncertainty" nor the direction of time we all take for granted; how can we be moving through spacetime at the always constant speed of light? There are many mysteries.

 

[atyy]

So abstract. argh.

It's very concrete. When you go round a bend in a car, the acceleration is directed into the circle, but the centrifugal force pushes you outwards. The centrifugal force is "fake gravity".

 

[Makep]

Hi all,

There are a few doubts I hope I can get enlightened.

If we were in a lab in outer space, free of gravitational influence and the lab accelerates downwards, what will we experience? do we 'move' to the top of the lab?

What I'm confused about also is, why is that when you have an acceleration of -g, in space, the lab experiences the same thing as if it was on the surface of the earth(motionless). Therefore, you cannot distinguish blah blah blah that whether you are accelerating upwards in space or under the influence of gravity.

So abstract. argh.

In the state as you describe in space, you are already in a state of free-fall. When the lab experiences an acceleration of -g, it is acclerating. If the lab is hollow, it will leave you behind traveling at a constant velocity. Otherwise, you accelerate with it in the same direction as it travels.
The lab experiences the same thing as it does on Earth when experiencing -g because, g and -g nullifies each other. You are in a state of free fall.

 

[Chaste]

ok, so according to the scenario I described for a lab accelerating downwards with a=g, we will move to the top of the lab.

But in my point of view, I see that it's like as if the lab was on the surface of the Earth!
where a=g as well! but why are we stuck to the bottom of the lab instead of the top?

and also, why is that when a= -g, in free fall, that it has equivalent experience as that of surface of the Earth. Still trying to absorb what makep said, g and -g nullifies each other. So no forces are being acted on us... won't we be floating then?

 

[Fredrik]

But in my point of view, I see that it's like as if the lab was on the surface of the Earth!
where a=g as well! but why are we stuck to the bottom of the lab instead of the top?

Because you specified that the acceleration is downwards. That makes the situation equivalent to being in an upside down lab on Earth. The acceleration on Earth is in the "up" direction because "not accelerating" means "falling freely".

and also, why is that when a= -g, in free fall, that it has equivalent experience as that of surface of the Earth. Still trying to absorb what makep said, g and -g nullifies each other. So no forces are being acted on us... won't we be floating then?

Yes, you'll be floating if your lab falls freely (regardless if it's straight down or with a sideways velocity that's high enough to miss the Earth). But you don't have a=-g in free fall, it's a=0.

 

[Chaste]

Because you specified that the acceleration is downwards. That makes the situation equivalent to being in an upside down lab on Earth. The acceleration on Earth is in the "up" direction because "not accelerating" means "falling freely".

Why is acceleration on Earth in the up direction? I've always perceived it as "down".

Yes, you'll be floating if your lab falls freely (regardless if it's straight down or with a sideways velocity that's high enough to miss the Earth). But you don't have a=-g in free fall, it's a=0.

so we are floating because the net accleration is 0? meaning downward acceleration and upward accleration cancel each other?
Is that what happens in space where there's no gravitational attraction?

 

[Fredrik]

Why is acceleration on Earth in the up direction? I've always perceived it as "down".

It's down in Newton's theory, and up in GR. The answer to the question "accelerating relative to what?" is different in the two theories.

Newton: "the surface of the Earth"
GR: "an object in free fall"

so we are floating because the net accleration is 0? meaning downward acceleration and upward accleration cancel each other?

I'd say that you're floating because there's no external influence that tries to get you or the lab to accelerate in either direction.

Is that what happens in space where there's no gravitational attraction?

If you're in free fall, your world line is always a "straight line" (technically a geodesic) in spacetime. The only effect a heavy object in your vicinity would have is to change which curves are the geodesics.

 

[Naty1]

In the state as you describe in space, you are already in a state of free-fall

I disagree: free fall is characterized by "no external forces are felt". If you feel a force you are accelerating.

 

[Naty1]

so we are floating because the net accleration is 0? meaning downward acceleration and upward accleration cancel each other?

That's ok as a description in my book. You "float" when you feel no forces applied, hence you are not accelerated.

 

[Naty1]

Why is acceleration on Earth in the up direction? I've always perceived it as "down".

Gravitational force is pulling you DOWN; That's how you would move in free fall. The fact that you are NOT moving down in free fall, the fact that you feel gravity's force pressing UP against your feet when standing means you MUST be accelerating UP.

 

[Chaste]

It's down in Newton's theory, and up in GR. The answer to the question "accelerating relative to what?" is different in the two theories.

Newton: "the surface of the Earth"
GR: "an object in free fall"

I shall focus on asking about the principle of equivalence first.

Why does GR states that acceleration is upwards?

so standing motionless on the surface of the Earth = falling freely?

 

[HallsofIvy]

??Nothing in GR states that "acceleration is upwards". YOU specifice that the "lab accelerates downwards". People explained, properly that, in that case, the lab would move "past" you until you struck the top of the lab and felt an upward force. It was then pointed out that by the eqivalence principle, the downward force of gravity you feel on the surface of the Earth would be equivalent to an upward acceleration (locally- the equivalence principle is only valid locallyZ). That was a specific case and certainly doesn't mean that "acceleration is always upward"! And standing motionless on the Earth is certainly not the same as "falling freely"! I don't know how you could come to that conclusion- Naty1, in post 10, said specifically that feeling a force is NOT falling freely.

