# Distinguishing between acceleration and gravity

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Einstein said there was no way to distinguish between acceleration and the force of gravity and came up with special relativity, E=mc^2. If the equation is correct then mass becomes a variable that increases from acceleration but is constant in gravity so using an electrical or magnetic force, which are independent, you can do an experiment to see if the mass is increasing and distinguish between acceleration and gravity. If the premise is right then the conclusion is wrong. If the conclusion is right the premise is wrong. If the magnets all fall off your refrigerator door you are experiencing acceleration not gravity.

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Einstein said there was no way to distinguish between acceleration and the force of gravity and came up with special relativity, E=mc^2. If the equation is correct then mass becomes a variable that increases from acceleration

The equation is not correct, so this is moot.

E=mc2 was derived for an object at rest and cannot blindly be applied to an object that is moving. The equation that applies is E2=p2c2 +m2c4

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As swansont pointed out, E=mc2 refers to the energy within any matter with mass. It is from the Special Theory of Relativity not the General Theory.

Einstein showed us inertia and gravity are two manifestations of the same force. If I am standing still there are billions of stars in front of me. Almost all of them are so far away that each on of them has an infinitesimal affect on my. But since there are billions of them they add up to a strong gravitational force in front of me. But they don't pull me forward because there is just as many stars behind me pulling me backwards. These gravitational forces keep me in my place unless I apply a force to move. Once I start moving I am passing by some matter in the universe but as long as I am going a constant speed there are just as many stars in front of me as behind. For that reason their gravitational force keep me moving the same speed. I just explained inertia as if it was gravity. That's the General Theory of Relativity.

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How very Machian of you.

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Once I start moving I am passing by some matter in the universe but as long as I am going a constant speed there are just as many stars in front of me as behind. For that reason their gravitational force keep me moving the same speed. I just explained inertia as if it was gravity. That's the General Theory of Relativity.

Are you sure?

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Are you sure?

Yes, this is true because the universe is uniform.

This is how the General Theory explains inertia as another manifestation of gravity.

Or put another way, there are gravitational waves all over the universe, going every direction, much like the background radiation. These omnipresent gravitational forces keep everything that is still from moving without an external force applied. These gravitational forces also keep everything that is moving, moving a constant speed unless an external force is applied.

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If it is impossible to make the distinction, why is it so difficult to make people accept that gravity is acceleration ?

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Yes, this is true because the universe is uniform.

This is how the General Theory explains inertia as another manifestation of gravity.

Or put another way, there are gravitational waves all over the universe, going every direction [...]

Really really sure?

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This is Ernest Mach's idea from the 1880s. GR has a Machian "flavour" since Einstein was familiar with Mach's work.

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If it is impossible to make the distinction, why is it so difficult to make people accept that gravity is acceleration ?

No, gravity is not acceleration. Gravity can cause acceleration but they are not the same. I am going to stop short of saying you don't understand relativity because language and expressing yourself can often get in the way and may be your problem. I'd like you hear you explain yourself more thoroughly.

Let me start off by taking a step back and talk about the theory of relativity. Lets say you are in a very powerful spaceship. You blast off and for two months you accelerate so fast you are pressed back against your seat. You finally take some measurements and determine that you are now going faster than 186,000 miles per second (300,000 kilometers per second). EUREKA, you are now going faster than the speed of light! To double check your accomplishment you measure the speed of the light coming from the Sun that you left 2 months ago. This sunlight is passing you up at 186,000 miles per second. Light is passing you up exactly as if you are standing still! How could that be?

Einstein explained this in his General Theory of Relativity. In general (not accelerating) motion is relative. Einstein said that you could consider that you were burning up all that fuel just to maintain your position in the universe. It's plausible that the Earth was the one that was always moving at an extreme speed. Now you are only standing still. After all that effort light is still passing you up as if you are standing still.

But now it looks like we have a contradiction. Back on Earth you made these same measurements and found out that light was passing up Earth as if Earth was standing still. Now you have measured your speed in the spaceship to be in EXCESS of 186,000 miles per second but yet you are still standing still! ?! ? ! How could this be?

Einstein showed in his General Theory of Relativity that speed is relative. He showed that all the dimensions (space and time) are relative. At relativistic speeds these dimensions become distorted (compared to Earth, or whatever you are measuring your 'relative' speed). The length of such a spaceship becomes shorter. Time on this spaceship runs slower. And it's mass would increase. If a spaceship were ever able to reach the speed of light, its length would become zero, time would no longer progress and its mass would then become infinite. Since these three conditions are impossible, it is not possible for any spaceship to reach the speed of light. As the mass of a spaceship increases it takes more effort to accelerate it. It would never be possible for the mass to approach infinity.

