What is the Flaw of General Relativity Regarding Uniform Gravitational Fields?

Click For Summary

Discussion Overview

The discussion revolves around the perceived flaws of general relativity in relation to uniform gravitational fields, particularly focusing on the equivalence principle and the experiences of observers in different frames of reference, such as a crew in a rocket versus an observer on a planet. The scope includes theoretical considerations and conceptual clarifications regarding acceleration, velocity, and their implications in the context of general relativity and special relativity.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants assert that the equivalence principle indicates that a crew in a rocket experiences a uniform gravitational field similar to that of an observer on a planet.
  • Others argue that the observations made by the crew regarding free-rising objects are contingent on the rocket's speed and acceleration, which may not apply similarly to the observer on the planet.
  • Some participants challenge the connection between the acceleration experienced by the crew and the speed-dependent effects discussed in relation to the observer on the planet.
  • A few participants emphasize that the statements regarding acceleration and velocity are distinct and should not be conflated, suggesting that this distinction is crucial to understanding the implications of the equivalence principle.
  • There is a contention about whether the experiences of the crew and the observer can be directly compared, with some asserting that they can, while others maintain that the differences in their frames of reference lead to different observations.

Areas of Agreement / Disagreement

Participants express disagreement regarding the implications of the equivalence principle and the relationship between acceleration and velocity. There is no consensus on whether the observations made by the crew in the rocket can be directly equated to those of the observer on the planet, leading to an unresolved discussion.

Contextual Notes

Participants note that the discussion hinges on the definitions of acceleration and velocity, and how these concepts relate to the experiences of different observers. The arguments presented involve assumptions about the nature of spacetime and the applicability of special relativity in the context of general relativity.

Zanket
Messages
307
Reaction score
0
Numbered for reference:

1. The equivalence principle tells us that the crew of a rocket, traveling in flat spacetime and where the crew feels a constant acceleration, experiences a uniform gravitational field identical to that experienced locally by an observer on a planet.

2. Special relativity http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html that in principle the crew can traverse between any two points A and B in flat spacetime in an arbitrarily short proper time, where the two points are at rest with respect to each other and the rocket accelerates from rest at point A to the halfway point and then decelerates from the halfway point to rest at point B.

3. Then the crew can observe free-rising objects (such as an object floating stationary at the halfway point) to recede apparently arbitrarily fast—a million c is not out of the question—while causal contact is maintained since the actual velocity is always less than c.

Example: Let the rocket travel from Earth to Andromeda, two million light years away as we measure. (Assume that Earth and Andromeda are at rest with respect to each other and the spacetime between them is flat.) Let a buoy float stationary at the halfway point. Let the half of the trip from the buoy take ten proper years as the crew measures. Then during this half the buoy recedes by one million proper light years in ten proper years, an apparent (not actual) velocity of one hundred thousand c. From the crew's perspective the buoy free-rises in a uniform gravitational field.

4. Then why does general relativity not predict the same possible observation for the observer on the planet?
 
Last edited by a moderator:
Physics news on Phys.org
I assume you are referring to the fact that two objects a distance [itex]L_0[/itex] apart in their own frame can be passed by a rocket within an arbitrarily short time (according to the rocket) if the rocket moves fast enough with respect to the objects. But this is entirely due to the rocket's speed, not its acceleration.
 
Which numbered point are you objecting to? How does what you're saying refute the point?
 
I fail to see any argument for your point (#4). #1 has to do with acceleration, while #2 & #3 have to do with speed. Your conclusion (#4) does not follow.
 
You must disagree with #1, 2, or 3 for #4 to not follow. (I added some clarification. Take another look.) Free-rising objects have speed for either the crew or the observer on the planet.
 
#1 has nothing to do with #2 or #3. (Note that #2 & #3 apply regardless of acceleration.) #4 is a non sequitur.
 
Zanket said:
You must disagree with #1, 2, or 3 for #4 to not follow. (I added some clarification. Take another look.) Free-rising objects have speed for either the crew or the observer on the planet.