 

[DrGreg]

Why does GR states that acceleration is upwards?

If you drop an apple (on Earth), it accelerates downwards relative to you. That means you accelerate upwards relative to the apple.

so standing motionless on the surface of the Earth = falling freely?

No. The apple is falling freely, i.e. "floating". Standing "motionless" is really accelerating upwards (relative to falling apples).

 

[Naty1]

Chaste: as a suggestion forget the quote from Fredrik in your Post # 13. Save that one for last since it's sophisticated.

Here is another way to think of your acceleration upward when standing on earth. Imagine first a mass accelerating you horizontally...you feel pressure pushing you as you gain speed. Now just invert the scene so you are now on top with the mass pushing you vertically up instead horizontally...can you picture you must be getting pushed UP?? same as per my post # 12...

Einstein's equivalence principle recognized that the force of gravity and an equivalent force producing equivalent acceleration force were indistinguishable...not at all obvious as no one else apparently realized it for, say, 2,000 years! You need to read these explanations and think about them...carefully ...getting this in perspective takes some time and for most of us repeated consideration. But it won't take 2,000 years!

 

[Fredrik]

Why does GR states that acceleration is upwards?

GR doesn't tell us what the acceleration is. It just tells us that a certain set of curves in spacetime are "special" in the sense that they are what correspond to straight lines in a flat geometry. That suggests that it might be a good idea to define zero acceleration as the motion that's represented by such a curve. If we do that, then the acceleration of an object resting on the surface of the Earth is going to be upwards, because the curves that we have defined as representing zero acceleration are the ones that describe the motion of objects that are falling freely.

Imagine that the origin of your coordinate system is falling freely. Then how does the z coordinate (altitude) of something resting on the surface change? It's increasing, right? And the speed with which it's increasing is increasing too. So the acceleration is in the positive z direction, i.e. "up".

so standing motionless on the surface of the Earth = falling freely?

Absolutely not.

 

[Chaste]

Chaste: as a suggestion forget the quote from Fredrik in your Post # 13. Save that one for last since it's sophisticated.

Here is another way to think of your acceleration upward when standing on earth. Imagine first a mass accelerating you horizontally...you feel pressure pushing you as you gain speed. Now just invert the scene so you are now on top with the mass pushing you vertically up instead horizontally...can you picture you must be getting pushed UP?? same as per my post # 12...

Einstein's equivalence principle recognized that the force of gravity and an equivalent force producing equivalent acceleration force were indistinguishable...not at all obvious as no one else apparently realized it for, say, 2,000 years! You need to read these explanations and think about them...carefully ...getting this in perspective takes some time and for most of us repeated consideration. But it won't take 2,000 years!

I see, it's a matter of perspective. so our acceleration is like the 3rd law of Newton where we produce an equal and opposite force of motion against the gravity of the earth. Gravity pulls us DOWN while we accelerate UPWARDS relative to the earth. How much gravity pulls us down is how much we accelerates upwards, right?
and since we are standing perfectly well on the surface of the earth, that means we experience no NET acceleration. if not we'll either sink into the ground or flying up, right?
and is the 'mass' that is pushing us upwards the ground itself?

Naty1: I get the picture of 'Rotating the horizontal acceleration' to a vertical one.

the equivalence principle is the same in the sense that we are accelerating upwards on earth, we cannot tell if we are also accelerating upwards in outerspace(free of gravitational fields) since we experience the very same stuff.
so how did Einstein eventually realize that inertia mass = gravitational mass if we cannot distinguish whether acceleration caused is due to a local gravitational field or acceleration upwards? what has this acceleration got to do with mass?

 

[atyy]

There are two different definitions of acceleration. In Newtonian physics being acted on by gravity, friction, electric fields etc produces non-zero acceleration ("3-acceleration"). In general relativity, being acted on by gravity causes zero "4-acceleration", while friction and electric fields cause non-zero "4-acceleration".

The intuition for this is that if acted on by gravity alone (no other forces like friction or electric fields), all objects fall with the same 3-acceleration and will not 3-accelerate relative to each other, as demonstrated by the legendary Galileo leaning tower of pisa experiment. (Yes, the Principle of Equivalence was known to Galileo and Newton.) Newtonian gravity describes Galileo's results using 3-acceleration and by setting gravitational mass equal to inertial mass. Einstein's gravity describes Galileo's results by using 4-acceleration and the curvature of spacetime. In very weak fields like those on earth, space is very nearly flat and the curvature is mainly in time.

 

[Fredrik]

I see, it's a matter of perspective.

It is, in the sense that there's more than one way to define what no acceleration means.

Gravity pulls us DOWN while we accelerate UPWARDS relative to the earth.

No. It's one or the other (depending on which curves we choose to think of as not accelerating), not both. If we define no acceleration as resting on the surface of the Earth, then you have to treat gravity as a force that pulls you down. The acceleration due to gravity is down since F=ma and m>0. You would be falling if there wasn't also an upward force from the ground that exactly cancels the gravitational force. In this case your net acceleration is 0.

If we instead define no acceleration as falling freely, then gravity isn't a force and the only force acting on you when you're resting on the surface of the Earth is the normal force from the ground. It's in the up direction, so the acceleration due to the normal force is in the up direction too. In this case your net acceleration is 9.8 m/s².

How much gravity pulls us down is how much we accelerates upwards, right?

In the case where your net acceleration is up, there's nothing pulling you down.