A simple observation regarding the equivalence of acceleration and gravity

[girlwonder]

Oh my goodness, DaveC426913 (can i just call you Dave?), i think we are on the same page!

However, object A and B are in very deep space and there is no external source of gravity, i should have stated that.

Also, what is accelerating each object is also unspecified.

In order to simplify things i did specify that the ACTUAL gravity of A and B
was not being referred to, but rather the SIMULATED effect of gravity due to their respective acceleration.

i would avoid assuming the inconsequential nature of each objects mass and gravity, i merely avoided referring to them in order to draw attention to the resultant simulation.

Anyway, if B is contained by A and both are accelerating towards each other at a constant rate, wouldn't you agree that at the point where they touch the kinetic energy would increase over a period of time?

 

[cesiumfrog]

object A and B are in very deep space and there is no external source of gravity [...] i would avoid assuming the inconsequential nature of each objects mass and gravity

Let's skip this A inside B thing (I do now suspect you misunderstood the equivalence principle.. plus, if you were inside a hollow mass, then the gravitational forces would tend to cancel out); are you happy with the scenario where (in deep space away from external gravitational sources) some two objects A & B (each having mass) happen to (initially) be stationary a finite distance apart from each other?

In the Newtonian picture, the two objects will just attract (accumulating kinetic energy) and collide. According to GR there is no attractive force whatsoever.. but space-time is twisted so strangely that the only way that the objects could have seemed initially stationary (to us distant observers) is if they had really always been moving straight towards each other on a collision course. (Note, the kinetic energies here don't really increase, but they are very ambiguous for any observer to measure.)

Now, say we put a stout rod between the objects, so that they keep a small distance apart. According to Newton the rod is pushing each object with a force to exactly cancel the gravitational pull on that object (resulting in no motion or acceleration).

In the GR picture there is no gravitational pull, but the rod is still pushing on each object with the same force as before. This causes each object to accelerate outwards. However, space-time (i.e., in this case, the definition of "outwards") is curved around in such a way that, despite their individual accelerations, the objects don't get any further apart.

The objects of course can't tell the two pictures apart, since being accelerated (as in an elevator) feels just the same as standing stationary against a massive planet's gravity. (Although they might detect the space-time curvature, by some clever scheme to send probing signals around the region.)

Anyway, if B is contained by A and both are accelerating towards each other at a constant rate, wouldn't you agree that at the point where they touch the kinetic energy would increase over a period of time?

As for kinetic energy in my last two pictures, the two objects each remained a constant distance from other, so each should concede that the other has zero relative velocity (and therefore, continually, no kinetic energy in the other's frame of reference).

 

[DaveC426913]

Anyway, if B is contained by A and both are accelerating towards each other at a constant rate, wouldn't you agree that at the point where they touch the kinetic energy would increase over a period of time?

I don't know what this has to do with the EP.

I need to ask for clarification (even if it means we repeat a lot of what we've covered): Are you looking for understanding of the main principle of EP, or are you looking at add some additional elements to examine the implications?

Are you satisfied with EP in and of itself?

 

[JesseM]

here goes a simpler, better explanation.

I'm tired of the man in the room thing. Let's call the room a solid hollow object A, and call the man solid object B. To simplify things i will specify that i am not referring to the ACTUAL gravity of A or B, rather, i will refer to the SIMULATED gravitational attraction of either by their respective acceleration.

The problem is that the equivalence principle is not about simulating the attraction between the room and the person, it is specifically assumed that the mass of the room and the person are both totally negligible, and thus that their own gravity is negligible as well. (and even if it weren't, why would you need to 'simulate' their gravity, when their own gravity will be exactly the same regardless of whether they're in deep space or on Earth?) The equivalence principle is about simulating the effects of a gravitational field caused by some gigantic external mass, like a planet. If you accelerate the room at 1G in deep space, then the effects experienced inside will be virtually identical to those experienced if the room is sitting at rest on the surface of the Earth. The reason the planet has to be gigantic in comparison to the room is that the equivalence principle specifically assumes you are only making measurements in a small enough region of spacetime that tidal forces can be treated as negligible--tidal forces have to do with the fact that the gravitational field actually varies over space and time, like the fact that the Earth's gravitational pull is noticeably stronger on the surface than it is millions of miles away, or that in a sufficiently large room you might notice that the path of dropped objects is not perfectly parallel since they're both moving on converging straight lines towards the center of the Earth. For the equivalence principle to work, you have to assume that the region of spacetime you're doing your experiments in is very small compared with the distances and times in which these kinds of effects would be noticeable--the equivalence principle is a limit principle in the calculus sense, you must either take the limit as the volume of the room (and the time-interval in which the measurements are made) goes to zero, or else maybe you could take the limit as the size of the source of the gravitational field goes to infinity. Either way, if either the room or the person inside had enough mass so that their own gravitational effects were non-negligible, this would obviously imply measurable tidal forces (since different points inside the room would experience different gravity due to different distances from the person/sides of the room).

