Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: flr on 24/05/2012 20:44:36
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The concept of mass can be understood as the resistance of an object to change its constant velocity motion.
This is obvious from the well known formula:
F=ma
On the other hand mass can also be introduced via formula:
p=mv
where p is the linear momentum (a conserved quantity) and v is velocity. No acceleration is required in the last formula, only the momentum p and velocity v.
I am a bit confused: Can we actually understand mass without acceleration?
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Its only by changing momentum that you can evaluate mass, and that means the velocity changed, so there had to be acceleration - I think :)
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The best way is to consider the object...still [:)]
An oject's mass is its energy (divided c2) when the object is still.
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The concept of mass can be understood as the resistance of an object to change its constant velocity motion.
In my opinion its a "resistance" (whatever that is) to a change in momentum where momentum = p = mv
I use the term motion in the Newtonian sense, i.e. as
This is obvious from the well known formula:
F=ma
That's Euler's definition of force, not Newton's. Newton's was dp/dt where p = mv.
On the other hand mass can also be introduced via formula:
p=mv
Excellant! :)
I am a bit confused: Can we actually understand mass without acceleration?
Yes since it depends on velocity, not acceleration.
Pete
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The best way is to consider the object...still [:)]
An oject's mass is its energy (divided c2) when the object is still.
By "still" I guess you mean "proper frame".
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The concept of mass can be understood as the resistance of an object to change its constant velocity motion.
This is obvious from the well known formula:
F=ma
On the other hand mass can also be introduced via formula:
p=mv
where p is the linear momentum (a conserved quantity) and v is velocity. No acceleration is required in the last formula, only the momentum p and velocity v.
I am a bit confused: Can we actually understand mass without acceleration?
I believe the way this is interpreted as acceleration is that if direction changes that represents acceleration. added Also and more important, anything that has mass IS accelerating in space-time.
I don't think we can.
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p = mv is a meaningless equation unless you have a way to measure p or m. P and m are useful only for predicting how objects will accelerate in the vicinity of other objects. Until an acceleration is observed, there is no way to determine the values of p and m.
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p = mv is a meaningless equation unless you have a way to measure p or m. P and m are useful only for predicting how objects will accelerate in the vicinity of other objects.
Particle physicists don't usually concern themselves with the acceleration of particles. From what I've read they only use expressions of the conservation of 4-momentum.
As p = mv goes I conceed that there may be a circularity floating around.
I always say that m is defined so that mv is conserved. Then define p as mv.
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The best way is to consider the object...still [:)]
An oject's mass is its energy (divided c2) when the object is still.
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By "still" I guess you mean "proper frame".
Yes, is the same. An object' status of motion can be stated only after having defined a frame of reference.
Still/stationary/motionless, don't know which is the best term in english, means that the velocity of the system's centre of mass is zero, with respect to that frame of reference.
In that situation, mass is just the system's energy (divided c2). And notice that here I mean *invariant mass* (or "proper mass", but I prefer the first), not "relativistic mass".
Example: you take a piece of iron and you weigh it: 1kg.
Then you give it an amount of energy E, for example heating it, then you weigh it again: 1 + E/c2 kg.
You don't need to move or to accelerate the object...
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The best way is to consider the object...still [:)]
An oject's mass is its energy (divided c2) when the object is still.
"
By "still" I guess you mean "proper frame".
Yes, is the same. An object' status of motion can be stated only after having defined a frame of reference.
Still/stationary/motionless, don't know which is the best term in english, means that the velocity of the system's centre of mass is zero, with respect to that frame of reference.
In that situation, mass is just the system's energy (divided c2). And notice that here I mean *invariant mass* (or "proper mass", but I prefer the first), not "relativistic mass".
Example: you take a piece of iron and you weigh it: 1kg.
Then you give it an amount of energy E, for example heting it, then you weigh it again: 1 + E/c2 kg.
You don't need to move or to accelerate the object...
But anything that has mass IS accelerating in space-time.
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But anything that has mass IS accelerating in space-time.
Err, I don't think so. Perhaps you are confusing mass with weight?
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But anything that has mass IS accelerating in space-time.
In which sense?
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But anything that has mass IS accelerating in space-time.
