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Equivalence principle 
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#1
Dec706, 10:25 AM

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Sorry for so many questions.
In Einsteins equivalence principle, it states that an observer in a close room at 1G accel would not know the difference between that or whether he was standing on the Earth. This makes fine sense to me. But it also states as well that it is independent of velocity. The problem I'm wondering about is, the artificial force is created by the room's acceleration. Once the room stops accelerating, it will no longer generate this force. So, would you not eventually reach a speed limit? You would have to keep going faster and faster to keep up the force. 1. Imagine a main inside the room. The room is accelerating. The man feels a downward force. 2. Now, the man jumps up. The room is still accelerating, so the room comes up to meet him in the air. To the man, it appears he has fallen back down. 3. Now, the room stops accelerating, and just continues to move in a continuous velocity. The man jumps, but the room does not come to meet him, because now the man, and the room, are moving at the same velocity. In fact, the man is now moving at a higher velocity, since he jumped. He would move towards the ceiling of the room. This is the problem I have with that illustration, anyway. The room would have to accelerate forever. So if this is true, how can "warped spacetime" cause "constant acceleration"...so we are, in a sense, pushed into the Earth. niko 


#2
Dec706, 10:35 AM

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Think of the movie 2001  or any time you see the GForce simulator  they are moving in a circullar motion. Because you are continually changing direction, you are always accelerating in a different direction.



#3
Dec706, 10:47 AM

P: 23

Yes, but in this case I am not referring to moving in a circle. The room moves in a straight line.
I'm just pointing out that the illustration, while helping one to understand the ideas, it flawed in that it cannot work "forever". Also to go along with that, it does not help understand why a body "wants" to continue "accelerating". I mean if a body is following a freefall inertial frame of spacetime, but the Earth keeps them from doing so (so that body feels the force of the Earth against them)  why doesn't the body just "stop". Just like a body at rest tends to stay at rest. I don't understand the connection here. Why does a body want to keep trying to move thru the Earth instead of just stopping, and then of course feeling no force at all? niko 


#4
Dec706, 03:33 PM

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Equivalence principle
You can accelerate at a constant rate (say 1G for definitness) for as long as you like, and you will never quite reach the speed of light.
This is ultimately a consequence of the way velocities add in special relativity. vtotal = (v1 + v2) / (1 + v1*v2/c^2) For the details of your velocity vs time for a constant acceleration, see the webpage on the "relativistic rocket equation". http://math.ucr.edu/home/baez/physic...SR/rocket.html 


#5
Dec806, 05:06 AM

P: 23

Of course you can accelerate for as long as you like, and you never can get to the speed of light.
But the analogy falls apart is my point. You have to keep going faster and faster to keep up the gravitational force, because it does not work unless you are accelerating. And, the faster you go, the more your mass increases, and the more you weigh. In fact you have 2 curves: 1. In one curve, you have to go faster. As you go faster you weigh more (according the relativity theory) 2. Since you weigh more, you need less acceleration over time, to feel the same effects. At some point, these two curves pass over each other. After that point, you will weigh so much that you will be barely accelerating at all. Isn't it considered somewhat strange that since spacetime is curved (I know that of course relativity is always somewhat nonintuitive)  but what I mean to say is, if freefall and gravitation are the same, then there is one connection I am missing. When a object is in free fall in space, it will not move unless acted upon. According to relativity theory, an object under "gravity" is really moving thru spacetime, which is curved. The object is in freefall, so it wants to continue moving in the shortest path, which is in this case the geodisc of spacetime. However what I don't get yet, is why does the object "want" to keep moving. Once it hits the earth, its inertial motion would be stopped. For example, if we have a freemoving object in inertial motion in space, it feels not gravity. If something pushes against it with an acceleration, it feels a force because of inertia. If that acceleration stops, the object continues until it hits something. When it hits that something, it feels a force again until its momentum is spent. Then it would simply be stopped again, feeling no force. So why, if we are following curved space because of our inertia, do we continue to accelerate and keep banging into the earth. It seems it needs to be more than just our own inertia. Somehow our body wants to be in a lower energy state or something. Otherwise why would it keep attempting to accelerate along the curvature. niko 


#6
Dec806, 06:13 AM

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#7
Dec806, 09:04 AM

P: 23

Well the whole reason Einstein (the given reason anyway) came up with the idea of equivalence principle relating to gravity is because he noticed the effects of inertia could be similar, so you could think of gravity in "reverse"  instead of gravity pulling us down, it's really our own inertia along a spacetime curve that forces us in. At least I thought it was talking about inertia. It sure seemed like he was thinking of them as being the same.
Perhaps it should have rather been called "The similarity principle" ? niko 