So now back to your measurements. You measured that you are moving faster than 186,000 miles per second. Because of the distortions of the dimensions that Einstein predicted you are not really going faster than 186,000 miles per second. That 186,000 miles that you measured is actually only 150,000 miles. And that second that you measured that it took you to get that far was actually almost a minute. So your spaceship is only going 150,000 miles per minute.

But wait a minute. You were accelerating so fast you were pressed against your seat for 2 months. How's that? Well, your mass also increased. It was taking more and more energy to accelerate you. And your mass was pressing harder and harder back against the seat. It was getting extremely hard for the engines to accelerate you and your spaceship.

Because of this increase in mass nothing that weighs anything (mass greater than 0) can ever reach the speed of light. But everything that weighs nothing (such as photons) always travels the speed of light.

Now back to inertia and gravity. In Einstein’s Special Theory of Relativity he said even accelerating motion is relative. If you are spinning and feel centrifugal force you could think of it as if you are standing still and the entire universe is spinning causing the force on you. Also if you are accelerating you could think of the entire universe as accelerating and causing the force on you.

This is Ernest Mach's idea from the 1880s. GR has a Machian "flavour" since Einstein was familiar with Mach's work.

Exactly. EigL gets the cupie doll. Einstein based his Special Theory of Relativity on Mach's Principal. Einstein didn't think Mach brought his principal far enough so Einstein wrote his Special Theory of Reactivity

Really really sure?

Yes, I am really, really sure.

Oh, wait, I have one more thing to say, and this may prevent you from making one more post.

I am really, really, really sure.

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Well you can't be that sure because you have special and general mixed up.

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No, gravity is not acceleration. Gravity can cause acceleration but they are not the same. I am going to stop short of saying you don't understand relativity because language and expressing yourself can often get in the way and may be your problem. I'd like you hear you explain yourself more thoroughly.

Let me start off by taking a step back and talk about the theory of relativity. Lets say you are in a very powerful spaceship. You blast off and for two months you accelerate so fast you are pressed back against your seat. You finally take some measurements and determine that you are now going faster than 186,000 miles per second (300,000 kilometers per second). EUREKA, you are now going faster than the speed of light! To double check your accomplishment you measure the speed of the light coming from the Sun that you left 2 months ago. This sunlight is passing you up at 186,000 miles per second. Light is passing you up exactly as if you are standing still! How could that be?

Einstein explained this in his General Theory of Relativity. In general (not accelerating) motion is relative. Einstein said that you could consider that you were burning up all that fuel just to maintain your position in the universe. It's plausible that the Earth was the one that was always moving at an extreme speed. Now you are only standing still. After all that effort light is still passing you up as if you are standing still.

But now it looks like we have a contradiction. Back on Earth you made these same measurements and found out that light was passing up Earth as if Earth was standing still. Now you have measured your speed in the spaceship to be in EXCESS of 186,000 miles per second but yet you are still standing still! ?! ? ! How could this be?

Einstein showed in his General Theory of Relativity that speed is relative. He showed that all the dimensions (space and time) are relative. At relativistic speeds these dimensions become distorted (compared to Earth, or whatever you are measuring your 'relative' speed). The length of such a spaceship becomes shorter. Time on this spaceship runs slower. And it's mass would increase. If a spaceship were ever able to reach the speed of light, its length would become zero, time would no longer progress and its mass would then become infinite. Since these three conditions are impossible, it is not possible for any spaceship to reach the speed of light. As the mass of a spaceship increases it takes more effort to accelerate it. It would never be possible for the mass to approach infinity.

So now back to your measurements. You measured that you are moving faster than 186,000 miles per second. Because of the distortions of the dimensions that Einstein predicted you are not really going faster than 186,000 miles per second. That 186,000 miles that you measured is actually only 150,000 miles. And that second that you measured that it took you to get that far was actually almost a minute. So your spaceship is only going 150,000 miles per minute.

But wait a minute. You were accelerating so fast you were pressed against your seat for 2 months. How's that? Well, your mass also increased. It was taking more and more energy to accelerate you. And your mass was pressing harder and harder back against the seat. It was getting extremely hard for the engines to accelerate you and your spaceship.

Because of this increase in mass nothing that weighs anything (mass greater than 0) can ever reach the speed of light. But everything that weighs nothing (such as photons) always travels the speed of light.

