Could Equivilance kill DE?

[TakenItSeriously]

Could the principle of equivalence explain the apparent rate of expansion in the universe so that we don't need DE?

 

I'm not a physicist but I'm good with logical constructs.

 

The equivalence model for a body at rest on the surface of the Earth is a body accelerating at 1g through inertial free space. The property of equivalence has proven to hold up well under GR, so let's assume for now that it's true.

 

I think it's easier to see if we just use equivalence to model gravity as the acceleration of local spacetime in towards the planet, as opposed to curved spacetime.

 

We have always just thought of the inertial free space equivalence model as a hypothetical and completely isolated arbitrary system but in reality, I think any claims involving gravity must also involve vectors. It's an integral part of gravity because, gravity is always pointing in.

 

If we take vectors into account then we would now say that a body at rest on the surface of a planet is equivalent to a body in freespace accelerating away from the planet at a rate of 1g. No matter how we think about equivalence, for free fall or at rest on the surface, it has to involve a vector of 1g in recession.

 

Notice that this change doesn't change anything about the behavior of local spacetime so all evidence which was used to verify GR still applies. The only difference that happens when considering vectors is that space at a distance should now be accelerating away at 1g for any particular body in space.

 

I also noticed that as we replace a gravity field with an accelerated inertial field, it doesn't make any changes to how we should treat time in local spacetime. All adjustments involve space only. For example, the rate of acceleration at the surface of the Earth is always 9.8m/s² but their is no velocity that changes over time because velocity relative to the gravitational frame is always 0.

 

So it would appear that when we look at the behavior of gravity, it's primarily a local attractive inwards force over time, but after including vectors, it's also an expanding outwards force over distance. Even the units would only be an inverse unit of time which is one way we think about the Hubble constant which of course is a key constant for measuring the kind of expansion over distance that they have found.

 

So, while I have no idea how much this would impact the calculations for DE it sure seems like all the units, vectors, and even dimensions seem to align properly.

 

Am I making a mistake in the way I'm understanding the principle of equivalence?

Is there a specific reason vectors shouldn't be considered with the principle of equivalence?

 

Thanks.

Edited March 1, 2016 by TakenItSeriously

[ajb]

The property of equivalence has proven to hold up well under GR, so let's assume for now that it's true.

Here I think you are using just the weak equivalence principle.

 

I think it's easier to see if we just use equivalence to model gravity as the acceleration of local spacetime in towards the planet, as opposed to curved spacetime.

I am not sure what the highlighted means.

 

We have always just thought of the inertial free space equivalence model...

What model is this? I an not aware of a model with this name.

 

...I think any claims involving gravity must also involve vectors. It's an integral part of gravity because, gravity is always pointing in.

Vectors are essential across physics. And by 'gravity is always pointing in' you mean that gravity is always attractive?

 

Am I making a mistake in the way I'm understanding the principle of equivalence?

The modern understanding would be the weak equivalence principle which states (in the form to what you are using)

 

'The local effects of gravitation (curvature of space-time) are indistinguishable from those of an accelerated observer in flat space.'

 

A slightly stronger statement was given by Einstein as the above holds and

 

'Any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in space-time.'

 

The first statement means that locally, so in a small enough region, space-time is flat. This is mathematically the statement that space-time is a (pseudo)Riemaniann manifold. The second part added by Einstein says that in a small enough region the non-gravitational laws of physics reduce to their special relativistic form.

 

 

Is there a specific reason vectors shouldn't be considered with the principle of equivalence?

I do not sure why vectors are no included already in once sense, and in another I am not sure that they have anything to do with the equivalence principle.

[swansont]

We don't measure an acceleration of earth as the result of expansion. Expansion is relative while acceleration is not.