#8
Dec806, 09:31 AM

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Mathematically, I believe the Equivalence Principle is always described the other way around, i.e. in terms of the equivalence between an observer moving inertially in flat spacetime and an observer in freefall in a gravitational field. In the limit of a smaller and smaller patch of spacetime, the laws of physics measured by a freefalling observer passing through this patch will get arbitrarily close to those measured by an inertial observer in flat spacetime, so that GR reduces to SR "locally". This could be stated in some precise way in terms of the equations of GR.
But you can derive the equivalence between an accelerating observer in flat spacetime and an observer at rest in a gravitational field from this more fundamental version of the equivalence principle. Just imagine the freefalling observer passing by a small box which is at rest in the gravitational field (sitting on a platform on top of a pole planted in the ground, say, with the ground outside of the patch of spacetime that the freefalling observer is making their observations in), and which contains tiny experimenters doing their own experimentsthe freefalling observer will see this box moving upwards in exactly the same way that an inertial observer in flat spacetime would see a similar box that was accelerating "upwards" at a constant rate (with this box sitting on a platform on top of a pole which is connected to the nose of an accelerating rocket, with the rocket outside of the patch of spacetime that the inertial observer is making their observations in). So, because of the equivalence principle between the inertial observer and the freefalling observer, they both should see exactly the same results for any experiments that are being done by the miniexperimenters in the box. 


#9
Dec806, 11:11 PM

P: 2,251

from the point of view of some "stationary" observer (let's say unaccelerated, which is an absolute property), you appear to be increasing velocity in the direction of motion (but that might be perceived as decreasing velocity if, from this person's frame of reference you were originally already speeding away from him/her and your acceleration was in this observer's direction. then your relative velocity is decreasing as is also the relativistic mass.) but in your own frame of reference, if an energy and propellant source was no problem, you could accelerate forever at 1 G and it would feel just like gravity (but eventually the nearby stars might start looking funny). 


#10
Dec906, 10:00 AM

P: 23

Agreed exactly.
Just like I said it is kinda neat  that as you go faster, your mass increases, so it takes less acceleration to feel the same effect, so eventually you will be hardly accelerating at all, just before you hit the speed of light but you will never get there (the limit). Now, I was just wondering from that analogy, if that is the state our atoms are in..cause I don't feel like I'm accelerating into the earth more and more.. So i was just observing that the by the analogy's standpoint you have to keep accelerating forever to keep up the force, but eventually, it will be as though (or very close to) not accelerating at all. :P niko 


#11
Dec906, 03:01 PM

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which I will quote in part. The sense in which gravity in the rocket is the same as on a planet is related to the Christoffel symbols of the spacetime rather than the curvature tensor. However, there doesn't seem to be be any clear way to describe the difference between these two different mathematical objects without using technical language which unfortunately a lot of people don't understand. What this means in practice is this: The gravity in the accelerating rocket is the same at a point, but the tidal forces (the rate of change of the gravitational forces) are not the same, even at a point. 


#12
Dec1006, 08:30 AM

P: 4,006

Yes, the acceleration of the room needs to last forever. So if the acceleration stops, so does the artifical force. greets marlon 


#13
Dec1106, 04:22 AM

P: 4

[QUOTE=nikolatesla20;1182439]Sorry for so many questions.
In Einsteins equivalence principle, it states that an observer in a close room at 1G accel would not know the difference between that or whether he was standing on the Earth. This makes fine sense to me. But it also states as well that it is independent of velocity. Einsteinīs principle was probably his biggest blunder and one should not lose too much time on it. To begin with, in the form of equivalence free fallinertial motion, Einstein forgot that a fall is characterised by its landing. If there are no gravitating masses then it makes no sense of speaking of a free fall. Second, in an accelerated frame which should correspond to an observer standing on, say a planet, clocks at the same height but an horizontal distance L apart, cannot be synchronized any more. This is in contradiction with experiment and even the prediction of general relativity. 


#14
Dec1106, 07:21 AM

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#15
Dec1206, 04:05 AM

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dear JesseM
The equivalence principle (ep) has two formulations, either the free fallinertial frame one or the standing stillaccelerated frame one. 1) If the principle has any meaning, I must be able to transpose the results from one situation to the other. Spacetime changes then must be predicted by the ep to form the basis for a theory of gravity. So, I have to look at how clocks strike in an accelerated frame in flat spacetime. There, I find that clocks at a different height (i.e. at a distance along the direction of acceleration) strike differently, in particular, one finds blue and red shifts. There, we have agreement between this prediction and measurements in gravity at rest. If I do the same thing perpendicular to the direction of acceleration, I get disagreement. So, the ep can only be used for completely local measurements. 2) talking of local measurements In an inertial frame without gravity, I never encounter any graviating masses, a nobrainer, of course. In free fall, I need gravitating masses, so I can encounter them and measure them locally. This does not stop my free fall necessarily but it constitutes a local measurement that distinguishes free fall and inertial motion. This contradicts the ep. 


#16
Dec1206, 06:31 AM

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