If what you're basically concerned about is the fact that gravitational attraction should be reciprocal, then maybe we could think of it this way. Suppose we have a room on Earth in which we're doing experiments, and then I want to know if I would get precisely the same results if the room were instead in deep space being accelerated at 1G by the rocket. Because gravity is reciprocal, when I move around in the room on Earth, this actually has some slight gravitational effects on the Earth itself--if I climb a ladder to the top of the room my body's pull on the Earth is weaker, while if I stand near the floor my body's pull on the Earth is stronger. Of course because the Earth's mass is so huge, my movements will only affect it to a tiny degree, but these small movements of the Earth would nevertheless have a slight effect on the gravity experienced within the room, which would in principle be measurable (assuming for the sake of the argument that there were no other objects on Earth moving around and affecting its movements too). So if we want to have a really accurate simulation of conditions on Earth by accelerating the room at 1G, it seems we can't just accelerate the room at precisely 1G for all time--we'd have to very slightly alter the rate of acceleration as the person inside moved around to simulate these sorts of tiny changes in the Earth's gravitational pull due to the Earth moving around in response to the person's movements.

Would this be a reasonable example of what you're trying to argue, or am I still missing the point? If it is an OK example, then my answer would be that, again, the equivalence principle is a limit principle, the effects of the person's movement on the entire Earth (and thus on the gravitational field of the Earth as measured inside the room) will go to zero in the limit as the room and everything inside it become smaller and smaller.

 

[JesseM]

Anyway, if B is contained by A and both are accelerating towards each other at a constant rate, wouldn't you agree that at the point where they touch the kinetic energy would increase over a period of time?

If the main thing you're concerned about is two objects pushing against each other, here's another example. Suppose we have two giant cubes--planet-sized, or at least asteroid-sized--mutually attracted by gravity, with a surface of each cube pressed against the other's surface. If something is trapped in between the two surfaces, it will experience a tremendous force from each side, squashing it flat as a pancake.

Now, as I said before, the equivalence principle is understood only to work as you zoom in on a small region of spacetime, so that tidal forces become negligible--the jargon for this would be something like "general relativity reduces to special relativity locally". So obviously when thinking about the equivalence principle, we can't consider a region large enough to encompass the full mass of each cube--the gravitational force would vary considerably in force and direction along a line from the center of one cube to the center of the other, for example. But you might think that even if you zoomed in on a small region where the surfaces of each cube were pressed against each other, there would be a problem with the equivalence principle because the force still wouldn't be uniform--an object squashed in the middle is experiencing a strong force in one direction from cube A, and a strong force in the opposite direction from cube B. The important thing to realize is that these equal and opposite forces in your small region are not gravitational. In your small region, the gravitational force should be pretty much uniform--in fact, if the cubes are equal in size and mass, there will be no significant gravitational force in that region. Instead, the force pressing the squashed object together is electromagnetic, it's the force that keeps the material that the cube is made out of basically rigid, so that if you push strongly on one side, the other side must move along with it. The average gravitational force throughout each cube is pulling each one strongly towards the other one, and individual regions which themselves are not experiencing much gravity are pulled along with the rest due to these electromagnetic bonds between atoms.

