# Naked Science Forum

## Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: geordief on 11/01/2020 00:44:27

Title: Is the equivalence principle only approximately correct?
Post by: geordief on 11/01/2020 00:44:27
I have been reading E's Popular Exposition of SR and  GR (it is for the layman and so I may be reading too much into what may be relatively simplistic scenarios) and the following "objection" to his closed room experiment occurred to me.
The gist of his argument seems to be that an observer in a sealed container  will not be able to tell if he or she is being accelerated or experiencing gravity.

However  ,if the propulsion is being caused by a rope tugging a hook in the centre of the ceiling it would be possible by  examining the ceiling to verify that the force is in fact being directed at that particular area (the room cannot be 100% rigid) and so it is possible to distinguish between a gravitational  effect vs acceleration.

If the room was vanishingly small (Or completely rigid) this would indeed  then be impossible.

Am I right or just being pedantic? (Or misunderstanding the scenario in the round?)
Title: Re: Is the equivalence principle only approximately correct?
Post by: Kryptid on 11/01/2020 01:09:52
I think in order to get it to be a better analogy for the equivalence principle, you should probably assume that there are many ropes pulling equally on each part of the ceiling.
Title: Re: Is the equivalence principle only approximately correct?
Post by: geordief on 11/01/2020 01:26:04
Thanks.I think you have addressed my concern.
Title: Re: Is the equivalence principle only approximately correct?
Post by: Colin2B on 11/01/2020 07:48:47
As this is just an illustration of a principle it is reasonable to assume an perfectly rigid box. Having said that, you would be hard pressed to notice the lifting points on a standard commercial lift  ;)
Title: Re: Is the equivalence principle only approximately correct?
Post by: jeffreyH on 11/01/2020 11:39:47
I think in order to get it to be a better analogy for the equivalence principle, you should probably assume that there are many ropes pulling equally on each part of the ceiling.

Gravitation acts on all points of an object simultaneously. This is very like your many ropes analogy. It acs on all points of an accelerometer simultaneously, which is why you won't detect the acceleration due to gravity in freefall.

When supported against gravity you are still being accelerated. However, now you will be able to detect acceleration.

EDIT: The ground now acts like the many ropes.
Title: Re: Is the equivalence principle only approximately correct?
Post by: geordief on 11/01/2020 14:24:27
Just as a historical note, since we went into space the mechanics of low gravity environments  (and artificial gravity) have become second (almost first) nature to us.

Was it surprising that Einstein (and  others,perhaps?) seems to have "twigged" gravity without the advantage of these  very elementary first hand observations?
Title: Re: Is the equivalence principle only approximately correct?
Post by: alancalverd on 11/01/2020 14:43:04
Returning to the original question: it's a good example of the difference between physics and engineering.

Physics provides mathematically perfect solutions to an ideal world of rigid boxes and flexible weightless strings. No approximations (or at least highly qualified ones like "tanθ = sinθ = θ for very small θ") or safety factors.

Engineering provides economically adequate solutions to a real world full of wind, rain, and courts of enquiry. The roof of a real lift will bend, so the emergency brakes need sufficient clearance to avoid snagging at all ambient temperatures but within wear limits.....  Spot the engineering vocabulary!

The physics of zero-g was demonstrated one afternoon by Galileo. The engineering of a space toilet took thousands of man-hours studying anatomy, physiology, mechanical engineering, bacteriology…..to improve on a hole in the ground.
Title: Re: Is the equivalence principle only approximately correct?
Post by: Halc on 11/01/2020 15:36:29
Also in reply to the OP and other posts:
The box being accelerated by one string is equivalent to a stationary box suspended similarly by a crane in a gravity situation.  Yes, the box will tip as the mass is moved from side to side, but you can't tell which situation you're in from that.

Similarly, the box need not be rigid or bendy since both will behave equivalently in both situations.  None of the experiments suggested (examining the box) really constitutes a non-local experiment, so they're all fair game.
Title: Re: Is the equivalence principle only approximately correct?
Post by: jeffreyH on 11/01/2020 22:13:06
One question that springs to mind is what is the source of the gravitational field of any composite object? It is a combination of all the gravitational fields of the atoms that make up the object.

While electrons and protons have opposite charges that cancel they do not have opposite gravity.

The charges of the electron and proton are equivalent in strength, just opposite in sign. This equivalence in charge is not reflected in gravity. The gravitational field of the electron is not the same as that of a proton or neutron. Since their masses are different.
Title: Re: Is the equivalence principle only approximately correct?
Post by: jeffreyH on 11/01/2020 22:27:25
Another question is does the conservation of mass suggest that the conservation of gravity is a physical law? If so then the conservation of energy, since energy has an equivalent mass, cannot be separated from conservation of gravity.
Title: Re: Is the equivalence principle only approximately correct?
Post by: jeffreyH on 11/01/2020 22:31:03
So the black hole has properties of mass, charge, angular momentum and gravity.
Title: Re: Is the equivalence principle only approximately correct?
Post by: PmbPhy on 11/01/2020 22:37:00
Equivalence Principle - at any point of space-time the effects of a gravitational field cannot be experimentally distinguished from those due to an accelerated frame of reference.

I don't see how this is related to the posts above.
Title: Re: Is the equivalence principle only approximately correct?
Post by: jeffreyH on 11/01/2020 23:11:28
Well conservation is important to this point. To continually accelerate at 1g without limit you would need infinite energy. In order to maintain this equivalence then time must be dilated. Thus the absolute speed of c would never be reached and you could carry on forever.

This is of course an absurd thought experiment but it does indicate that over a finite amount of time you would be unable to tell the difference. However, given enough time, you would. Since your fuel would diminish.

