Relation between acceleration and gravity...

[Dustin Kesselberg]

I understand that gravity is caused by the reaction of space-time to objects of mass. Which causes space-time to basically push in all directions against anything with mass in some attempt to even itself out. I also understand that when you move very fast your mass increases as does your affect on space-time. Super-fast objects tend to bend space-time.

However my question is this...What is the relation between acceleration and gravity? Why is it that when I hit the gas pedal on my car I am pushed back into my seat? Is this the same thing as gravity? Is this due to the bending of space time caused by the acceleration of my vehicle?

If not..Then if speedy objects have more mass and affect space-time does their gravity increase also? Is the gravity of a spaceship traveling 30,000 mph more than the gravity of a stationary spaceship? If so then why is it that astronauts in such spaceships feel weightless?

 

[The Don]

However my question is this...What is the relation between acceleration and gravity? Why is it that when I hit the gas pedal on my car I am pushed back into my seat? Is this the same thing as gravity? Is this due to the bending of space time caused by the acceleration of my vehicle?

No, the reason why you are "pushed back into your seat" is due to the fact that the accelleration is applying a force to you. In effect you aren't being pushed back into the seat, the seat is attempting to travel through your body and out the other side

If not..Then if speedy objects have more mass and affect space-time does their gravity increase also? Is the gravity of a spaceship traveling 30,000 mph more than the gravity of a stationary spaceship? If so then why is it that astronauts in such spaceships feel weightless?

The force applied by an object on any other is proportional to its mass, therefore the gravitational attraction would increase as the mass of hte object increases.

At only 30,000 mph the effect is infinitessimal as the increase in mass would be of the order 1/100000000 of the original mass

Spaceship astronauts feel weightless because the gravitational force exerted by (primarily) the Earth is equal to the other forces the astronaut is experiencing (remember he is moving in an orbit)

 

[Dr Aardwolf]

Hi Dustin
I don't really understand this stuff, but I believe your question is answered by Einstein's Principle of Equivalence, which shows that a person accelerating at 9.8 metres per second experiences the same apparent 'force' as someone in an Earthlike gravitational field. Check this link at Wikipedia for a fuller explanation.
http://en.wikipedia.org/wiki/Principle_of_equivalence

 

[3point14]

why is it that astronauts in such spaceships feel weightless?

Astronaughts in spaceships feel apparent weightlessness. In fact they and the craft they are travelling in, are in freefall. Constantly falling towards the centre of gravitational attraction, but not losing altitude because they're travelling fast enough so that the curve of the earth means that the ground below them is constantly moving away.

I feel I may have expained this very badly. Someone else care to have a go?

 

[Crossbow]

Dustin:

In the case of the car problem you describe, it is a case of every action has an equal but opposite reaction.

Specifically, as the engine is used to accelerate the car forward direction, then there is an equal amount of force generated in the backwards direction. Another way to think of this is to imagine the same car on an icy surface, if the engine was similarly used, then the car would not accelerate and consequently the opposite force would not be generated.

 

[Cuddles]

I understand that gravity is caused by the reaction of space-time to objects of mass. Which causes space-time to basically push in all directions against anything with mass in some attempt to even itself out. I also understand that when you move very fast your mass increases as does your affect on space-time. Super-fast objects tend to bend space-time.

Spacetime does not need to push against anything. One of the best, and most common, explanations is the rubber sheet analogy. Imagine spacetime as a rubber sheet. Place a weight on it. The sheet will have a debt with the weight at the bottom. Now what happens if you place a ball somewhere else on the sheet? It rolls towards the weight due to the slope. If you push the ball it will not travel straight towards the weight but will follow a curved path. If you eliminate friction (as is effectively the case in space) you can cause the ball to roll around the weight, in essence it will orbit it.

However my question is this...What is the relation between acceleration and gravity? Why is it that when I hit the gas pedal on my car I am pushed back into my seat? Is this the same thing as gravity? Is this due to the bending of space time caused by the acceleration of my vehicle?

The relationship is that gravity is a force and forces cause acceleration. One of the key points of relativity was to realise this, that there is nothing special about gravity, it is simply one case of acceleration among many. In your car, you are not pushed back in your seat, the seat is pushed forwards into you, since it is attached to the engine and you are not.

If not..Then if speedy objects have more mass and affect space-time does their gravity increase also? Is the gravity of a spaceship traveling 30,000 mph more than the gravity of a stationary spaceship? If so then why is it that astronauts in such spaceships feel weightless?