Err, I don't think so. Perhaps you are confusing mass with weight?
But anything that has mass IS accelerating in space-time.
In which sense?
"Mass tells space-time how to curve, and space-time tells mass how to move." John Wheeler (commenting on Relativity)
All mass warps space time. The effects of matter and space-time on each other are what we perceive as gravity. Gravity is acceleration in space-time.
An accelerometer placed on the Earths surface will measure about 1g acceleration.
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Mike,
You seem to be confusing weight with mass. Weight is a consequence of accelerating mass in a particular gravitational field, but mass is independent of any gravitational field other than its own.
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But anything that has mass IS accelerating in space-time.
....All mass warps space time. The effects of matter and space-time on each other are what we perceive as gravity.
You can't just state that anything that has mass is accelerating in space-time and expet people to read your mind and know that you're refering only spacetime. The acceleration of a particle is frame dependant. The 4-acceleration of a particle which is moving only under the force of gravity is zero. Please don't assum things such as "I'm thinking about spacetime." and expect people to know what you mean, i.e. that it only pertains to curved spacetime. In any case gravity doesn't always exist in all regions of a curved spacetime. Gravity doesn't exist at all in a curved E.g please see http://home.comcast.net/~peter.m.brown/gr/grav_cavity.htm
And there exist zero acceleration of any sense in a the word in flat spacetime in a uniform gravitational field.
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Mike,
You seem to be confusing weight with mass. Weight is a consequence of accelerating mass in a particular gravitational field, but mass is independent of any gravitational field other than its own.
"In the physics of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference."
http://en.wikipedia.org/wiki/Equivalence_principle
So, gravity is acceleration.
As "mass warps space-time" and "the effects of matter and space-time on each other are what we perceive as gravity." Therefore, as gravity is acceleration, "anything that has mass IS accelerating in space-time". It accelerates in space-time within its own "gravitational field" (warped or curved space-time)
The Earths mass produces its own local space-time curvature within which it accelerates.
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But anything that has mass IS accelerating in space-time.
....All mass warps space time. The effects of matter and space-time on each other are what we perceive as gravity.
You can't just state that anything that has mass is accelerating in space-time and expet people to read your mind and know that you're refering only spacetime. The acceleration of a particle is frame dependant. The 4-acceleration of a particle which is moving only under the force of gravity is zero. Please don't assum things such as "I'm thinking about spacetime." and expect people to know what you mean, i.e. that it only pertains to curved spacetime. In any case gravity doesn't always exist in all regions of a curved spacetime. Gravity doesn't exist at all in a curved E.g please see http://home.comcast.net/~peter.m.brown/gr/grav_cavity.htm
And there exist zero acceleration of any sense in a the word in flat spacetime in a uniform gravitational field.
That's why I said space-time and all space-time is curved.
The gravitational 'field' is only uniform (the same) at any given radius from the center of mass. Space-time is anything but flat surrounding a massive object.
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But anything that has mass IS accelerating in space-time.
So how do you explain why it's possible for a body with mass to be stationary between two other bodies with mass?
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But anything that has mass IS accelerating in space-time.
So how do you explain why it's possible for a body with mass to be stationary between two other bodies with mass?
Although they can be stationary in the space aspect of space time (relative each other), as a system they are all moving together (accelerating) in the time aspect of space-time.
added 29th May
If they are a gravitationally bound system then they share a common time frame although all three may have a different local time frame. Just as a clock in orbit has a different time frame than its counterpart on Earth but share a common time frame. end of edit
Mass/gravity dilates time, therefore as a body passes through time it goes from a position of more dilated time to a position of less dilated time. This is acceleration. Gravity is acceleration. We are used to thinking of acceleration as something that we can see but we can't see acceleration due to time contraction.
I will try and explain in more detail but have run out of time at the moment.
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Geezer
Think of the world line of an object, let’s say the Earth. The Earth follows that world line along the direction of time. If we imagine the world line to not go through the center of the Earth but to wrap around its circumference then the line stretches as it goes around the Earth as half the circumference is more than its diameter. Local time dilates (is stretched) near to the Earth in relation to time at a distance. As the Earth follows its world line so it is continually entering an area of space-time that is time contracted in comparison to where the Earth is at any moment. From a local time perspective the Earth is continually accelerating in the time dimension of space-time.
