# The equivalence principle and weightlessness.

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Einstein describes  how an accelerating sealed chamber is indistinguishable  from a gravitational field to an observer in the chamber.

I have learned and read a little about this in the past 5 years or so and also that Einstein described this as his happiest idea.

It seems to be possibly the kernel of General Relativity  and yet I wonder whether his appreciation was any different or more profound  than the appreciation of weightlessness and artificial gravity that became common knowledge as soon as astronauts went into space in the 60s.

True ,Einstein realized this without  seeing astronauts floating around the spacecraft but what I want to ask is whether  the common or garden appreciation of weightlessness and artificial gravity that is really second nature to most people (well I hope so) is equally enlightening as Einstein's Equivalence Principle  or  is there more to it than that(I appreciate that astronauts do not accelerate to the extent of causing light rays to bend in front of their eyes😀

)

Edited by geordief
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There are not one equivalence principle, but two, strong and weak.

It is necessary to distinguish between "weak equivalence principle" and "strong equivalence principle"[13]. A strong equivalence principle can be formulated as follows: at each point of space-time in an arbitrary gravitational field, one can choose a "locally inertial coordinate system", such that in a sufficiently small neighborhood of the point under consideration, the laws of nature will have the same form as in non-accelerated Cartesian coordinate systems of SRT, where "laws of nature" mean all laws of nature[14].
The weak principle differs in that the words "laws of nature" are replaced in it by the words "laws of motion of freely falling particles"[13]. The weak principle is nothing but another formulation of the observed equality of gravitational and inert masses, while the strong principle is a generalization of observations of the influence of gravity on any physical objects. https://ru.wikipedia.org/wiki/Принцип_эквивалентности_сил_гравитации_и_инерции

I believe that these equivalence principles should be applied depending on the situation.

If the same system is observed by several observers in different places of the gravity well, they should all observe the same picture only at different time scales. There is a strong equivalence principle at work here.

If one observer observes several identical systems but located in different places of the gravity well, then only a weak equivalence principle should work here.

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16 hours ago, geordief said:

It seems to be possibly the kernel of General Relativity  and yet I wonder whether his appreciation was any different or more profound  than the appreciation of weightlessness and artificial gravity that became common knowledge as soon as astronauts went into space in the 60s.

Read this (1962 edition) from Einsteins's friend ,nobel Physicist, Max Born.

Sorry it's all words.

No Pictures.

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6 hours ago, SergUpstart said:

If the same system is observed by several observers in different places of the gravity well, they should all observe the same picture only at different time scales.

What do you mean by “observe”? You mean visually?

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6 hours ago, studiot said:

Read this (1962 edition) from Einsteins's friend ,nobel Physicist, Max Born.

Sorry it's all words.

No Pictures.

Thanks.

Words (=ideas) are hard for me (but  yes I did read it and will try again)

The question ,though I am asking is whether ,if Einstein had not existed would a physicist  have found it a lot easier to understand the Equivalence Principle once he or she became familiar with the concept of weightlessness ,as was the general public once  astronauts started floating around in their cabins a la Gagarin.

I know Einstein's mind's eye   showed him the workman falling off his ladder and so being weightless for a very short time....

(I wasn't sure whether to post this thread in the hard science section as my question was maybe as much  historical as involving the nitty gritty of the theory)

Edit:top of page 376 is that a misprint: "mb=K superscript1"? Does "mk=K superscript1" make more sense?

Edited by geordief
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5 hours ago, Markus Hanke said:

What do you mean by “observe”? You mean visually?

Yes

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5 hours ago, SergUpstart said:

Yes

That’s not the case though, not even in the most symmetric spacetimes. Consider a freely falling particle in Schwarzschild spacetime - a faraway observer will see the particle recede, and then slowing down and getting dimmer and redder as it approaches the horizon. Another observer falling in parallel to the particle (at not too great a distance) will not see this effect, for him the particle appears the same the entire time, and will actually get closer to him as they fall.

So visual appearance in curved spacetime does depend on the observer, because different events are linked by different sets of null geodesics.

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To me, the interesting part is the limitation on equivalence.
Take my example, I've existed for over seventy years, with a gravitational force acting on me, equivalent to an acceleration of nearly 10 m/sec2.

If I had been in deep space, accelerating at 10m/sec2 for seventy years, I would be moving faster than the speed of light. So equivalence doesn't hold for longer time intervals. It gets more equivalent, the shorter the interval, so presumably is only really true for an interval of zero time.  In other words, it's not a true equivalent, but a useful approximation.

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3 hours ago, mistermack said:

If I had been in deep space, accelerating at 10m/sec2 for seventy years, I would be moving faster than the speed of light.

You have been.
Thank goodness for the ground forcing you to stay in place.

