## Thursday, 22 September 2016

### Gravity is more or less the same as acceleration.

From Quora:

Q: Obviously, the source of acceleration (without gravity) is transfer of energy from one object to another or change of its own energy structure so that one of its components changes into increasing energy of motion. But gravity occurs with no measurable energy transfer nor is the gravitating mass changing its energy structure in order to produce gravity.

If the cause of acceleration and gravity is not related at all is the Equivalence principle just a coincidence that the resulting effects are physically identical and indistinguishable?

A: By Frank Heile, PhD in Physics from Stanford University

I will try to describe in detail how gravitation works and how acceleration works and why the two different phenomena are really equivalent...

There follows a long and complicated explanation and comparison, but in folksy terms, anybody who has ever swung a bucket of water over his head at the right angle and speed knows this. As far as the water in the bucket is concerned, there is no difference between the gravity and the centripetal force/acceleration* while it is upside down. See also Einstein's famous thought experiment with the man in the accelerating spaceship.

* Acceleration is change in speed OR in direction, see here.

I refer you now to the comment by Nobel Prize nominee Ralph Musgrave:

Assume there’s just one atom in a car cylinder which is at room temperature. The atom bounces up and down between the piston and the top of the cylinder. Atoms at room temperature move around at about 1,000mph. If the piston then moves upwards at 1mph to its “maximum compression” point, the atom will gain a good 100mph in speed.

How is that possible, given the paltry speed of the piston? Answer… During the half second or so during which the piston is moving, the atom collides with it a hundred times or so, and it gains 1mph each time. I’d appreciate nominations for a Nobel Prize for this amazing insight.

So for air at ground level, the effect of gravity is like being driven by a giant piston accelerating at that speed and every time it bounces off the piston (the surface of the earth), it travels back faster than it set off (I'm not clever enough to work out how much faster at this stage and if so, relative to what). Relative to the surface of the earth there is no change in observed speed, just in direction (which as explained above, is acceleration).

Now imagine sweeping up sawdust with long straight strokes of a broom, you will get a bow wave in front of the broom where the sawdust is deeper, the broom is pushing saw dust which is pushing more sawdust etc. The pile is deepest directly in front of the broom and slopes away from it, the sawdust far ahead of the broom is entirely unaffected.

Which is why the atmosphere is thicker at the bottom. Which is another way of explaining why, from the point of view of an individual O or N molecule, in gravity/pressure/temperature* terms, the atmosphere is not static, it is constantly being accelerated from underneath by a giant piston (the surface of the earth), the same as the sawdust in front of the broom is being accelerated by the broom itself or by other bits of sawdust etc.

Like a bow wave, the force is carried ever upwards, so molecules in the upper atmosphere are bounced further out than they would reach under their own devices. So the upper atmosphere is less dense than it 'should' be and hence is cooler than it 'should' be, i.e. cooler than the surface of the Earth in the same way as the lower atmosphere is warmer than it 'should' be etc. To use another analogy, the atmosphere acts like a heat pump or fridge, it transfers heat from some places (cools them) to other places (warms them) but without changing the overall amount of 'heat'.

* I accept that there is minority few that increasing the pressure of a gas does not directly increase its temperature, which would mean that a lot of textbooks are very, very wrong on this one!

mombers said...

So if it's constantly being accelerated, how come the earth doesn't explode in a nuclear fireball as particles approach the speed of light? The relativity thing I believe is that you can't tell if you are being accelerated by a force or by gravity - not that the two are identical.

Bayard said...

When in a hole, remember that it is not always a good idea to keep digging.

"Gravity is more or less the same as acceleration."

No it isn't. Gravity is a force, measured in Newtons. Using Newton's second law of motion, Force = mass x acceleration you can calculate the force of gravity on a body if you know its mass, using the gravitational constant (at the surface of the earth, g approx = 10 m/s2. However, a body does not have to be accelerating to experience gravitational force. It's just, because of Newton's Law of motion, g shares the same units as acceleration. g, the gravitational constant, is defined as the acceleration due to gravity,, i.e the acceleration that an object experiences under the force of gravity. If gravity was the same as acceleration then g would be "the acceleration due to acceleration" which is either a tautology or nonsense.

"As far as the water in the bucket is concerned, there is no difference between the gravity and the centripetal force while it is upside down."

Well apart from the fact that when the bucket is upside down. the force on it is the centripetal force less gravity and when it is the right way up it is the sum of the two forces, yes.

"As far as the water in the bucket is concerned, there is no difference between the gravity and the centripetal acceleration while it is upside down."

No, the bucket doesn't have to be accelerating for there to be a centripetal force. Newton's first law states "an object either remains at rest or continues to move at a constant velocity, unless acted upon by a net force" Since the bucket is being constrained to travel in a circle, its velocity is constantly changing direction, therefore there needs to be a net force on it, which we are referring to as the centripetal force.

"So for air at ground level, the effect of gravity is like being driven by a giant piston accelerating at that speed and every time it bounces off the piston (the surface of the earth), it travels back faster than it set off"

Well you state that, but unfortunately, this is not the case. The surface of the earth is demonstrably not accelerating, nor is the piston in Ralph's example. "If the piston then moves upwards at 1 mph" he says, not "if the piston accelerates upwards at 1m/s2". So not only is the effect of gravity nothing like a giant accelerating piston, but if it was it would be nothing like Ralph's example. Also in Ralph's example the atom gains speed by bouncing off a moving piston, but in yours, "there is no change in observed speed, just in direction".

The falsity of the "giant accelerating piston" analogy rather scuppers your sawdust analogy as well. There is no need to postulate
giant accelerating pistons. The force of gravity is well understood and has been since Newton.

paulc156 said...

Well to be fair, Einstein's theory of general relativity absolutely makes plain that acceleration and gravity are identical.
That's its great insight. That gravity is not a real force at all but thinking of it as a force as Newton did is just a very very good approximation. Eg. It was all the voyager space craft needed for a number of planetary liaisons on route to interplanetary space...but useless for satellites which provide sat nav data on planet earth. Gravity as a force is just a remarkably good proxy for the the real (relativistic) thing.