[TakenItSeriously]

Here I think you are using just the weak equivalence principle. I am not sure what the highlighted means.What model is this? I an not aware of a model with this name.Vectors are essential across physics. And by 'gravity is always pointing in' you mean that gravity is always attractive?The modern understanding would be the weak equivalence principle which states (in the form to what you are using)'The local effects of gravitation (curvature of space-time) are indistinguishable from those of an accelerated observer in flat space.'A slightly stronger statement was given by Einstein as the above holds and'Any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in space-time.'The first statement means that locally, so in a small enough region, space-time is flat. This is mathematically the statement that space-time is a (pseudo)Riemaniann manifold. The second part added by Einstein says that in a small enough region the non-gravitational laws of physics reduce to their special relativistic form.I do not sure why vectors are no included already in once sense, and in another I am not sure that they have anything to do with the equivalence principle.

I'm not sure why, but the quote button (iPad) bunched the entire post it all into a single paragraph.

 

I'm basing this post on an early version of the Equivalence Principle described in the Wikipedia article under that name.

 

It used an accelerated reference frame of 1g moving radially towards the planet to adapt gravity to a form that could be treated by SR. I'm not sure if there's an official name for this framework. To my knowledge it's still a valid method that predicts the bending of light or the lens effect, but there's much that was added to GR later, I'm sure.

 

I like it because it's the only intuitive model I could find for understanding the Equivalence Principle and the modern version involving curved spacetime and tensors goes over my head on the math. I'm also sure this was how Einstein first thought about GR. I believe the article mentioned it was changed by a friend to use the modern framework to make it compatible for testing against other gravity theories of the time.

 

Here's a relevant quote from Einstein that expresses a corollary to the quote you gave.

 

we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system.

 Einstein, 1907

I think your right in that its probably best represented as the weak Principle of Equivalence in modern physics.

 

The models I was referring to were Einsteins mental models that included observers in white rooms for comparing a person in free fall or standing on the surface of a planet to their equivalents in inertial empty space which is roughly speaking a person who is floating or drifting and a person who is in uniform acceleration of 1g respectively.

 

My arguement was that those models of equivalence didn't seem to be complete without including the vectors of motion since gravity vectors would always be a force of attraction as you put it. Sorry I struggle with finding the correct verbiage to use as I'm not a physicist.

 

Once we add those vectors, then making those comparisons always results in the inertial free space frame being accelerated 1g away from the planet, unless I made a mistake, and which seemed to have striking implications about the expansion of the universe.

Edited March 1, 2016 by TakenItSeriously

[ajb]

It used an accelerated reference frame of 1g moving radially towards the planet to adapt gravity to a form that could be treated by SR. I'm not sure if there's an official name for this framework. To my knowledge it's still a valid method that predicts the bending of light or the lens effect, but there's much that was added to GR later, I'm sure.

You mean free fall = inertial motion?

 

I like it because it's the only intuitive model I could find for understanding the Equivalence Principle and the modern version involving curved spacetime and tensors goes over my head on the math. I'm also sure this was how Einstein first thought about GR.

You should have a look at this approach properly. I am not familiar with these early papers. And for sure they cannot form a proper theory of gravity.

 

For sure, if you start to deal with non-inertial frames in special relativity then you need a formalism that is very close to a more general setting of curved space-times.

 

My arguement was that those models of equivalence didn't seem to be complete without including the vectors of motion since gravity vectors would always be a force of attraction as you put it. Sorry I struggle with finding the correct verbiage to use as I'm not a physicist.

I am not really following what you are trying to say.

 

You can use the equivalence principle locally, which in part means that we have no tidal forces. Einstein's lift has to be small enough so that the occupant only detects this downwards force. Changes of the gravitational field on the scale of the lift would invalidate the equivalence principle.

 

Once we add those vectors, then making those comparisons always results in the inertial free space frame being accelerated 1g away from the planet, unless I made a mistake which seemed to have striking implications about the expansion of the universe.

You are going to need to be more careful with what you mean here.

 

The problem is, as you recognise, one of language and terms.

[Mordred]

To add some details the FLRW metric models the Universe in terms of a fundamental observer

 

Ned Wright has a decent coverage.