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4 hours ago, mistermack said:

If I had been in deep space, accelerating at 10m/sec2 for seventy years, I would be moving faster than the speed of light.

You would be moving pretty fast relative to your starting point, but not faster than c. Remember the laws of Special Relativity!

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1 hour ago, MigL said:

You have been.
Thank goodness for the ground forcing you to stay in place.

You heat me to it, and you expressed it better.  +1

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1 hour ago, Markus Hanke said:

You would be moving pretty fast relative to your starting point, but not faster than c. Remember the laws of Special Relativity!

I think you're putting the boot into a straw man there. I didn't suggest it was possible. It's the fact that it's not possible, that is the difference between the two scenarios. A rock can sit for a thousand years on the surface of the Earth, with a constant force acting on it from below, and yet would not be moving "pretty fast" at the end of it. Whereas the same rock, with the same constant force acting on it in zero gravity, would be moving pretty fast after just a few days.

Another way that the two cases are not equivalent, is that "real" acceleration involves a force acting on a mass over a distance. In the case of me, standing on the Earth, a force is acting on my mass, but not over any distance. So real acceleration involves work, whereas standing still in a gravitational field doesn't.

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1 hour ago, mistermack said:

Another way that the two cases are not equivalent, is that "real" acceleration involves a force acting on a mass over a distance. In the case of me, standing on the Earth, a force is acting on my mass, but not over any distance.

Ahh, but they are equivalent ( except for 'special' effects ).
Acceleration is due to a force acting on a 'free' mass, and weight is due to a force ( gravitational ) acting on a 'fixed' mass.
That is part of the Equivalence Principle.

Edited by MigL
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2 hours ago, mistermack said:

So real acceleration involves work, whereas standing still in a gravitational field doesn't.

The salient point though is that there is no local experiment you can perform which distinguishes these cases. The equivalence principle is always a purely local statement. Measuring force and distance over long periods of time gives you a region of spacetime that is too large to be considered ‘local’, so of course there is no equivalence. But if you put an astronaut into a windowless box and ask him to tell whether the downward force is due to gravity or due to acceleration, without any outside references, then there isn’t anything he can do to tell the difference.

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8 hours ago, Markus Hanke said:

The salient point though is that there is no local experiment you can perform which distinguishes these cases. The equivalence principle is always a purely local statement. Measuring force and distance over long periods of time gives you a region of spacetime that is too large to be considered ‘local’, so of course there is no equivalence.

Yes, but that's basically what I said in my first post. The more local you look, the more equivalent are the two phenomena. And the less local, then the less they are equivalent. So it's a useful approximation, only actually true for a time interval of zero.

In the case of my seventy years, if I was free floating in space, it would take an infinite amount of energy to maintain a force of 200lbs on me for seventy years. On earth it needs none at all.

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10 hours ago, mistermack said:

Yes, but that's basically what I said in my first post. The more local you look, the more equivalent are the two phenomena. And the less local, then the less they are equivalent. So it's a useful approximation, only actually true for a time interval of zero.

Yes, though in the real world the limitation on locality is most often given by the spatial extension of the frame, since gravity due to sources such as planets is tidal in nature; so if the frame becomes too large, then tidal effects become detectable, which destroys the equivalence.

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The other side of the coin of course, is that free falling in a sealed chamber in a gravitational field is also indistinguishable from floating in zero gravity. With similar local limitations.

The Astranauts in the space station are doing that, free falling in orbit, but I suspect there would be a way to tell that you were orbiting something, rather than just floating or free falling directly towards the source of gravity

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7 hours ago, mistermack said:

The other side of the coin of course, is that free falling in a sealed chamber in a gravitational field is also indistinguishable from floating in zero gravity.

Yes indeed.

7 hours ago, mistermack said:

but I suspect there would be a way to tell that you were orbiting something

There wouldn’t be any purely local way to tell, but you can construct some scheme that relies on outside references, or on longer-lasting measurements (to detect tidal forces).

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On 10/5/2021 at 9:18 PM, geordief said:

what I want to ask is whether  the common or garden appreciation of weightlessness and artificial gravity that is really second nature to most people (well I hope so) is equally enlightening as Einstein's Equivalence Principle  or  is there more to it than that

I suspect the general enlightenment about gravity is little better now than it was in Einstein’s time and the popularity of the flat earth theory makes me wonder if has gone the other way.

Einstein’s delight in the Equivalence Principle was in knowing that he had discovered two ways of thinking about the same problem so he could test his theories about gravity against his understanding of free fall looking for consensus between the two. More importantly, the Equivalence Principle gave him simple examples he could use to explain his ideas to others.

Everyone knows that astronauts are weightless in space but it is my impression that popular opinion holds that there is no gravity in space and I don’t think it is generally understood that astronauts are subject to much the same gravity as we are on the surface of the Earth. The difference between us and the astronauts is that they are in continuous free fall.