A rubber sheet if often used as an analogy to demonstrate gravity. If the sheet is divided up into a grid of squares then the lines curve (warp) and stretch wherever the Earth is situated. As the Earth follows its world line, so time stretches around the Earth. The next instant of time that the Earth is about to enter is always shorter that the present instant. The Earth only accelerates in its own local ‘bubble’ of time. It does not accelerate from the perspective of a distant observer.
Does this clarify the matter?
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Local time dilates (is stretched) near to the Earth in relation to time at a distance. As the Earth follows its world line so it is continually entering an area of space-time that is time contracted in comparison to where the Earth is at any moment. From a local time perspective the Earth is continually accelerating in the time dimension of space-time.
The dilation is constant. Another way to think about it is that the speeding up effect must also be accompanied by a slowing down effect, so the net change is always zero.
Therefore, there is no acceleration.
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Local time dilates (is stretched) near to the Earth in relation to time at a distance. As the Earth follows its world line so it is continually entering an area of space-time that is time contracted in comparison to where the Earth is at any moment. From a local time perspective the Earth is continually accelerating in the time dimension of space-time.
The dilation is constant. Another way to think about it is that the speeding up effect must also be accompanied by a slowing down effect, so the net change is always zero.
Therefore, there is no acceleration.
The net change from the perspective of a distant observer is zero. The acceleration is a purely local effect. The Earth accelerates in its own ‘bubble’ or ‘shell’ of space-time.
The world line only points forward. The Earth at any instant is about to enter the next instant of time, not the last.
Think of any massive object like the Earth as being surrounded by concentric shells of space-time (like a Russian doll). Time is most dilated nearest the Earth and less so in each concentric shell as you move radially out from the surface of the Earth. This was predicted by Relativity and shown to be true by atomic clocks in orbit. As the Earth moves through space-time so we can think of the shells of space-time as collapsing upon the Earth. The innermost shell accelerates and stretches the most as it is the closest to the Earth. (We know this to be true as a second on the Earth is longer than a second in orbit. If it is longer then it must have been stretched and if it is not constant then it must be accelerating.) Therefore, space-time accelerates toward the Earth. Space-time accelerating toward the Earth is the same as the Earth accelerating in space-time.
Does that help?
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The world line only points forward. The Earth at any instant is about to enter the next instant of time, not the last.
Actually, I don't believe there is any proof that time is irreversible.
Is this theory of "time acceleration" your theory, or is it supported by some testable proof?
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The world line only points forward. The Earth at any instant is about to enter the next instant of time, not the last.
Actually, I don't believe there is any proof that time is irreversible.
Is this theory of "time acceleration" your theory, or is it supported by some testable proof?
Nor do I. I believe the arrow of time is double ended but entropy ensures that we only experience the one end of that arrow. Perhaps in an antimatter universe the arrow points in the opposite direction relative to our universe.
Einstein said that gravity and acceleration are equivalent.
An accelerometer on the Earths surface will register about 1g of acceleration.
The Earth travels through space-time. That's EQUIVALENT to space-time traveling through (or over) the Earth. Time is more dilated closer to the Earths surface than in space. That's been proven by comparing two synchronized atomic clocks. One on the Earths surface and one in orbit. So space-time dilates as it reaches the Earth. That's EQUIVALENT to the Earth accelerating in space-time.
Is it my theory? I don't think so, "I personally believe" it was what Einstein meant when he said gravity and acceleration are equivalent.
Is it supported by testable proof. Yes, the accelerometer and time dilation measurements as mentioned. The accelerometer shows that the Earth is accelerating in space-time. The Earths diameter is not getting any larger as it accelerates therefore it cannot be accelerating in the three dimensions of space, it can only accelerate in the time dimension of space-time. The difference in clock times shows that time is relative and passes more slowly near to the surface of the Earth as predicted by GR.
If we put an atomic clock on a rocket and send it into space. The clock will not only accelerate in the space aspect of space-time but in the time aspect of space-time. (As a second becomes progressively shorter[in comparison to a second on the Earth], the ship covers the same distance in less time from the occupants perspective.) The Earth essentially does the same but just in the time aspect of space-time. Again it is a local effect.