Now back to inertia and gravity. In Einstein’s Special Theory of Relativity he said even accelerating motion is relative. If you are spinning and feel centrifugal force you could think of it as if you are standing still and the entire universe is spinning causing the force on you. Also if you are accelerating you could think of the entire universe as accelerating and causing the force on you.

(...)

Maybe I don't understand Relativity, you tell me.

What I understand from Relativity is that Relativity describes what an observer measures concerning the state of motion of some other observer.

In your example, the observer on the spaceship does not observe any change in mass, nor in length, nor in time upon his own spaceship. All these changes are observed by an observer on Earth. And it is THIS OBSERVER ON EARTH who observes the changes of mass, time & length of the spaceship.

So IOW it does not take more fuel to accelerate the spaceship. The spaceship accelerates as usual. Only that the observer on Earth does not observe the spaceship accelerating as usual. And the observer on Earth observes the increasing fuel accelerating less an increasing mass.

As observed from the spaceship, the mass of the astronaut does not increase on his seat. The observer on Earth observes an increase of mass of the astronaut.

That is my understanding.

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[...] You blast off and for two months you accelerate so fast you are pressed back against your seat. You finally take some measurements and determine that you are now going faster than 186,000 miles per second (300,000 kilometers per second). [...]

That's enough to state that you don't know Relativity. You shouldn't try to explain it to other people.

By the way, not telling for which observer mass, length, time are changed does not permit sound statements.

And under "Are you sure?" you could have understood "you're wrong" and stopped timely.

No, gravity is not acceleration. [...]

In your own theory, or your own understanding, maybe. But in Relativity yes.

[...] That is my understanding.

Mine as well.

If it is impossible to make the distinction, why is it so difficult to make people accept that gravity is acceleration ?

In daily life, and almost always in engineering and physics, it is more convenient to offset all accelerations by 1g - so much that our intuitive perception includes the offset. Could that be a reason?

Also, the Euclidean space (-time) is very convenient and fits our normal life experience, so that adding a gravity force separate from acceleration is a small cost to keep a big simplicity.

After all, the best specialists for GR can completely compute just very few situations: the Universe, a black hole, and very little more. The rest are corrections applied to classical mechanics when relativistic effects are small. Why should normal people in their daily life prefer a mental image that specialists can't use?

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Einstein said there was no way to distinguish between acceleration and the force of gravity .

This is not quite correct. The principle of equivalence establishes the equivalence between a uniform gravitational field and uniform acceleration.

The non-uniform gravitational fields exhibit tidal forces and such fields cannot be made equivalent to (uniform) acceleration, so EEP does not apply to them.

Edited by xyzt
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Yes, Michell123456 you have it right, motion is relative and these distortions of spacial and temporal dimensions are relative to the viewer. So in your spaceship a clock seems to be running just fine. Why? Because it isn't moving relative to the viewer. Motion is relative. You could think of it as if your spaceship is still (from your point of view it is) Everything you are passing seems to be going by fast. Everything you pass seems to be distorted and time is running slow.

How could you check the speed of the spaceship? Lets say you set up two lasers 186,000 miles apart. You could then measure how long it takes for your spaceship to cross from one laser beam to the other. As you are traveling at an extreme speed you seem to to be crossing those laser beams in less than a second. THAT's how you would (at first) think that you are going faster than the speed of light.

As you are flying your spaceship across those 2 lasers you realize they can't really be 186,000 miles apart. You are right. You could take measurements from your spaceship and find out that they are much closer together. This is because the space between the lasers is compressed because of the your motion. From your point of view the lasers seem to be moving at an extreme speed. The distance between them is much less than the point of view of the people that set them up.
SPEED IS RELATIVE. THESE DISTORTIONS ARE RELATIVE TO THE VIEWER. If an object is not moving relative to the viewer it is not distorted.
The same is true of the clocks. A clock on the spaceship doesn't match up with a clock on Earth or any thing being passed up by the spaceship.

Because of these distortions you can always go faster. You could calculate your speed to be 99.99% of the speed of light and then accelerate so fast you are pressed back into your seat. A month later you are still not going the speed of light. It's because of these distortions. Motion is relative. These distortions are also relative.

So “Gravity IS acceleration”? Enthalpy, I would like you to explain this to me. In the mean time let me explain how I see them as being related.
First off, acceleration is an increase in speed. Gravity can cause acceleration if you are not applying a force to counteract that gravitational force. The gravitational force here on Earth is strong enough to accelerate you 32 feet per second squared. In other words gravity will accelerate you 32 feet per second faster than the second before.
For example, lets say you jump off a building. (lets ignore wind resistance and other forces). After one second you would be going 32 feet per second. After another second you would be going 64 feet per second. No matter what your speed is, gravity will accelerate you 32 feet per second faster than the second before. So far, with gravity, I have only been talking about classical physics.