There is also an erroneous impression that there is no gravity in deep space far from any massive bodies. Einstein’s Equivalence Principle seems to be less difficult to comprehend than what Einstein called Mach’s Principle which deals with universe wide influence of gravity and it is the latter that is the most enlightening about gravity.

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On 10/9/2021 at 5:54 AM, mistermack said:

Yes, but that's basically what I said in my first post. The more local you look, the more equivalent are the two phenomena. And the less local, then the less they are equivalent. So it's a useful approximation, only actually true for a time interval of zero.

In the case of my seventy years, if I was free floating in space, it would take an infinite amount of energy to maintain a force of 200lbs on me for seventy years. On earth it needs none at all.

It wouldn't take infinite energy and you wouldn't reach a speed of c relative to anything. If you accelerated away from Earth with a constant proper acceleration for seventy years, the coordinate acceleration of Earth away from you would decrease and approach zero as its speed approached c, because of the velocity addition or composition law of SR.

I don't think the difference in energy use is related to localness of effects, or whatever. You could hover over the Earth on a stationary platform that uses energy to create 200 lbs of thrust for 70 years. The equivalence principle still applies. You can't tell whether you're accelerating away or overcoming gravity. You could also simulate gravity by being in a rotating ship in freefall for 70 years, and use no energy, and experience no gravitational acceleration. The equivalence principle might not apply since that would be a rotating frame of reference.

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13 hours ago, bangstrom said:

There is also an erroneous impression that there is no gravity in deep space far from any massive bodies. Einstein’s Equivalence Principle seems to be less difficult to comprehend than what Einstein called Mach’s Principle which deals with universe wide influence of gravity and it is the latter that is the most enlightening about gravity.

Are you saying that ,far from any mass it is possible for there to be an object with the independent means to rotate about itself and to create an artificial gravity?

(I have not read very much about Mach's Principle  or the significance attached by Einstein to Mach's ideas.)

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4 hours ago, geordief said:

Are you saying that ,far from any mass it is possible for there to be an object with the independent means to rotate about itself and to create an artificial gravity?

(I have not read very much about Mach's Principle  or the significance attached by Einstein to Mach's ideas.)

No, it is still possible to use rotation to create artificial gravity. The point is that an object floating free in the depths of space is still within the effects of the gravity originating from the sum of all the massive bodies in the universe. This gravity determines our perception of distance and time. There is no place in the universe that is free of gravity.

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4 hours ago, geordief said:

Are you saying that ,far from any mass it is possible for there to be an object with the independent means to rotate about itself and to create an artificial gravity?

I wouldn't say that exactly. I'd also call it "inertia" instead of artificial gravity. But objects do tend to have some rotation, and inertia does contribute to forces acting on things (eg. the Earth bulges around the equator, along with a feeling of less pull of gravity than at the poles, at a fixed distance from the centre of the Earth), and for a static object that inertia does not require energy to maintain.

My point is that if you choose a force that requires constant use of energy for one observer, and another force that doesn't for another observer, that's not a difference that concerns the equivalence principle. The principle doesn't say that any 2 different things you choose should be the same, and if there's a detectable difference (eg. in energy use) then the principle doesn't hold. Effectively it says if you make everything else the same, gravity is not detectably different from acceleration.

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On 10/8/2021 at 8:45 PM, Markus Hanke said:

The salient point though is that there is no local experiment you can perform which distinguishes these cases. The equivalence principle is always a purely local statement. Measuring force and distance over long periods of time gives you a region of spacetime that is too large to be considered ‘local’, so of course there is no equivalence. But if you put an astronaut into a windowless box and ask him to tell whether the downward force is due to gravity or due to acceleration, without any outside references, then there isn’t anything he can do to tell the difference.

If the astronaut climbed onto a shelf at the top of the box,  and was in a gravitational field of a planet,  wouldn't his G meter show a tiny decrease in force due to his greater distance from the CoG?  I guess what I'm asking,  in a nonserious way,  is what scales are truly local.

Edited by TheVat
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1 hour ago, TheVat said:

If the astronaut climbed onto a shelf at the top of the box,  and was in a gravitational field of a planet,  wouldn't his G meter show a tiny decrease in force due to his greater distance from the CoG?  I guess what I'm asking,  in a nonserious way,  is what scales are truly local.

Yes, indeed. That’s an example of tidal gravity.

As a general rule of thumb, “local” means a region in the order of ~1/g, so near Earth’s surface for example it would be a box no larger than ~10cm. But of course it depends on your required level of accuracy.

23 hours ago, bangstrom said:

the popularity of the flat earth theory makes me wonder if has gone the other way.

I think the recent spread of FET has more to do with the algorithms on social media platforms such as YouTube, than with understandings of gravity.

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