If this isn't the explanation of what Einstein meant when he said that gravity and acceleration are equivalent then what other explanation is there?
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It's frame dependent, and all measurements use two frames of reference, unless you're at Plank scale possibly, measuring on yourself. And whose 'frame of reference' is the correct one is a meaningless question as both frames will define the universe from their own clock and their own ruler. So you can't, or can :) define the universe from yourself, then defining time dilations and Lorentz contractions when comparing other frames to yours. But they can do the exact same using their ruler and clock.
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If we refer the arrow to interactions and the time it take for something to decay for example, then that decay will be measured the same in all frames of reference as I see it. Assuming that we do it 'locally'. That constitutes a proof for that the arrow never change - locally - for you, no matter where you go (mass) or how fast you go.
Using that as thumb rule you now need to ask if what you measure, comparing your clock and ruler to other frames of reference, is as real as it can be? And if you accept the theory of relativity it must be. So depending on 'motion' you can contract the universe, as measured by you locally.
The other thing one need to ask is if there exist any other way of measuring than using your local definitions of 'time and distance'. I can't really see any other types of 'real time' direct measurements possible, except conceptually as in Lorentz transformations of others clocks and rulers.
So your local time is always the same as I understands it, it never change. And that is what you use when comparing 'frames of reference'.
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To me it becomes a geometrical effect in both ways, as 'time' and as 'distance'. It's as if the arrow, although locally invariant as measured by you, is something that 'distort' in its relations to other frames mass and motion. The next question, if this was right, would be to ask where one can set a limit for calling something 'local', and there I provisionally expect that you will find it at Planck scale. Using that as a definition of a smallest 'locality' as defined by a clock and a ruler you then have to assume that all those Plank 'points' must find time dilations as well as Lorentz contractions relative each other.
But it's somehow geometrical, all of it seems to be so to me. Even the arrow, although the arrows 'origin' (as in what I call 'time') is to be found locally as I suspect, at Planck scale. It becomes a 'inflated' universe, defined from a very small invariant 'point' as I think of it.
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And what that makes is a universe in where distance and motion both must be limited expressions, working here where we are, but not correct for what creates it. Then to that one can add the question how mass, as in the matter we consist of can exist, if we now constantly are 'exposed' to Planck sized time dilations and Lorentz contractions. There I think it should have to do with equilibriums and 'symmetries' as we go down to particle levels, or if you like the 'forces' we see keeping particles together and also 'adhering' one particle to another creating molecules and the matter we touch.
Whatever the arrow is, it's not as we thought of it historically. Although?
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The world line only points forward. The Earth at any instant is about to enter the next instant of time, not the last.
Actually, I don't believe there is any proof that time is irreversible.
Is this theory of "time acceleration" your theory, or is it supported by some testable proof?
Nor do I. I believe the arrow of time is double ended but entropy ensures that we only experience the one end of that arrow. Perhaps in an antimatter universe the arrow points in the opposite direction relative to our universe.
Einstein said that gravity and acceleration are equivalent.
An accelerometer on the Earths surface will register about 1g of acceleration.
The Earth travels through space-time. That's EQUIVALENT to space-time traveling through (or over) the Earth. Time is more dilated closer to the Earths surface than in space. That's been proven by comparing two synchronized atomic clocks. One on the Earths surface and one in orbit. So space-time dilates as it reaches the Earth. That's EQUIVALENT to the Earth accelerating in space-time.
Is it my theory? I don't think so, "I personally believe" it was what Einstein meant when he said gravity and acceleration are equivalent.
Is it supported by testable proof. Yes, the accelerometer and time dilation measurements as mentioned. The accelerometer shows that the Earth is accelerating in space-time. The Earths diameter is not getting any larger as it accelerates therefore it cannot be accelerating in the three dimensions of space, it can only accelerate in the time dimension of space-time. The difference in clock times shows that time is relative and passes more slowly near to the surface of the Earth as predicted by GR.