This is not really related to the previous point, but is also interesting. The simple answer is yes, if something travels faster it gains more mass and therefore has a stronger gravitational field. This is because of the mass-energy equivalence from the popular equation E² = p²c² + m²c⁴ (commonly written as E = mc², but this misses the term that is actually important). In fact, anything with more energy will have stronger gravity. If you heat a cake in the oven it will weigh more when you take it out than when you put it in.

As already said by someone else, this is not why astronauts feel weightless. Apparent weightlessness is a consequence of freefall, where you are travelling at the same speed as everything around you. If you jump out of a plane you will experience freefall and will feel as though you don't weigh anything, even though you are very obviously still within the Earth's gravity and not travelling especially fast. In fact, this is how many zero-G experiments are carried out, rather than travel all the way out to space you can simply nose-dive a plane towards the ground and have exactly the same effect for a short time.

 

[Roboramma]

Thanks for an informative post cuddles.

This is because of the mass-energy equivalence from the popular equation E = p²c² + m²c⁴ (commonly written as E = mc², but this misses the term that is actually important).

Minor quibble - I might be wrong but shouldn't that be E² = p²c² + m²c⁴ ?

 

[steenkh]

I understood that Einstein in his general theory of relativity actually showed that gravity and acceleration is exactly the same thing. At least that is what Susskind tried to convince me of in his excellent "String Theory and the Illusion of Intelligent Design".

 

[Cuddles]

Minor quibble - I might be wrong but shouldn't that be E² = p²c² + m²c⁴ ?

Don't know what you mean.


Yes

 

[Ziggurat]

This is not really related to the previous point, but is also interesting. The simple answer is yes, if something travels faster it gains more mass and therefore has a stronger gravitational field.

That's a bad way to think about it. It's sometimes taught that way in order to maintain the whole kinetic energy = mv² equation (absorbing the correction into a modified "mass"), but that's actually a TERRIBLE way to try to think about it. Why? Because in some reference frame, your body would have enough mass to be a black hole. But the existence of an event horizon should not be (in fact, CANNOT be) reference frame-dependent. You could account for that with equations for gravity that use a corresponding velocity dependence, but that just makes the equations more complicated in order to fix a problem artificially introduced in order to make a previous set of equations look simpler, when there was never a need to do so in the first place.

In the end it's far simpler to use a reference frame-independent mass, and just accept that the equations for momentum and kinetic energy are more complicated than the Newtonian formula. For example, the whole
E² = p²c² + m²c⁴equation rather explicitly does NOT use a velocity-dependent m - velocity dependence is accounted for entirely within the momentum term.

In fact, anything with more energy will have stronger gravity. If you heat a cake in the oven it will weigh more when you take it out than when you put it in.

The analogy doesn't work. You are correct that heating a cake increases its mass ever so slightly, but you're wrong that this is equivalent to making the cake move at high velocity. The kinetic energy of a cake is reference-frame dependent: throwing it will increase its kinetic energy in some frames, but decrease it in other frames. But heating it will increase its energy in ALL reference frames. The additional mass from heating the cake is not reference frame dependent.

 

[Ziggurat]

I understood that Einstein in his general theory of relativity actually showed that gravity and acceleration is exactly the same thing. At least that is what Susskind tried to convince me of in his excellent "String Theory and the Illusion of Intelligent Design".

The equivalence is actually a little more restrictive than that, and it's actually not what general relativity demonstrates (you can demonstrate it experimentally without GR), it's the postulate Einstein used as a base hypothesis for forming general relativity. And it isn't really that remarkable a claim in and of itself.

The real equivalence claim is that being stationary in a uniform gravitational field (ie, sitting on earth) is locally equivalent to uniform acceleration in a flat space-time. The reason that you can't just say that gravity = acceleration is that gravity is not purely local, and we're primarily interested in gravitational fields that are not in fact uniform (and by that I don't mean irregular, I just mean that the strength of the field varies with distance). Extrapolating from that local equivalence to figure out what it means globally (in other words, reconciling that claim with the requirements of special relativity and the weak-field limiting behavior of Newtonian gravity) is highly non-trivial, and it's why going from special relativity to general relativity took so much time and effort. Reconciling Newtonian gravity, that local equivalence, and Galilean relativity is actually trivial, and produces nothing new (which is why nobody ever thought about it much prior to Einstein).