 

https://ned.ipac.caltech.edu/level5/Peacock/Peacock3_1.html.

 

Essentially we take our local conditions into consideration.

 

Now in the Einstein field equations the Universe is modelled as an ideal gas. So each contributor has an equation of state.

The equation of state for the Cosmological constant being w=-1.

 

Expansion occurs when the kinetic energy of each contributor overcomes its self gravity.

 

You don't need the cosmological constant to have expansion. Its only needed to explain the added rate of expansion. Essentially it's a placeholder until we can determine the process of the added expansion rate.

[TakenItSeriously]

You mean free fall = inertial motion?

Yes, but for both conditions:

free fall = inertial motion

standing on the surface = inertial acceleration

 

I am not really following what you are trying to say.

 

You can use the equivalence principle locally, [...]

If we look at the example for an observer standing on the surface of the planet and the equivalence of the observers inertial acceleration through empty space, then your right: Einstein had concluded that if we remove the gravity field then we can replace it with an inertial reference frame that was accelerating past the observer locally.

 

However, what he may have failed to consider were the implications of what happens in the other reference frame of the observer's inertial acceleration through empty space.

 

In that case, If I'm right, the inertial observer is always accelerating away from the planet through empty space. It doesn't matter where on the planet the observer is standing, or even where you chose your empty space.

 

This is the point that resonates with me. Apparently, equivalence is telling us that gravity doesn't only have a near field attractive effect over time but that it also seems to have a far field repellant effect over distance.

 

This is very similar to the current view of expansion in the universe. It's expanding at an increasing rate with distance, and expanding at a decreasing rate over time.

 

BTW, the sense I got from my reading was that the current method of using curved spacetime was adopted from Einstein's idea of an accelerated reference frame, not a start from scratch, but I don't know this for sure.

 

I'm sure there are good reasons for using curved spacetime over using an accelerated reference frame. As I said, the math is beyond me. But I don't think flat vs curved frame is mutually exclusive in terms of their validity. From various readings, I think either is accepted in terms of their own validity, but there are limitations to what a flat frame could do.

 

Again, I freely accept that I could be wrong but out of hand dismissals seems a bit undue at this point.

To add some details the FLRW metric models the Universe in terms of a fundamental observer

Ned Wright has a decent coverage.

https://ned.ipac.caltech.edu/level5/Peacock/Peacock3_1.html.

Essentially we take our local conditions into consideration.

Now in the Einstein field equations the Universe is modelled as an ideal gas. So each contributor has an equation of state.

The equation of state for the Cosmological constant being w=-1.

Expansion occurs when the kinetic energy of each contributor overcomes its self gravity.

You don't need the cosmological constant to have expansion. Its only needed to explain the added rate of expansion. Essentially it's a placeholder until we can determine the process of the added expansion rate.

I noticed the article is for isotropic cases. However from an observers view point within a gravity field, I doesn't seem like an accurate assumption since gravity is unidirectional. For instance, a view of gravity from an observer on the ground is different than that from an observer several miles higher.

 

Is that assessment an incorrect application of isotropic?

Edited March 2, 2016 by TakenItSeriously

[ajb]

If we look at the example for an observer standing on the surface of the planet and the equivalence of the observers inertial acceleration through empty space, then your right: Einstein had concluded that if we remove the gravity field then we can replace it with an inertial reference frame that was accelerating past the observer locally.

You seem to be mixing things up a little here.

 

The statement is more like an observer standing on the surface of a planet, as experienced locally, is equivalent to a pseudo-force experienced by an observer in an non-inertial frame.

 

As we have some forces here we cannot really have an inertial frame of reference, other than in the locality of a point in space-time, ie, in a very small region. (You can make this mathematically precise).

 

So in a gravitational field only in small enough regions in space-time can we think about local inertial frames which follow the motion of freely falling particles.

 

However, what he may have failed to consider were the implications of what happens in the other reference frame of the observer's inertial acceleration through empty inertial space.