If we put an atomic clock on a rocket and send it into space. The clock will not only accelerate in the space aspect of space-time but in the time aspect of space-time. (As a second becomes progressively shorter[in comparison to a second on the Earth], the ship covers the same distance in less time from the occupants perspective.) The Earth essentially does the same but just in the time aspect of space-time. Again it is a local effect.
If this isn't the explanation of what Einstein meant when he said that gravity and acceleration are equivalent then what other explanation is there?
Mass can be evaluated quite easily without any gravitational field by measuring acceleration. Weight is the measurement of the interaction between mass and gravity.
Gravitational acceleration has not the slightest thing to do with the mass of an object because the acceleration is completely independent of the mass.
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Mass can be evaluated quite easily without any gravitational field by measuring acceleration. Weight is the measurement of the interaction between mass and gravity.
Gravitational acceleration has not the slightest thing to do with the mass of an object because the acceleration is completely independent of the mass.
Mass creates its own gravitational field therefore you can’t have mass without a gravitational field. So you can’t measure mass without a gravitational field because a gravitational field is associated with mass. Likewise, you can’t have acceleration without gravity because they are equivalent, although in the case of a small mass the gravitational component is not so obvious until the acceleration is approaching the speed of light.
This is true but what is your point?
“In science and engineering, the weight of an object is the force on the object due to gravity. Its magnitude (a scalar quantity), often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g; thus: W = mg.”
http://en.wikipedia.org/wiki/Weight
added 06 June
As I see it, a weighing machine measures weight because it is in a non-inertial reference frame, that is, it is in an accelerating reference frame. As the acceleration of that reference frame is constant, so is the measure of weight. Therefore, a non-inertial reference frame (accelerating) is required to be able to measure weight.
end of edit
This is only true when considering an object in free fall in a gravitational field. It’s not true for the mass (Earth) that is generating that gravitational field. See reply #12 in this thread.
Gravitational acceleration of the Earth (gravity) or any other massive gravitating body is entirely dependent upon mass, as it is mass that bends space-time. (Assuming velocity to be insignificant)
I am talking about the acceleration due to gravity of a massive object like the Earth, not acceleration of an object in free fall.
Where Einstein said that energy and mass are equivalent he meant equivalent not exactly the same. You can make things from mass (matter) but you need energy to do it. Although equivalent, they are not the same. When he said that gravity and acceleration are equivalent, I believe he meant they are the same thing, identical.
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I am talking about the acceleration due to gravity of a massive object like the Earth, not acceleration of an object in free fall.
It makes no difference. A massive object like the Earth is in free-fall as it orbits the Sun.
Anyway, as I said earlier, a gravitational field won't allow you to evaluate mass. It will only allow you to evaluate weight. You can infer the mass from the weight if you know the acceleration produced by the gravitational field, but that has nothing to do with the weight.
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I am talking about the acceleration due to gravity of a massive object like the Earth, not acceleration of an object in free fall.
It makes no difference. A massive object like the Earth is in free-fall as it orbits the Sun.
Anyway, as I said earlier, a gravitational field won't allow you to evaluate mass. It will only allow you to evaluate weight. You can infer the mass from the weight if you know the acceleration produced by the gravitational field, but that has nothing to do with the weight.
That's true but it is still not the same as the gravitational acceleration produced by mass. An accelerometer in free fall does not register acceleration, an accelerometer on the surface of the Earth does. It's the reference frame that is different.
You say that a gravitational field wont allow you to evaluate mass but then you go on to explain how a gravitational field can be used to evaluate mass?
We seem to be at cross purposes here. You keep mentioning weight and I am not quite sure why. You need a non-inertial reference frame (accelerating) to be able to measure weight or mass. The non-inertial reference frame needed to evaluate weight is due to the gravity (acceleration) of the surface of the Earth. To evaluate mass in a low gravity environment still requires acceleration (which is equivalent to gravity). Both require a non-inertial reference frame. A 1kg mass weighs 1kg on the Earths surface as the Earths surface is accelerating at 1g. The same mass accelerating at 1g in low gravity (far away from the Earths surface) still weighs 1kg. That is due to gravity and acceleration being equivalent.
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It makes no difference. A massive object like the Earth is in free-fall as it orbits the Sun.