No he doesn't. He just has to show that #4 doesn't FOLLOW from #1, #2, and #3. He did that, by pointing out that the acceleration mentioned in #1, and which you invoke in the gravity of #4, has nothing to do with the speed statements in #2 and #3. Three true statements that have nothing to do with one another do not lead to a conclusion, other than their union.
 
Doc Al said:
#1 has nothing to do with #2 or #3. (Note that #2 & #3 apply regardless of acceleration.) #4 is a non sequitur.

#1 shows that whatever the crew can experience, the observer on the planet can also experience locally. #3 shows what the crew can experience, based on #2. Then if you agree with #3, #4 is a valid question.
 
selfAdjoint said:
No he doesn't. He just has to show that #4 doesn't FOLLOW from #1, #2, and #3. He did that, by pointing out that the acceleration mentioned in #1, and which you invoke in the gravity of #4, has nothing to do with the speed statements in #2 and #3. Three true statements that have nothing to do with one another do not lead to a conclusion, other than their union.

See my reply to him above. If he agrees with #1, 2, and 3, then #4 is a valid question--it follows.
 
  • #10
Zanket said:
#1 shows that whatever the crew can experience, the observer on the planet can also experience locally. #3 shows what the crew can experience, based on #2. Then if you agree with #3, #4 is a valid question.

You seem to think that "acceleration" implies "velocity". I think there's more a flaw in your understanding of kinematics rather than there's a flaw in GR.

I can show you something with zero velocity, yet it has an acceleration. Therefore, #2 and #3 that DEPENDS on velocity doesn't apply to #1, they are not automatically related. That is why you are being told that #4 makes no sense.

Zz.
 
  • #11
Zanket said:
#1 shows that whatever the crew can experience, the observer on the planet can also experience locally.
#1 states that the effect of the rocket's acceleration is equivalent to the planet's gravity.

#3 shows what the crew can experience, based on #2.
#3 and #2 discuss effects due to the rocket's speed not its acceleration. So #1 is irrelevent.

Then if you agree with #3, #4 is a valid question.
If the planet moves at the same speed with respect to those objects as does the rocket, then the planet observer will see the same speed-dependent effects. (Nothing to do with the equivalence principle.)
 
  • #12
ZapperZ said:
I can show you something with zero velocity, yet it has an acceleration. Therefore, #2 and #3 that DEPENDS on velocity doesn't apply to #1, they are not automatically related. That is why you are being told that #4 makes no sense.

Zz.

Regardless of what #3 depends on, the observer on the planet should be able to experience the same observation as described in #3, according to #1. A free-rising object in the local frame of the observer on the planet has velocity relative to the observer.

Let's try this:

A. #1 shows that whatever the crew can experience, the observer on the planet can also experience locally.

B. #3 shows what the crew can experience, based on #2.

C. Then if you agree with #3, #4 is a valid question.

Which of these statements do you object to?
 
  • #13
Doc Al said:
#1 states that the effect of the rocket's acceleration is equivalent to the planet's gravity.

Given that, whatever the crew can experience, the observer on the planet can also experience locally.

#3 and #2 discuss effects due to the rocket's speed not its acceleration. So #1 is irrelevent.

#3 is based on #2. Neither are based on #1. According to #1, #3 is an effect that applies equally well to a free-rising object in the local frame of an observer on a planet. A free-rising object has speed relative to either the crew or the planetary observer.

If the planet moves at the same speed with respect to those objects as does the rocket, then the planet observer will see the same speed-dependent effects.

Then #4 is a valid question, since the free-rising objects in either case can move at the same speed.
 
  • #14
Zanket said:
Regardless of what #3 depends on,

No, you can't sweep this under the carpet. It DOES depends on velocity. This is not negotiable because if you ignore this, you are ignoring SR. So then why are we even discussing this if you wish to make up your own laws?

Acceleration is not velocity.

Zz.
 
  • #15
Zanket said:
1. The equivalence principle tells us that the crew of a rocket, traveling in flat spacetime and where the crew feels a constant acceleration, experiences a uniform gravitational field identical to that experienced locally by an observer on a planet.

This is roughly true.