So, if you looked at the small chunks of each cube contained within your small region, and then you transported these two chunks into an identically-shaped region of deep space with no matter outside the region to create gravity, and you accelerated the region in such a way as to duplicate whatever gravitational force was experienced in the original region (again, if the cubes were identical in size and mass the gravity in the original region would be negligibly different from zero, so you wouldn't have to accelerate the second region in deep space at all), and you duplicated the electromagnetic forces on the boundary of the original region which were causing the two chunks of cube within that region to be pressed against each other so forcefully, then in this case there would be no significant difference between what would be experienced within this second region in deep space and the original region which was surrounded by those giant cubes. So there is no problem with the equivalence principle here--as long as you pick a small region within a gravitational field, then if you look at all the objects and non-gravitational forces both within and on the boundary of that region, then if you duplicate the same objects and non-gravitational forces in a similar region in deep space, and accelerate it to match the gravitational forces felt in the original region within the gravitational field, then measurements made within either region will give all the same results. And remember, because your first region within the gravitational field must always be small enough so that the gravity within the region is essentially uniform (no tidal forces), this means the second region in deep space just needs a single uniform acceleration, you never need to accelerate different parts of it in different ways to duplicate gravitational forces in different directions.

 

[yogi]

. According to Newton, the man must not be passive. He must have his own force, which is why he must have his own rocket pack to accelerate him the direction of the floor of the room. This is the opposite direction the room is accelerating in..

The man has his own force - its consequent to his inertia F = ma This reactionary force has the same validity (just as real) as the primary force that produces the elevator motion

 

[girlwonder]

I'm throwing out the whole object A object B thing. i was just trying to sound smart. Really, when i did the math on it, it seemed like if you accelerated two ojects against each other, the force would increase where they touched. Apparently there is a million ways of discounting that in actual practice. i was actually investigating the possibility that gravity has more to do with spacetime and less to do with matter then we think, and that maybe gravity isn't really an essential part of mass, but rather, mass and gravity both being the rsult of the same spacetime mechanism, hence their co-relation.

Although I've gotten nowhere in my reasoning on this thread, i just got someone on another thread to admit that spacetime is "something", so i feel better now.

And i still think that if two objects perpetually accelerated against each other, the force where they touch would increase over time, if both objects were accelerating at a constant rate.

 

[DaveC426913]

And i still think that if two objects perpetually accelerated against each other, the force where they touch would increase over time, if both objects were accelerating at a constant rate.

But ... if they're touching each other, then both their acceleration and their velocity are zero.

 

[girlwonder]

If both were equal masses and perfectly centered neither would appear to move, but the force would be measurable and increasing.

i actually discussed it with an auto mechanic in terms of what would happen if you did that with cars. Pretty interesting.

 

[DaveC426913]

A couple of edits:

If both were equal masses and perfectly centered neither would <STRIKE>appear to</STRIKE> actually move, but the force would be measurable <strike>and increasing</strike>, though the acceleration and velocity would remain zero.

I was thinking along the same lines, two cars pushing against each other - but it's a terrible analogy. A car's acceleration might not have anything to do with the forces it applies. For example, how do you get a constant acceleration in a moving car? Do you hold the pedal steady and let the car pick up speed? Or do you continually apply more gas as time passes? This is also why your mechanic friend is not a good person to talk to - he's not talking about pure physics, he's talking about auto mechanics. We could digress, but let's not.

The simplest model is the use of two rockets. The force is a direct result of thrust and is quite trivial to get your head around the constant application of forces.



It also shows that your suspicion is incorrect. Two constant forces opposing each other will cancel, and the pressure between them will not increase over time. Don't misunderstand, the forces don't disappear, they still apply pressure - a constant pressure in fact - but they don't do any work.

 

[country boy]

Here's a situation that turns the problem around, and sometimes gives an alternative view of the equivalence principle.

If the man is in orbit around a planet but is in a closed compartment (say a space shuttle without windows), how does he know that he is in a gravitational field? It would seem to him that no force is acting and that there is no acceleration.

In general relativity, talk of gravitational force is removed and we are supposed to instead think in terms of following undeviating trajectories.

 

[girlwonder]

I think mechanics know a lot about mechanics. teehee. They do though, really. No physics, no car. EVERYTHING operates on physical law.

I think the car is a perfect example. The effect I'm talking about could also be reproduced by "containing" the cars with a chain back to back. The wheels would spin and the speedometer would move as if it were accelerating and the force on the chain (and the cars) would increase over time, even if the rate of acceleration of both vehicles were constant.