Anyway, as I said earlier, a gravitational field won't allow you to evaluate mass. It will only allow you to evaluate weight. You can infer the mass from the weight if you know the acceleration produced by the gravitational field, but that has nothing to do with the weight.
Nice response Geezer!!
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The same mass accelerating at 1g in low gravity (far away from the Earths surface) still weighs 1kg. That is due to gravity and acceleration being equivalent.
Right - which proves that mass and gravity are independent.
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The same mass accelerating at 1g in low gravity (far away from the Earths surface) still weighs 1kg. That is due to gravity and acceleration being equivalent.
Right - which proves that mass and gravity are independent.
Could you explain the logic of that please?
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The same mass accelerating at 1g in low gravity (far away from the Earths surface) still weighs 1kg. That is due to gravity and acceleration being equivalent.
Right - which proves that mass and gravity are independent.
Could you explain the logic of that please?
You can accelerate a mass without any gravitational field by using, for example, a chemical energy source. A rocket would work.
The point is that mass could care less about gravity. Mass remains with, or without, gravity.
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The same mass accelerating at 1g in low gravity (far away from the Earths surface) still weighs 1kg. That is due to gravity and acceleration being equivalent.
Right - which proves that mass and gravity are independent.
Could you explain the logic of that please?
You can accelerate a mass without any gravitational field by using, for example, a chemical energy source. A rocket would work.
The point is that mass could care less about gravity. Mass remains with, or without, gravity.
You can't have mass without a gravitational 'field' but apart from that, this is true and I never said otherwise but it is missing my point, which was acceleration and gravity are equivalent.
That’s not strictly speaking correct. Mass warps space-time. That interaction is what we call gravity and it involves time-dilation. You can’t have mass without gravity. If you try to accelerate mass in a gravitational field (other than its own), it certainly "cares" as evidenced by the variable amounts of energy required to change velocity (in the sense of direction).
That mass remains is almost certainly true (and I have never said otherwise), or it would cause problems for the conservation of mass/energy but that is not what we have been debating. The question was “Do we need acceleration to define the concept of mass?" Whether or not mass remains (and it almost certainly does), it still requires acceleration by way of a non-inertial reference frame to evaluate it. That is, we can weigh it or use an accelerometer.
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which was acceleration and gravity are equivalent.
Who cares! It doesn't help answer the question.
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which was acceleration and gravity are equivalent.
Who cares! It doesn't help answer the question.
Well I do and Einstein did.
Yes it does.
The question was “Do we need acceleration to define the concept of mass?" "... it still requires acceleration by way of a non-inertial reference frame to evaluate it. That is, we can weigh it or use an accelerometer.
Unless you know differently of course.
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Yes it does.
Other than the fact that you assert that it does, why does it help answer the question?
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Yes it does.
Other than the fact that you assert that it does, why does it help answer the question?
The question was “Do we need acceleration to define the concept of mass?" My answer was "... it still requires acceleration by way of a non-inertial reference frame to evaluate it. That is, we can weigh it or use an accelerometer."
"For example imagine a big rock floating in space. Give it a slap with a calibrated hand so you know exactly how much energy you gave it. Now measure how fast the rock is moving."
http://education.jlab.org/qa/mass_01.html
That's one way of measuring the mass and it involved acceleration of the mass.
"There are a couple of ways to measure mass. The most common method is to use a balance." " If you go to a different planet, the balance weights change by the same factor as the object you are measuring. Your mass measured with a balance would be the same on the moon as it is on Earth."
http://education.jlab.org/qa/mass_01.html
This way of measuring mass relies upon comparing a known mass with an unknown mass in a non-inertial (accelerating) reference frame.
A spring balance can also measure mass but strictly speaking only measures weight. The weight on the Moon would be 1/6 that of Earth although the mass remains the same. Again it relies upon a non-inertial reference frame.
To the best of my knowledge that is self evident. I don't know of any other way of evaluating or measuring mass and if you can't measure it you can't fully define it. In that way I believe it does help to answer the question.
Does anyone know of any way of measuring mass that does not rely upon acceleration?
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1. Put super-critical lump of mixed radioactive Pu and U in large water pool - measure rise in temperature - do maths - get mass lost.