 

[69dodge]

Is the gravity of a spaceship traveling 30,000 mph more than the gravity of a stationary spaceship? If so then why is it that astronauts in such spaceships feel weightless?

I don't understand the question. The spaceship isn't travelling 30,000 mph relative to the astronauts inside it, so why should its speed relative to Earth matter to them?

Anyway, if the spaceship is sitting motionless on Earth with the astronauts in it, they don't feel weightless, but their weight isn't caused by the spaceship---it's caused by the Earth. The spaceship itself is very light compared to the Earth, so it exerts very little gravity on astronauts or on anything else.

The reason they feel weightless when they're in the spaceship out in space is that you never feel gravity unless something is preventing you from moving the way gravity wants you to move. If you're sitting in your chair on Earth, gravity wants you to move down, but your chair is in the way. So you feel gravity pulling down on you. Astronauts in space are free to move in whatever orbit gravity wants them to; so they do, and consequently they feel weightless.

 

[69dodge]

The reason that you can't just say that gravity = acceleration is that gravity is not purely local, and we're primarily interested in gravitational fields that are not in fact uniform (and by that I don't mean irregular, I just mean that the strength of the field varies with distance). Extrapolating from that local equivalence to figure out what it means globally (in other words, reconciling that claim with the requirements of special relativity and the weak-field limiting behavior of Newtonian gravity) is highly non-trivial, and it's why going from special relativity to general relativity took so much time and effort.

Does one have to "reconcil[e] that claim with [...] the weak-field limiting behavior of Newtonian gravity" explicitly? I'm not entirely sure, but I thought that Newtonian gravity just fell out naturally from the combination of equivalence with special relativity.

 

[Ziggurat]

Does one have to "reconcil[e] that claim with [...] the weak-field limiting behavior of Newtonian gravity" explicitly? I'm not entirely sure, but I thought that Newtonian gravity just fell out naturally from the combination of equivalence with special relativity.

With just equivalence and special relativity, you can get the concept of curved space-time. But that alone doesn't tell you what makes it curved (namely, its relationship to mass), only that it is curved. You need something else to plug in to indicate the role that mass plays in creating gravity (equivalence and special relativity alone won't tell you that gravity is stronger on Jupiter than on Earth), and the simplest way to do that is to use Newtonian gravity as the weak-field limit.

 

[Schneibster]

I understand that gravity is caused by the reaction of space-time to objects of mass. Which causes space-time to basically push in all directions against anything with mass in some attempt to even itself out. I also understand that when you move very fast your mass increases as does your affect on space-time. Super-fast objects tend to bend space-time.

Well...

Velocity is rotation in spacetime that translates some of what the observer sees as "space" into "time," and vice versa. But remember that such effects are symmetric; that is, since there is no absolute motion, neither the object nor the observer can say, "I am motionless, and he/that is moving," or vice versa; in the absence of absolute motion, either one can assume that they are motionless and the other moving, and all the laws of physics will be the same. So to the observer, the moving object has translated some of its motion through time into motion through space; therefore, by moving in space, the object sacrifices some of its inherent movement through time. You can think of this as a rotation in spacetime. Another observer, stationed on the object, says that the first observer has undergone the equal rotation, translating some of his movement in time into movement in space, and moving slower in time as a result.

The term that relativistic physics uses to describe this rotation is "rapidity." You can google that up and find some very interesting physics pages.

However my question is this...What is the relation between acceleration and gravity? Why is it that when I hit the gas pedal on my car I am pushed back into my seat? Is this the same thing as gravity? Is this due to the bending of space time caused by the acceleration of my vehicle?

This is actually a deep question.

In the General Theory of Relativity, there is a postulate, a foundational one, that states that acceleration and gravity are indistinguishable. It's called the "equivalence principle." Now, in the real world where gravity fields emanate from spherical sources, there IS a way you can tell the difference; it's called "tidal forces." But if you could make a gravity field that wasn't spherical, there would be no way you could tell the difference between gravity and acceleration.

If not..Then if speedy objects have more mass and affect space-time does their gravity increase also? Is the gravity of a spaceship traveling 30,000 mph more than the gravity of a stationary spaceship? If so then why is it that astronauts in such spaceships feel weightless?