What I'm getting at is that the reason why the equivalence of acceleration and gravity works, is because only the floor is accelerating towards the man, and not vice versa, clearly it doesn't work then. Obviously the man was right. What's wrong is our present understanding of gravity and spacetime.

 

[girlwonder]

Oh- and country boy rocks.

 

[cesiumfrog]

Although I've gotten nowhere in my reasoning on this thread, i just got someone on another thread to admit that spacetime is "something", so i feel better now.
[...]
i actually discussed it with an auto mechanic [...] I think mechanics know a lot about mechanics. teehee. They do though, really. No physics, no car. EVERYTHING operates on physical law.
[...]
What's wrong is our present understanding of gravity and spacetime.

...

 

[girlwonder]

There, there, don't cry.

i didn't cry when you said you wanted to burn me. Seven people now do. Scientists are mean, that's for sure.

 

[JesseM]

I think the car is a perfect example. The effect I'm talking about could also be reproduced by "containing" the cars with a chain back to back. The wheels would spin and the speedometer would move as if it were accelerating and the force on the chain (and the cars) would increase over time, even if the rate of acceleration of both vehicles were constant.

But it wouldn't increase over time, this is a well-understood situation in Newtonian physics--you'd just reach an equilibrium where the force pushing the car in one direction is equal and opposite to the force pushing the car in the opposite direction, and at that equilibrium neither the car or the chain would move, and the forces would be constant.

Obviously the man was right. What's wrong is our present understanding of gravity and spacetime.

Noooo! Assuming that your intuition is right and all the physicists who say it's wrong are mistaken, before you have even studied the field in depth to know their reasons for saying so, is the path to the Dark Side! That way lies madness...people who think like that persistently tend to end up becoming crackpots, hardened in their beliefs that they know better than the whole physics community. Don't take those first steps down that road! Remember that all the physicists who did come up with genuine revolutions in physics, like Einstein, were people who had studied existing physics front-to-back and understood it in great depth, and moreover the area where they came up with a breakthrough was almost always one that was widely acknowledged to be a "problem area" by the physics community, like reconciling the "aether theory" of electromagnetism with the observation that light was always measured to move at the same speed in Einstein's day, or the problem of reconciling quantum physics with general relativity today.

i didn't cry when you said you wanted to burn me. Seven people now do. Scientists are mean, that's for sure.

Hey, don't take the "burn her" votes too personally, it's just that you set up the poll so that was the only logical option to pick for someone who didn't think you had found any sort of genuine problem with the equivalence principle.

 

[girlwonder]

OKay, maybe you're right, but i trust my mechanic and he said that eventually the force would get so strong as to break the cars, so i wouldn't do it with my car.

Anyway, because i continue to learn and be open minded i will not be a crackpot. Can't you see that i must ellicit arguements by digging my heels in. And the simplicity of what I've said has restrained the responses. And maybe I'm not showing all my cards either.

Anyway, i was curious to know how many people would burn someone else for suggesting something blasphemous. They could have just not voted, like most people, when confronted with no honest choice. They got a kick out of voting to burn me, probably cause they thought it would hurt my feelings. Just like i got a kick out of getting them to show their true colors. i guess I'm twisted too. teehee.

 

[girlwonder]

And there is no problem with the equivalence of acceleration and gravity. The problem is what we think we know about the relationship between gravity and mass. And you have to admit, our understanding of gravity is a bit loose, non?

 

[DaveC426913]

I think mechanics know a lot about mechanics. teehee. They do though, really. No physics, no car. EVERYTHING operates on physical law.

Yes, not auto mechanical law, as you'll see here:

I think the car is a perfect example. The effect I'm talking about could also be reproduced by "containing" the cars with a chain back to back. The wheels would spin and the speedometer would move as if it were accelerating and the force on the chain (and the cars) would increase over time, even if the rate of acceleration of both vehicles were constant.

"...the speedometer would move as if it were accelerating..."

Yes. it would. And it would be LYING. Because the car is NOT accelerating.


"...force on the chain (and the cars) would increase over time..."

Prove it.


I think the force on the chain would increase over time because you would be applying an INCREASING force, not a constant force.

And this is why it is a lousy example, and this is why a mechanic is the wrong person to ask.