2. measure energy of photons given off by matter/anti-matter annihilation - do maths - get mass of pair
3. measure volume of ideal gas at stp - do maths - get mass
4. count atoms - do maths - get mass (ok that one is silly)
5. take complex hydrocarbon - burn to buggery - do maths - know mass of result (without measuring energy given off)
(and I know BC or JP will haul me over the coals for the liberties I have taken in the above)
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1. Put super-critical lump of mixed radioactive Pu and U in large water pool - measure rise in temperature - do maths - get mass lost.
There you go!
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The Pound-Force was defined in the context of the force/acceleration due to Earth's gravity - which is a problem as the acceleration due to gravity varies slightly at different points on the earth's surface.
There is an interesting article at: http://spectrum.ieee.org/consumer-electronics/standards/the-kilogram-reinvented/0
Summary: At present, the definition of mass in the metric system is a specific lump of metal in Paris. (ie it is not a weight, so it is already independent of the acceleration due to Earth's gravity.)
However, there is currently a project underway to define mass more reproducibly in terms of:
(i) Avogadro's Number: A specific number of atoms of a particular isotope of Silicon
(ii) The Ampere: The force exerted by a certain electric current (which again might be viewed as the cause of an acceleration, from a certain viewpoint)
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it still requires acceleration by way of a non-inertial reference frame to evaluate it. That is, we can weigh it or use an accelerometer.
No - that won't work.
If you weigh an object in a gravitational field using the deflection of a spring (as in a bathroom scale or an accelerometer), you cannot properly evaluate the mass because you are only measuring the deflection of a spring, and the deflection will vary according to the intensity of the gravitational field.
If you weigh an object using a comparison with another mass (as in a beam balance) you are using an arbitrary object for comparison, but that's not getting you any closer to "the concept of mass".
On the other hand, if you apply a quantity of energy to an object so that its momentum changes, you can get some idea of the relationship between mass and energy.
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it still requires acceleration by way of a non-inertial reference frame to evaluate it. That is, we can weigh it or use an accelerometer.
No - that won't work.
If you weigh an object in a gravitational field using the deflection of a spring (as in a bathroom scale or an accelerometer), you cannot properly evaluate the mass because you are only measuring the deflection of a spring, and the deflection will vary according to the intensity of the gravitational field.
If you weigh an object using a comparison with another mass (as in a beam balance) you are using an arbitrary object for comparison, but that's not getting you any closer to "the concept of mass".
On the other hand, if you apply a quantity of energy to an object so that its momentum changes, you can get some idea of the relationship between mass and energy.
I have already explained above how that can be used to measure mass.
It's not arbitrary as it is comparing an unknown mass with a known mass.
All three cases involve acceleration and acceleration costs energy. In the case of the spring and triple balance the energy comes from gravitational potential energy. It makes little difference where the energy comes from it still causes acceleration and gives "some idea of the relationship between mass and energy".
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1. Put super-critical lump of mixed radioactive Pu and U in large water pool - measure rise in temperature - do maths - get mass lost.
2. measure energy of photons given off by matter/anti-matter annihilation - do maths - get mass of pair
3. measure volume of ideal gas at stp - do maths - get mass
4. count atoms - do maths - get mass (ok that one is silly)
5. take complex hydrocarbon - burn to buggery - do maths - know mass of result (without measuring energy given off)
(and I know BC or JP will haul me over the coals for the liberties I have taken in the above)
imatfaal
Thanks for the input. I will try to address all of your points.
1) I need to consider some more.
5) How do you know the starting and final mass without weighing it? (Without using a non-inertial reference frame)
1) The increase in heat of the water is equivalent to the loss of mass. So presumably you are referring to the equivalence principle E=mc2. The 2 in c2 represents acceleration.
2) The energy produced is unknown until it is measured which involves obliterating the photons making them give up their energy as momentum and re-radiating some photons at a lower energy level. The increase in momentum of the target is acceleration.
3) Presumably this relies upon knowing initially both the volume and mass of 1 molecule.
Knowing the mass of 1 molecule relies upon counting the total number of protons and neutrons and knowing the weight of a proton.
