# Gravitational force = inertial mass

## Main Question or Discussion Point

I am not trained in physics but find it extremely interesting to read about. As I was reading a book on Einstein it talked about about gravitational force being equal to inertial mass. A good deal of the discussion talked about a man in a box and the inability to distinguish one effect from the other and what would happen to a beam of light through a pin hole.

The answer to my question is probably painfully obvious but I did some searches and could find nothing to answer it.

I thought about this same guy in a box that is at the interface of two gravitational fields where there is a line where the pull is equal and the pull of either field is greater on their side of this line.

If this box intersected this line I would guess that the amount of force to accelerate the box would decrease sharply. If the box had equal mass on either side of the line including the man what would the effects be. He would feel a pull from both directions so what conclusion would he draw. As explained in the book if a pin hole let light in it would curve in the direction of gravity. If there where three holes on on the line and one on either side he would see a straight line and two curving rays going opposite ways. Again what conclusion would he arrive at.

I am sure all this is very obvious but when I think about two identical boxes each located across this line but one equally distributed and one with more mass on one side or the other, it seems to me that the amount of force to accelerate it or the weight of the box could be vastly different. I know they say that the guy in the box could not tell if he was feeling gravity or acceleration but what would he think if he felt gravity on both sides.

My simple mind cannot comprehend what any of this would mean. What if the guy sat on the floor on one side of the line and saw a light that was on the other side of the line as it curved away from the pull he felt. How would he calculate or determine what was going on?

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Mentz114
Gold Member
Your equation cannot be because the units are different on the two sides.

Your description of the man in the box is inadequate. You must give a reference or a quote otherwise we don't know exactly what you read and saw.

However, your man in the box sitting over a trojan line ( where two opposing fields cancel) can easily work out what is happening by releasing test bodies at various points and seeing which way they go. I'm assuming the box is positioned so the two acelerations cancel out.

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The man in the box came from a book on the life of Einstein. It was said that this was one of his thought experiments that led to his idea that light would be curved by gravity.

There really is not much to explain. There is a box suspended by a rope in a gravitational field. Since the man could only experience what is in the box that is his frame for reference. Initially, is seemed as this thought experiment was used to try to come up with a way to determine if the man could do anything to determine if the force he is feeling is gravity or acceleration that I guess creates inertial mass.

From the book this led to the idea of the pin hole with light shining in cowards the other side of the box. If you are moving, logic says that the light would appear to curve down from the pin hole to the other side. Since gravitational force is equal he concluded that the light would also curve due to gravitational forces.

All these observations were from the view point of the man in the box. What I was thinking is what would conclusions this same man would make if he were in a box that straddled a gravitational Trojan line. I have never seen this term so I hope I used it correctly.

I am sure that someone who is knowledgeable in Physics this is a straight forward matter. However to me I think it would be quite a confusing situation. For example, I think it would allow the man to do things that in a single field would be completely impossible.

I think he would be able to jump up and do a spiderman and cling to the top of the box. By placing a rope so that it had equal mass on either side of the line he could make the line suspend in air. Cut a piece off and it would rise to the ceiling or floor depending on which side of the line a piece was removed.

I had what to me was a funny thought that I would guess this line would be curved. So I thought that what if this line occurred at a point on the earth. Someone would walk toward it and once enough of them stepped into the other side they would fly up into the sky.

I am guessing that it would be quite interesting doing anything inside such a box that is bisected by what you call a Trojan line. Imagine a game of baseball.

I guess my question is to vague to really be answered. But if Einstein was able to conclude that gravity curved light by this very same thought experiment. How would this man come to the same conclusions given conflicting observations depending upon where in the box an observation was made. It seems to me that the box is accelerating in two directions. That does not seem possible.

I think that I mostly wonder what observations Einstein might have made about this situation. It seems that a good deal of his theories evolved from thinking about simple situations and what they might mean. Given my simplistic understanding of physics this all may very well be a silly post. However, I think that at the very least it allowed me to think of situation that would be very interesting.

Mentz114
Gold Member

M

Thanks raptor5618, you raise a thought-provoking point. I have read Einstein's man in the box thought experiment and will review it again. Your placement of the box at a Trojan point is an interesting variant and it seems to me that you are fully capable of figuring out the answer. I will try to frame it in a way that makes sense to me and see what kind of an answer I can find.

I can immediately say that the man in the box, as you suspect, would feel a tug on either side of his body from the (unseen) mass on each side. He would not move if the two forces were equal. If they are equal and weak, he might not even feel them. If they are equal and strong, he would feel himself being pulled apart; he would be experiencing a "tidal force" just like the oceans experience with the motion of the earth-moon-sun system. If they are unequal, he will be pulled in the direction of the stronger force.

The details you refer to such as the rope and adding people in the box are not entirely clear to me; I would have to re-read your post very carefully and reframe your thoughts; I may not actually do that.

I am more interested in Einstein's original purpose in placing his man in the box. Would that man be able to tell whether his box was (1) accelerating because it was pushed by a rocket or (2) accelerating because it was being sucked into a black hole? The difference could be a matter of life and death.

The first instance is an example of a force acting on an INERTIAL mass causing it to accelerate; no space curvature is involved.

The second instance is an example of a mass accelerating as it "slides down" a depression in space caused by another mass.

The two conditions are physically very different but they are described by the same mathematics and every experiment the man in the box can conduct will fail to tell him which one he is experiencing. Obviously, the box is not transparent.

The great value of Einstein's General Theory of Relativity is that it answered the question that Newton had left unanswered; What is Gravity? Einstein demonstrated that gravity is a curvature in space-time caused by massive bodies. The unanswered question now is; What is Mass?

If the Standard Model of Physics is right, in September the new Large Hadron Collider in Europe will give us the answer; Mass is the property bestowed upon matter by the Higgs particle. I'm an engineer, not a physicist, so that doesn't mean much to me. I'm more interested in what they don't expect to find that is going to surprise them anyway. Truth be told, that's what the physicists are hoping for too.

Thanks again.

Thanks for the replies to my post. After some reading I came across a good bit of information on Lagrange Points which I think are what these areas are called with Trojan points consisting of points L4 and L5 which are are 60 degree angles to the two bodies. Apparently these points are being used for satellites and my intuition is that when they sling shot satellites around a planet they pass through a point such as this.

I still think it is interesting to think about forces when straddling one of these lines. Two boxes laying on a scale one taller but weighing the same as a smaller box. As you lift them up the taller one would lose weight as it crossed the line. At a point one box could be suspended while the other one fell to the ground.

I understand that this all is the result of the cumulative of forces on each object so how they would react is understandable and could be calculated. However, the concept that they would behave differently than our common experience is the aspect that captured my imagination. I also was thinking about how these opposing forces could be used to perform work without the losses of friction. I apologies if my comments are too simplistic but I can only speak about these things using that which I know. I assume that everyone here knows more than I do and had hoped to gain more knowledge to fill in some of the holes I know exist in my understanding of these lines or points.