Principle of Equivalence Re-examined

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    Equivalence Principle
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Discussion Overview

The discussion revolves around the principle of equivalence in physics, specifically examining whether it is possible to distinguish between being in a gravitational field and being in a uniformly accelerated frame. Participants explore hypothetical scenarios and examples that challenge or support the traditional understanding of the principle.

Discussion Character

  • Debate/contested
  • Exploratory
  • Technical explanation

Main Points Raised

  • One participant argues that an observer inside a box can distinguish between being at rest on a planet and being uniformly accelerated by measuring the length of a line drawn on the box's interior walls.
  • Another participant questions the validity of the initial example, suggesting that more details are needed to identify any errors in the reasoning.
  • Some participants mention the temperature of the aluminum walls as a potential factor affecting measurements, while others insist that the ambient temperature should be assumed constant.
  • There is a discussion about the relevance of gravitational tidal effects, with some asserting that if the region is small enough, these effects should not matter, while others maintain that they could still influence the outcome.
  • Participants debate the differences between forces applied in different ways (e.g., pushing versus pulling) and how this could affect the results of the equivalence principle tests.
  • One participant emphasizes the need for clearly defined conditions when discussing the principle of equivalence to avoid discrepancies in interpretations.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of the principle of equivalence and whether specific conditions must be met to validate the arguments presented. No consensus is reached on the validity of the initial example or the implications of the discussed scenarios.

Contextual Notes

Participants highlight the importance of specifying how the box is accelerated and the potential impact of mechanical properties on the measurements, indicating that assumptions about the system's conditions are crucial for the discussion.

e2m2a
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Many textbooks state the principle of equivalence as such: There is no experiment that can be done inside a small closed space, such as a box, that would allow an observer inside the box to distinguish between being in a uniformly accelerated box or being in a box that is at rest on the surface of a planet. (Assume the radius of the planet is large enough such that there is no detectable convergence of the gravitational field lines at the surface of the planet.) But this assertion about the principle of equivalence is not true.

Suppose initially there is a box made of aluminum in inertial space, far away from any gravitational fields. In the box is an observer with a measuring rod made of a diamond. One interior side of the box is painted blue and the opposite interior side is painted red. The remaining interior sides are painted yellow.

The observer places the measuring rod against one of the yellow sides with one end of the rod flush against the blue side. The observer draws a line on this yellow side, one meter in length, perpendicular to the blue side.

After drawing the line, the observer sends a radio signal to begin the first test, takes a sleeping pill, and goes to sleep. An hour later, the observer awakes. Relative to an outside observer at this time, the box is resting on the surface of a planet. At the surface the gravitational constant is equal to g. The inside observer takes the measuring rod and measures the length of the line.

After making the measurement, the observer sends a second signal to begin the second test, takes a sleeping pill again, and goes to sleep. An hour later, the observer awakes. At this time a cable attached to the outside of the box, opposite the interior red side, accelerates the box at a uniform acceleration g. The observer measures the line again.

The observer sends a radio signal, announcing correctly that the box is accelerating and that in the first test the box was resting on a planet. This disproves the assertion there is no experiment possible within a closed box to distinguish between being in a gravitational field or being uniformly accelerated. Anyone would like to guess how the observer knew this?
 
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If you think you have an interesting example, please post it. From the partial description, I suspect that your example is wrong, but nobody can help you find the error unless you finish explaining your scenario.
 
The aluminum wall of the box was cold in one instance and warm in the other.
 
bcrowell said:
If you think you have an interesting example, please post it. From the partial description, I suspect that your example is wrong, but nobody can help you find the error unless you finish explaining your scenario.

No, everything needed is included in this scenario. This is not a problem taken from a textbook. This is a hypothetical scenario that I have put together that shows one can tell the difference between being in a gravitational field or being accelerated.
 
Bill_K said:
The aluminum wall of the box was cold in one instance and warm in the other.

No. Assume the ambient temperature is the same for both.
 
This form of the EP only applies to a region of space so small that no gravitational tidal effects are measureable. So if it is tidal effects, it won't count.
 
Mentz114 said:
This form of the EP only applies to a region of space so small that no gravitational tidal effects are measureable. So if it is tidal effects, it won't count.

No. If the scenario is modified so that the line is short enough that tidal effects have no bearing, the observer would still be able to tell the difference.
 
I hope you're not focusing on the difference between pressure and tension (box 'pushed' by the planet surface versus 'pulled' by the cable). That is really silly. Compare, instead, being pulled by a cable versus pushed by a rocket. Now you have that 'pulling acceleration' is different from 'pushing acceleration'. If you want to bring mehanical properties of the box into consideration, you need to ensure forces are applied the same way: rocket versus sitting on the ground. NOT pushing versus pulling.
 
PAllen said:
I hope you're not focusing on the difference between pressure and tension (box 'pushed' by the planet surface versus 'pulled' by the cable). That is really silly. Compare, instead, being pulled by a cable versus pushed by a rocket. Now you have that 'pulling acceleration' is different from 'pushing acceleration'. If you want to bring mehanical properties of the box into consideration, you need to ensure forces are applied the same way: rocket versus sitting on the ground. NOT pushing versus pulling.

You are correct. When the box sits on the Earth the walls and rod are compressed by gravity. When the box is pulled the walls will stretch and the rod will still compress, thus giving two different results.

This may be silly, but in almost every discussion of the principle of equivalence you will see the case where the box is pulled, such as an elevator being accelerated by a cable.

The principle of equivalence test must specify how the box is accelerated, else this discrepency will arise.
 
  • #10
e2m2a said:
You are correct. When the box sits on the Earth the walls and rod are compressed by gravity. When the box is pulled the walls will stretch and the rod will still compress, thus giving two different results.

This may be silly, but in almost every discussion of the principle of equivalence you will see the case where the box is pulled, such as an elevator being accelerated by a cable.

The principle of equivalence test must specify how the box is accelerated, else this discrepency will arise.

Of course, if you want the 'pulling equivalence principle', just compare being pulled by a cable versus being suspended by a cable just above the planet surface. Compare apples to apples. Your argument really is irrelevant to the intent of the equivalence principle.
 
  • #11
PAllen said:
Your argument really is irrelevant to the intent of the equivalence principle.

You are right. Its just the teaching of it that requires more rigidly-defined conditions.
 

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