Zanket said:
2. Special relativity http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html that in principle the crew can traverse between any two points A and B in flat spacetime in an arbitrarily short proper time, where the two points are at rest with respect to each other and the rocket accelerates from rest at point A to the halfway point and then decelerates from the halfway point to rest at point B.

I agree completely.


Zanket said:
3. Then they can observe free-rising objects (such as an object floating stationary at the halfway point) to recede apparently arbitrarily fast—a million c is not out of the question—while causal contact is maintained since the actual velocity is always less than c.

Here, I'm a little lost.

What does "recede apparently arbitrarily fast—a million c is not out of the question" mean?

Regards,
George
 
Last edited by a moderator:
  • #16
ZapperZ said:
No, you can't sweep this under the carpet. It DOES depends on velocity. This is not negotiable because if you ignore this, you are ignoring SR. So then why are we even discussing this if you wish to make up your own laws?

Acceleration is not velocity.

Zz.

I'm not disagreeing with you on what #3 depends on. If you object by saying that #3 depends on velocity, then I say that velocity applies as well to the observer on the planet, because a free-rising object in the local frame of the observer on the planet has velocity relative to the observer. Whatever the crew can observe (velocity, acceleration, whatever), so can the observer on the planet in a local frame, according to #1.

Then what is your objection?
 
  • #17
Zanket said:
I'm not disagreeing with you on what #3 depends on. If you object by saying that #3 depends on velocity, then I say that velocity applies as well to the observer on the planet, because a free-rising object in the local frame of the observer on the planet has velocity relative to the observer. Whatever the crew can observe (velocity, acceleration, whatever), so can the observer on the planet in a local frame, according to #1.

Then what is your objection?

Show me an example of a "free-rising" object on a "planet" and show me how another inertial frame would observe this very same object in the idential way.

Zz.
 
  • #18
Zanket said:
I'm not disagreeing with you on what #3 depends on. If you object by saying that #3 depends on velocity, then I say that velocity applies as well to the observer on the planet, because a free-rising object in the local frame of the observer on the planet has velocity relative to the observer. Whatever the crew can observe (velocity, acceleration, whatever), so can the observer on the planet in a local frame, according to #1.

Then what is your objection?
If all you are saying is that an observer on a planet moving with the same speed as the rocket with respect to those objects will see the same speed-dependent effects as an observer on the rocket, then why all the mumbo jumbo with the equivalence principle? It's your argument that doesn't make sense, not that last statement (if that's what you were trying to say).

And what does this have to do with some supposed "flaw" in GR? What flaw?
 
  • #19
George Jones said:
What does "recede apparently arbitrarily fast—a million c is not out of the question" mean?

An example: Suppose the rocket travels from Earth to Andromeda, 2 million light years away as we measure, in 20 proper years. (Assume spacetime between is flat.) Then in the crew's frame a buoy floating stationary at the halfway point, between passing the buoy and arriving at Andromeda, recedes one million proper light years in ten proper years, an apparent (not actual) velocity of one hundred thousand c. From the crew's perspective the buoy free-rises in a uniform gravitational field.
 
  • #20
ZapperZ said:
Show me an example of a "free-rising" object on a "planet" ...

An apple thrown upwards.

... and show me how another inertial frame would observe this very same object in the idential way.

Why? The two frames discussed here, in which an object is free-rising, are non-inertial frames.
 
  • #21
Doc Al said:
If all you are saying is that an observer on a planet moving with the same speed as the rocket with respect to those objects will see the same speed-dependent effects as an observer on the rocket, then why all the mumbo jumbo with the equivalence principle?

Zanket is saying that the a person standing on the planet corresponds to the person accelerating in the rocket.

Maybe it would be better to consider a person using a rocket to hover above the surface of the planet. Then, I suppose the free-rising object corrresponds to a freely falling object.

But I'm not sure what the problem is.

Regards,
George
 
  • #22
Zanket said:
An example: Suppose the rocket travels from Earth to Andromeda, 2 million light years away as we measure, in 20 proper years. (Assume spacetime between is flat.) Then in the crew's frame a buoy floating stationary at the halfway point, between passing the buoy and arriving at Andromeda, recedes one million proper light years in ten proper years

No, this isn't true.