Einstein's General Theory of Relativity talked about gravity. It said that gravity actually warps the space time continuum. For this reason light bends as it passes by large bodies with very strong gravitational fields. This is also the reason he said gravity affects time. He also said this gravitational force and it's acceleration are relative. What's that mean? Well, if I am standing on the ground I feel gravity because my legs are pushing on Earth with 170 pounds of force. I feel gravity. If you were to put a heavy backpack on me I wouldn't want to carry it very far. But if I were in a spaceship drifting in space (no thrust from engines) far from any star or planet, that backpack wouldn't be pulling on me. But Einstein said there is gravity everywhere. Earlier I said I feel gravity only because my legs are pushing against Earth. So lets take our spaceship back to Earth or better yet a bigger planet with a very strong gravitational pull. Our spaceship is now plummeting toward this planet. We are already near the surface so our spaceship is accelerating much faster than 32 feet per second squared (as it would on Earth). We'll say this planet doesn't have an atmosphere (I'm trying to keep out all other forces and friction). Inside this falling spaceship Einstein showed that there is no experiment that could prove we are falling (even acceleration is relative). There is no experiment that could prove we are in a strong gravitational field. Einstein said gravity can even affect time. But that too is relative. Even if we were falling into something as massive as a black hole we would still think our clock is accurate. It seems to be clicking away normally. XYZT pointed out one minor exception. Tidal forces can show that you are near a strong gravitational force. But in my example tidal forces would be immeasurable. The right side of the ship is falling toward the center of this big planet and the left side of the ship is also falling toward the center of the planet. Its true that these 2 paths are not parallel but in a spaceship they are so close to parallel you could never detect the difference. If it was one planet or moon near anther planet then yes tidal forces could prove the existence of the gravitational field. What I am saying is tidal forces can be neglected in this spaceship example.

If you were near the event horizon of a black hole the tidal forces would also be extremely high.

A tidal force is when gravitational forces are not parallel even though they are pulling toward the same object. A tidal force can also mean the closest part of a body to the planet experiences higher gravitational force. The nose of our spaceship isn't much closer to the planet than the rear of the spaceship. These are the reasons I don't think we need to take into account tidal forces when we are talking about something as small as a spaceship.

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These are the reasons I don't think we need to take into account tidal forces when we are talking about something as small as a spaceship.

It's called gravity gradient and is taken into account in the design of any satellite.

But in my example tidal forces would be immeasurable.

Gravity gradiometers do it all the day in submarines. They are used for navigation.

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isn't it impossible to distinguish any 2 = forces?
a iron robot would be unable to tell if he experiencing gravity or magnetism or acceleration.

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isn't it impossible to distinguish any 2 = forces?

a iron robot would be unable to tell if he experiencing gravity or magnetism or acceleration.

Gravity can be shown to pull on anything with mass. Magnetism only affects some metals. Acceleration is not a force, it's the result when a force is applied. That was my point earlier. That I think it's more accurate to say inertia and gravity are the same (so says Einstien). Acceleration and gravity are not the same.

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No, its most accurate to say inertial mass and gravitational mass are the same.

As for acceleration and gravity, if they produce the exact same effect, how are they not equivalent?

Is acceleration not measured in Gs?

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No, its most accurate to say inertial mass and gravitational mass are the same.

If an object has 1 gram inertial mass it also has 1 gram gravitational mass.

So yes these values are always the same. Since they are the same everything falls at the same speed.

As for acceleration and gravity, if they produce the exact same effect, how are they not equivalent?

Is acceleration not measured in Gs?

How do acceleration and gravity produce the same effect? Yes they are both measured in Gs.

Gravity can cause acceleration.

If I am standing on a bathroom scale it says I weigh 170 pounds. I am not accelerating.

If I was in anything free-falling such as an elevator with broken cables or a free falling spaceship (disregard air and other friction) then I am accelerating but no longer pressing on the bathroom scale.

If I am standing on the earth I experience gravity because my legs are counteracting gravity (pressing against earth) But if I am free falling and not pressing with my legs then i don't notice gravity.

If I am in a spaceship drifting and suddenly press my legs on the side or floor as if jumping I can experience a g force AS I am accelerating.

If I turn on the spaceship engines I am pressed in the back of my seat as I am accelerating.