No. Here's why: time dilation. Remember that some of the natural movement in time is translated to allow an object to move in space; therefore, everything happens slower. This turns out to be a modification to the force; remember, acceleration (upon which force is dependent) is inversely dependent upon time, and if the time gets longer, the force gets smaller. It turns out to be just sufficient to account for the additional mass due to the velocity (not surprising since they are both modified by the same factor).

 

[Soapy Sam]

" Accerelation "? (See tags). Now there's a typo I never saw before. I rather like it. This word deserves a definition.

Well...

... since there is no absolute motion, neither the object nor the observer can say, "I am motionless, and he/that is moving," or vice versa; in the absence of absolute motion, either one can assume that they are motionless and the other moving, and all the laws of physics will be the same.

I've never understood this. In a lab experiment, it's possible to have two objects moving relative to one another at uniform velocity, but in reality that's an impossible situation. At least one of them has to be accelerated at some point in (space)time. There has to be a history. If a train pulls away from a platform , we can arbitrarily start paying attention either when the relative velocity is zero, or during the acceleration phase, or once the train reaches a constant velocity, but the fact remains it was the train that burned the fuel, not the platform.

We can pull back and say that the whole station was going around the sun and what the train is actually doing is braking it's orbital velocity- and the only reason it's not falling into the sun is that there's a planet in the way. (So it's only safe for trains to move at night? ), but it was STILL the train that burned the fuel.

I quess what I'm asking is at what point in the history of a system like this does it become valid to say that the POV of someone on the train is equivalent to that of an observer on the platform? If there is memory, or fuel bills, then the two are never equivalent.

 

[Schneibster]

Sam, you're confusing absolute space with absolute spacetime. Absolute space implies absolute motion; something we know doesn't exist otherwise SR wouldn't work. Absolute spacetime, on the other hand, doesn't imply absolute motion- but DOES imply absolute acceleration. That's why acceleration and gravity are equivalent.

 

[Soapy Sam]

I'll have a think about that when my head stops spinning.

 

[Big Al]

It's not all that hard to handle; you can deal with aspects other than time dilation and spacetime warping with Newtonian kinetics, which, at slow speeds, concur very well with general relativity.

The Newtonian laws of motion state:

1. A body remains at rest, or in uniform motion in a straight line, unless acted on by an external force.
2. Force equals mass times acceleration
3. For each action, there is an equal and opposite reaction.

For the train scenario, (ignoring visual and audible cues outside your frame of reference) you can posit either of the following:

The person on the platform is moving south at a constant 40 miles per hour, and you are moving north (backwards) at 40 miles per hour. There is no aceleration involved, and you are at rest relative to each other. The train you are on then decelerates steadily. Inertia tends to keep you moving backwards at 40 miles per hour (Newton 1), so you feel the seat pushing into your back with a force proportional to your deceleration (Newton 2 & 3). Once the train comes to a halt, the person on the platform rushes past you at 40 miles per hour. You are now no longer under deceleration, so you no longer feel any force pushing you back in your seat. The person on the platform has not accelerated or decelerated at all, so he feels no forces acting on him.

The person on the platform is not moving (OK, this does assume a universal standard of rest, but it's just an analogy) and neither are you. Again, there is no aceleration involved, and you are at rest relative to each other. The train you are on then accelerates steadily to the north (forwards). Inertia tends to keep you at rest (Newton 1), so you feel the seat pushing into your back with a force proportional to your acceleration (Newton 2 & 3). Once the train reaches its final velocity, you rush past the person at 40 miles per hour. You are now no longer under acceleration, so you no longer feel any force pushing you back in your seat. The person on the platform has not accelerated or decelerated at all, so he feels no forces acting on him.

In real life, there are many external cues, such as trees, the noise of the train wheels and so on, but they are cues from an external frame of reference. In this thought experiment, you have, a train with no windows, silent engines and frictionless bearings, and just, say, some sort of radar device that gives the distance between you and the person on the platform. Under these circumstances, with no external frames of reference accessible, you have absolutely no means of teling which of these possibilities is the right one.

The point about burning fuel, hot brakes and so on is a good one, but not a deal killer. If you brake while decelerating and apply engine braking, the brakes get hot and you burn fuel. If you accelerate while applying the brakes, ditto.

 

[Schneibster]

I'll have a think about that when my head stops spinning.

I laughed almost thirty seconds; thanks for my daily dose.

Folks who don't "get it" should google up "Newton's Bucket."