What other frames? You mean what does another observer see when he is far enough away? (or something like that?) I am not sure what you mean by inertial acceleration, maybe proper acceleration?

 

In that case, If I'm right, the inertial observer is always accelerating away from the planet through empty space. It doesn't matter where on the planet the observer is standing, or even where you chose your empty space.

I do not follow this. All we have is a notion of a local inertial observer.

 

 

Apparently, equivalence is telling us that gravity doesn't only have a near field attractive effect over time but that it also seems to have a far field repellant effect over distance.

I do not see it this way. The equivalence principle only holds locally, so I am unclear how we can get long range conclusions from this.

 

 

BTW, the sense I got from my reading was that the current method of using curved spacetime was adopted from Einstein's idea of an accelerated reference frame, not a start from scratch, but I don't know this for sure.

I think this is true. You can deal with non-inertial frames in special relativity, of course it does not look much like special relativity which states that we have a class of preferred frames, these are the inertial ones. Once you work with non-inertial frames you need most of the mathematics for curved space-times, but the underlying space-time is still Minkowski, even if it does not quite look that way.

 

I'm sure there are good reasons for using curved spacetime....

Things like gravitational redshift all point to using curved space-times. I an not sure that one can actually prove this as such, but all the arguments leads to the plausibility that we should model gravity using curved space-times.

 

 

 

...over using an accelerated reference frame.

I think the problem with your thinking is that you want to use globally defined 'accelerated references frames', which I think all you mean are the local inertial frames that you can always construct (by picking Riemannian normal coordinates centred on the point in question). This is what the weak equivalence principle is telling us.

Edited March 2, 2016 by ajb

[MigL]

I think I see where he's trying to go...

 

Consider two observers, one in free fall, and another suspended at a certain height above a planet.

As they pass each other, one observer sees the other accelerating downwards at 1g, while the other sees the first accelerating upwards at 1g.

 

I don't see how the two are equivalent since, as AJB has pointed out, the suspended observer is experiencing a force ( he has weight does he not ? ).

And as AJB has also pointed out, this effect is only local, i.e. if you increase the separation between observers, you start to note tidal effects such that the acceleration vectors would no longer be opposite but parallel, but wold have an angle, or tangential component.

[TakenItSeriously]

I clearly made a mess of this post, and my attempts to rewrite aren't going well. Therefore, I'm going to take some extra time using some of the queues already given and work on my syntactic form before trying to clean up this mess.

 

Live and learn.

 

Thanks for your patience.

Edited March 3, 2016 by TakenItSeriously

[ajb]

Thanks for your patience.

No problem. It has been fun.

[swansont]

I think I see where he's trying to go...

 

Consider two observers, one in free fall, and another suspended at a certain height above a planet.

As they pass each other, one observer sees the other accelerating downwards at 1g, while the other sees the first accelerating upwards at 1g.

 

I don't see how the two are equivalent since, as AJB has pointed out, the suspended observer is experiencing a force ( he has weight does he not ? ).

And as AJB has also pointed out, this effect is only local, i.e. if you increase the separation between observers, you start to note tidal effects such that the acceleration vectors would no longer be opposite but parallel, but wold have an angle, or tangential component.

 

 

They aren't. You can tell who is accelerating and who isn't. Acceleration isn't relative.

[MigL]

Agree with you, but, just to play devil's advocate...

 

Say one observer accelerating upwards at 1g is in an enclosed box, and similarly, the second observer is suspended in a 1g gravitational field is also in a box.

What experiments could they do to determine who is accelerating ?

 

If they each drop a ball and measure its behavior will there be any difference other than negligible tidal effects ?

Isn't this the thought experiment that led to the equivalence principle ?

 

What Takenitseriously fails to address is that, equating the accelerating expansion due to dark energy, to being at 'rest' ( i.e. not in free fall ) in a 'universal' gravity field, implies a center to the universe.

And its not that kind of expansion.

Edited March 3, 2016 by MigL