In an actual gravitational field, due to the conservation, time would not change the effect. Unless the object generating the field lost mass. Equivalent to the astronauts losing fuel.

So passage of time would allow you to distinguish. The same with free fall versus inertia. You hit the ground if you wait long enough.
Title: Re: Is the equivalence principle only approximately correct?
Post by: jeffreyH on 12/01/2020 02:10:15
Another follow up point. In an inertial frame all parts of an object can be considered to be either stationary or moving in the same direction with the same speed.

You cannot say this in free fall. The force exerted by gravity changes with height above the centre of mass of the gravitating body. No matter how small an effect, this creates tidal forces. These are not present in a truly inertial frame.

However, a truly inertial frame is not possible.

In the case of free fall, gravity can be said to be dragging along an approximate inertial frame.
Title: Re: Is the equivalence principle only approximately correct?
Post by: jeffreyH on 12/01/2020 02:34:21
https://phys.org/news/2020-01-satellite-space-fall-two-trillionths-percent.html (https://phys.org/news/2020-01-satellite-space-fall-two-trillionths-percent.html)
Title: Re: Is the equivalence principle only approximately correct?
Post by: Colin2B on 12/01/2020 09:03:05
You cannot say this in free fall. The force exerted by gravity changes with height above the centre of mass of the gravitating body. No matter how small an effect, this creates tidal forces. These are not present in a truly inertial frame..
The illustration Einstein created assumes a uniform gravitational field, not a planetary field. As I said before it’s an idealisation to illustrate a principle.
I’m pretty sure there’s something on Pete’s site about uniform grav fields
Title: Re: Is the equivalence principle only approximately correct?
Post by: jeffreyH on 12/01/2020 12:02:25
I understand about the uniform gravitational field. However, in reality they do not exist. It would nullify the inverse square nature of the gravitational field. That is why I said gravity produces approximate inertial frames.

If it is not an exact inertial frame then that matters.
Title: Re: Is the equivalence principle only approximately correct?
Post by: Colin2B on 12/01/2020 14:45:44
I understand about the uniform gravitational field. However, in reality they do not exist. It would nullify the inverse square nature of the gravitational field.
They do exist as a very close approximation in a small volume eg a lift. However, I suspect that is what you mean by:
That is why I said gravity produces approximate inertial frames.

If it is not an exact inertial frame then that matters.
Yes, the inverse square law is a result of the effective point source of the planetary field rather than the general nature of gravitation. Similar to the difference between a spherical, point light source (inverse sq law) and plane wave which does not obey inverse law eg photon.
As you say, that means that a planetary grav field can only be an appropriation of an inertial frame and should not be used to argue the equivalence principle.
Title: Re: Is the equivalence principle only approximately correct?
Post by: Halc on 12/01/2020 16:35:30
Answering a bunch of the questions.

Another question is does the conservation of mass suggest that the conservation of gravity is a physical law?
Gravity is not a quantified thing, and hence cannot be something 'conserved'.  That said, it is not something that can be turned up or shut off by expenditure of effort.
All those thought experiments about how long it would take Earth to stop orbiting if the sun was suddenly gone just have no real basis in reality.  The sun cannot suddenly just be gone.  The mass cannot disappear and hence the gravitational effects of that mass similarly cannot go away.[/quote]
So the black hole has properties of mass, charge, angular momentum and gravity.
Just the first three, per the no-hair theorem.  Gravity is not a separate quantifiable property that can vary independent of the mass.

Well conservation is important to this point. To continually accelerate at 1g without limit you would need infinite energy.
Uniform gravity is equivalent to proper acceleration, not frame dependent acceleration.  One can maintain 1g of proper acceleration indefinitely with only finite expenditure of power.  You'd never get to the speed of light since a thing's proper velocity is always zero.  This situation would be indistinguishable from just sitting still in a uniform gravitational field.

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This is of course an absurd thought experiment but it does indicate that over a finite amount of time you would be unable to tell the difference. However, given enough time, you would. Since your fuel would diminish.
Your fuel would diminish in both cases, so the two are still indistinguishable.

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So passage of time would allow you to distinguish. The same with free fall versus inertia. You hit the ground if you wait long enough.
If you hit the ground, it isn't a case of just gravity/acceleration anymore.  Yes, you can tell (in both cases) if an external force is suddenly applied.  You'd not know from this which case you were in.

Another follow up point. In an inertial frame all parts of an object can be considered to be either stationary or moving in the same direction with the same speed.
Only if it isn't accelerating, rotating or containing moving parts.  Anything, accelerating or not, can be considered from any inertial frame.

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You cannot say this in free fall.
Objects stationary or moving in a direction at some speed in some inertial frame IS freefall, so your statement is a contradiction.

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The force exerted by gravity changes with height above the centre of mass of the gravitating body. No matter how small an effect, this creates tidal forces. These are not present in a truly inertial frame.
Detection of tidal forces is considered a non-local test, as is noting that two plumb lines are not parallel but actually point to the center of the gravitational source.   I think Colin's reply is relevant here.

There are tidal forces in a continuously accelerating environment, so mere detection of tides does not distinguish the one case from the other, at least in the accelerating scenario. Clocks run at different rates if one is above the other, in a gravity/acceleration situation. I don't think your example above is one of acceleration.
Title: Re: Is the equivalence principle only approximately correct?
Post by: Colin2B on 12/01/2020 23:57:28
Detection of tidal forces is considered a non-local test, as is noting that two plumb lines are not parallel but actually point to the center of the gravitational source.   I think Colin's reply is relevant here.
Correct. The box is assumed so small that the local observer will see no effect, only the non-local will understand the point nature of the source.
There are many other strictures such as disallowing any test of the mass of the box - alternatively you have to assume it has planetary mass without creating any gravitational field.