Regards,
George
 
  • #23
Zanket said:
An apple thrown upwards.



Why? The two frames discussed here, in which an object is free-rising, are non-inertial frames.

Wait a second! Did you think an apple thrown upwards in a gravitational field is IDENTICAL to a free-floating object as seen by an accelerating frame?

Zz.
 
  • #24
Doc Al said:
If all you are saying is that an observer on a planet moving with the same speed as the rocket with respect to those objects will see the same speed-dependent effects as an observer on the rocket, then why all the mumbo jumbo with the equivalence principle?

Because GR does not predict that, in the local frame of an observer on a planet, a free-rising object can recede apparently arbitrarily fast while causal contact is maintained, as the equivalence principle demands given that the crew can observe that. Then ...

And what does this have to do with some supposed "flaw" in GR? What flaw?

... GR is inconsistent.
 
  • #25
George Jones said:
Zanket is saying that the a person standing on the planet corresponds to the person accelerating in the rocket.

Yes, in the local frame of the person on the planet.

But I'm not sure what the problem is.

The problem is that GR does not predict the same possible observation for the person on the planet as it does for the crew, even though the equivalence principle demands that it does.
 
  • #26
George Jones said:
No, this isn't true.

Please be specific about what you think isn't true.
 
  • #27
ZapperZ said:
Wait a second! Did you think an apple thrown upwards in a gravitational field is IDENTICAL to a free-floating object as seen by an accelerating frame?

Zz.

Not any free-floating object. But a free-rising object, yes. According to the equivalence principle, a free-rising apple in the crew's frame is equivalent to a free-rising apple in the local frame of the observer on the planet, all else being equal (like the acceleration they feel).
 
  • #28
Zanket said:
Not any free-floating object. But a free-rising object, yes. According to the equivalence principle, a free-rising apple in the crew's frame is equivalent to a free-rising apple in the local frame of the observer on the planet, all else being equal (like the acceleration they feel).

Where does it say that? And besides, you never define what is a "free rising object" in an accelerated frame.

If this is where in both cases someone throws a ball "upwards", then where exactly do these two differ?

And if it is what I think it is, which is where you are equating a free falling ball in a gravitational field with a free object being observed in an accelerated frame, then I can immediately tell you that those two are NOT identical.

Zz.
 
  • #29
The equivalence principle says nothing more than that a constantly accelerated frame is equivalent to a homogenous gravitational field, i.e objects move the same way in both conditions.

This is apparently true. Keep in mind that "real" gravitational fields are never homogenous.
 
  • #30
Zanket said:
Then in the crew's frame a buoy floating stationary at the halfway point, between passing the buoy and arriving at Andromeda, recedes one million proper light years in ten proper years

The distance that the buoy recedes in the crew's frame is not one million lightyears. For distances in an acclerated frame, see my posts #4 and #10 in https://www.physicsforums.com/showthread.php?t=110742&highlight=acclerated".

Exercise: What is the distance in the crew's frame?

Note also what ZapperZ and derz say, i.e., the gravitational field of a planet is not homogeneous, so that the metric can only be put into its special relativistic form at a single event.

Regards,
George
 
Last edited by a moderator:

Similar threads

Undergrad General Relativity rocket puzzle
  • · Replies 84 ·
3
Replies
84
Views
8K
Graduate Minimal property of Spacelike geodesics in GR/curved spacetime?
  • · Replies 76 ·
3
Replies
76
Views
4K
Graduate A global energy conservation law in general relativity
  • · Replies 36 ·
2
Replies
36
Views
2K
Undergrad Gravitational Field Transformations Under Boosted Velocity
  • · Replies 14 ·
Replies
14
Views
3K
Undergrad Gravitational wave propagation in GR
  • · Replies 39 ·
2
Replies
39
Views
4K
Undergrad Calculating Relative Change in Travel Time Due to Spacetime Perturbation
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Correspondence between areal radius differences and proper distances
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Forces and gravitational time dilation
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Calculating Spacetime Around Multiple Objects
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Noether's second theorem: two questions
  • · Replies 7 ·
Replies
7
Views
3K