If you want to underatand the problem, you must remove the extraneous variables. Simplify the experiment.

 

[country boy]

Hey, don't take the "burn her" votes too personally, it's just that you set up the poll so that was the only logical option to pick for someone who didn't think you had found any sort of genuine problem with the equivalence principle.

I wanted to vote, but there was no category for "send flowers."

 

[girlwonder]

okay I'm going to prove this to you all, and I'm going to do it real simple like, real low-tech and cheap just to be a brat, a little experiment.

 

[DaveC426913]

okay I'm going to prove this to you all, and I'm going to do it real simple like, real low-tech and cheap just to be a brat, a little experiment.

Before you do the experiment, will you do us the courtesy of critiquing your set up so we can be satisfied it's valid? eg. If you decided to do this with two cars, I would (continue to) raise serious objections about how you're going to achieve "constant acceleration".

 

[gabee]

I think mechanics know a lot about mechanics. teehee. They do though, really. No physics, no car. EVERYTHING operates on physical law.

lol

What I'm getting at is that the reason why the equivalence of acceleration and gravity works, is because only the floor is accelerating towards the man, and not vice versa, clearly it doesn't work then. Obviously the man was right. What's wrong is our present understanding of gravity and spacetime.

It WOULD work if the man were to accelerate toward the floor. Imagine the man wearing a belt, to which is attached a chain that passes through a small hole in the floor. Then the same "unseen force" pulls on this chain instead. The man pushes on the floor, which accelerates the room, and in his frame of reference the forces are exactly the same as before. The point is that you WON'T have two forces--one pulling on the man and one pulling on the room in the opposite direction. Newtonian gravitational force is a function of the two masses: GMm/r^2. To simulate the gravitational pull of the Earth in the man's frame of reference, you can EITHER pull on the man OR pull on the room. Not both, or the man would feel twice as heavy!

By the way, even if two forces were pulling on the man in opposite directions (as you describe with the two cars) there would be no net acceleration in either direction and the forces on the man would be constant. Instead of complicating the matter by trying to describe lying speedometers and burning rubber and friction against the road, just think of two forces. A constant applied force has a constant acceleration...not an increasing acceleration...so the net force would be zero and he would not move. Only if you increased the forces for some reason would the forces on the man increase (they won't do it naturally over time!).

 

[country boy]

okay I'm going to prove this to you all, and I'm going to do it real simple like, real low-tech and cheap just to be a brat, a little experiment.

Please don't hurt yourself. Some demonstrations are better left as thought experiments.

It is true that gravity is not like other forces we are familiar with. When you are being accelerated in your car, you feel the force on your back. However, when you are being accelerated by gravity (in free fall) you don't feel any force. The reason for this difference is that the force of gravity, as described by Newton, is proportional to each mass that it acts on, so that in F = ma the mass cancels. This means that the acceleration does not depend on the mass. The gravitational force is being applied to all parts of your body and all those parts are accelerating at the same rate. There is no transfer of force through your body, no pushing at your back, to give you a sensation of applied force.

When you are stationary in a room in a gravitational field you are being pulled down against the floor, but you don't move down because the floor is applying an equal force up against you. You feel that force pushing you up, but you don't move up because gravity is causing you to apply an equal force down. It's easy to see that the little man in the accelerating room feels these same forces. The case of your two cars pathetically tugging against each other with their wheels spinning is analogous to the room being pulled up by a chain while your ankles are being pulled down by another chain. (Gravity is nicer than a chain because it distributes the pull instead of concentrating it at your feet.)

The special property of the gravitational force that it acts on all masses equally, i.e., that it accelerates all bodies at the same rate, is what led Einstein to the equivalence principle. There is no apparent difference between being in free fall in a gravitational field (in a falling elevator) or floating freely with no gravity (in a room in deep space). Likewise, the accelerating room in zero gravity feels the same as the stationary room in a gravitational field. It's all because the inertial mass 'm' in F = ma is the same as the gravitational mass 'm' in Newton's gravitational force.

Note, I have now cast my vote.

Incidentally, are you related to Little Stevie?

 

[girlwonder]

Okay, I've really thought about it. You're right. i get it now. It was a misunderstanding. The force would still be constant, but what fun I've had.