If I am not applying any force to counteract gravity or inertial I am floating. I would float in a free falling elevator (even if I was on a huge planet). I would be floating in a spaceship with engines off far from any star or planet.

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Tidal forces and frame choosing aside, it would be more accurate saying gravity is equivalent to inertia, and resisting gravity is equivalent to acceleration (being accelerated).

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In GR the equivalence principle applies to inertial mass and gravitational mass, also, gravity is not a force but a space-time curvature. Being in free fall means there are no forces acting on you. The only force is the earth pushing 'up' on your feet when you are NOT in free fall. That's why we measure weight in units of force and acceleration in units of gravity.

Edited by MigL
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One reply; Einstein, General Relativity (or is that 2)

gravity is not a force but a space-time curvature.

Gravity is a force. Einstein explained this force as a space-time curvature but that doesn't mean he disproved classical physics as explaining gravity as a force. Newton and Kepler's equations are still accurate.

Being in free fall means there are no forces acting on you.

No forces??? How are you falling? In free fall here on Earth you will be accelerating 32 feet per second squared. Every second you will be going 32 feet per second faster than the second before. There must be a force. Gravity is accelerating you.

The only force is the earth pushing 'up' on your feet when you are NOT in free fall. That's why we measure weight in units of force and acceleration in units of gravity.

... and you pushing down with your weight. To every action there is an equal and opposite reaction. So when the earth is pushing up your weight is pushing down. When you are counteracting gravity this is the only time you notice it. Your earlier statement would be more accurate to say you never notice the gravitational force when you are in free fall. THAT's General Relativity. Accelerating motion is relative. Einstein showed gravity and inertia as being 2 manifestations of the same force. If you were in a spaceship accelerating 32 feet per second squared you would experience 1 G of force. You could walk around on the floor of your rocket and think you were on Earth. So as the accelerating rocket pushes against your feet you press back and once again you notice this "gravity" only because there is a force counteracting it. But is this really gravity or inertia? It's relative.

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One reply; Einstein, General Relativity (or is that 2)

Gravity is a force. Einstein explained this force as a space-time curvature but that doesn't mean he disproved classical physics as explaining gravity as a force. Newton and Kepler's equations are still accurate.

No Einstein explained Gravity as space time curvature and in doing so removed the need to think of it as a force. Newtonian gravity is remarkably accurate and hugely simpler - but in fairly simple equations and observations we can show that Newtonian gravity gets the incorrect answer and that GR is precise.

No forces??? How are you falling? In free fall here on Earth you will be accelerating 32 feet per second squared. Every second you will be going 32 feet per second faster than the second before. There must be a force. Gravity is accelerating you.

You are falling because you are following the shortest route through 4d spacetime. Heuristically you could say that you are merely travelling in a straight line at a constant velocity (thru 4d spacetime) - that is an equilibrium state; when an external force is applied - the normal from the ground, EM etc then you can vary from this constant state.

... and you pushing down with your weight. To every action there is an equal and opposite reaction. So when the earth is pushing up your weight is pushing down. When you are counteracting gravity this is the only time you notice it. Your earlier statement would be more accurate to say you never notice the gravitational force when you are in free fall. THAT's General Relativity. Accelerating motion is relative. Einstein showed gravity and inertia as being 2 manifestations of the same force. If you were in a spaceship accelerating 32 feet per second squared you would experience 1 G of force. You could walk around on the floor of your rocket and think you were on Earth. So as the accelerating rocket pushes against your feet you press back and once again you notice this "gravity" only because there is a force counteracting it. But is this really gravity or inertia? It's relative.

That's not general relativity - those ideas were understood prior GR. You are still talking about inverse square force laws - that is pre-Einstein.

You would notice it if you dropped a ball - even before it hit the ground. Here is a good explanation

http://www.einstein-online.info/spotlights/equivalence_principle

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No Einstein explained Gravity as space time curvature and in doing so removed the need to think of it as a force.

No need to think of it as a force? Just becouse Einstein says graity is a spacetime curvature doesn't mean it's not a force. This argument is like saying "a tiger isn't an animal, it's a mammal."

There are only four forces in the universe and gravity it one of them. For extra credit what are the other 3?

Newtonian gravity is remarkably accurate and hugely simpler - but in fairly simple equations and observations we can show that Newtonian gravity gets the incorrect answer and that GR is precise.

The equations for Newtonian grvity are correct. The issue is not accuracy. The issue is some experiments, such as the precession of the perihelion of Mercury's orbit, can't be explained by classical physics. Einstein says that precession is relative.

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