“Because atoms are exceptionally small, scientists typically work with atoms in larger quantities called moles. A mole is the amount of a substance with as many atoms as there would be in 12 grams of the isotope carbon-12. This number is roughly 600 sextillion (6 times 10 to the 23rd power) atoms, and is known as Avogadro's number for the scientist who defined it.”
http://www.wikihow.com/Calculate-Atomic-Mass
This method of calculating the mass depends upon initially knowing the atomic weight of one molecule and that requires ‘weighing’ it. Weighing it requires a non-inertial (accelerating) reference frame. It’s a calculation based upon a measurement taken in an accelerating reference frame.
4) Is essentially the same answer as 3 but substituting atom for molecule.
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It's not arbitrary as it is comparing an unknown mass with a known mass.
All three cases involve acceleration and acceleration costs energy. In the case of the spring and triple balance the energy comes from gravitational potential energy. It makes little difference where the energy comes from it still causes acceleration and gives "some idea of the relationship between mass and energy".
As Evan points out, the known mass is completely arbitrary, so the compared mass is also completely arbitrary. Consequently, any form of balance isn't really telling you anything about the mass.
If you use a spring type scale, or an accelerometer, you are determining weight, not mass. You could use a "known mass" to determine the intensity of a gravitational field by this method then do a comparison to determine the relative mass of another object, but then you are back to only establishing a comparitive arbitrary mass.
On the other hand, if you actually alter the momentum of an object, there are methods of directly quantifying the energy conversion.
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It's not arbitrary as it is comparing an unknown mass with a known mass.
All three cases involve acceleration and acceleration costs energy. In the case of the spring and triple balance the energy comes from gravitational potential energy. It makes little difference where the energy comes from it still causes acceleration and gives "some idea of the relationship between mass and energy".
As Evan points out, the known mass is completely arbitrary, so the compared mass is also completely arbitrary. Consequently, any form of balance isn't really telling you anything about the mass.
If you use a spring type scale, or an accelerometer, you are determining weight, not mass. You could use a "known mass" to determine the intensity of a gravitational field by this method then do a comparison to determine the relative mass of another object, but then you are back to only establishing a comparitive arbitrary mass.
On the other hand, if you actually alter the momentum of an object, there are methods of directly quantifying the energy conversion.
I agree it does not tell you anything about mass itself but it is not really arbitrary if you do the comparison with a known mass. Anyway that argument is beside the point.
The question was “Do we need acceleration to define the concept of mass?"
How do you propose to "alter the momentum of an object" without accelerating it?
If you accept that it accelerates then presumably you accept that you "Do .. need acceleration to define the concept of mass?" Which is what I said in the first place and repeated in post #40 of this thread.
"For example imagine a big rock floating in space. Give it a slap with a calibrated hand so you know exactly how much energy you gave it. Now measure how fast the rock is moving."
http://education.jlab.org/qa/mass_01.html
"That's one way of measuring the mass and it involved acceleration of the mass."
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If you use a spring type scale, or an accelerometer, you are determining weight, not mass. You could use a "known mass" to determine the intensity of a gravitational field by this method then do a comparison to determine the relative mass of another object, but then you are back to only establishing a comparitive arbitrary mass.
The acceleration of the Earths surface and hence the scale applies acceleration and hence change of momentum to the mass. (The Earth pushes the scale. The scale pushes the mass. This results in a change of momentum for the mass. This is acceleration)
A tripple balance compares an unknown mass with a known mass and the difference in gravity (acceleration) on different planets is compensated for by affecting both the known and unknown mass in the same proportion. The mass remains the same but the weight changes.
Whether you apply acceleration to the mass by the Earth pushing it or anything else pushing it, its the same thing, acceleration.
There is no difference between accelerating a mass by applying a force to it and the Earth accelerating the same mass by applying a pseudo-force to it (gravity). They are equivalent.
There is no difference in measuring a force applied to a mass and the distance it travels than measuring the pseudo-force the Earth applies to the same mass and the distance it travels.
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1) The increase in heat of the water is equivalent to the loss of mass. So presumably you are referring to the equivalence principle E=mc2. The 2 in c2 represents acceleration.
velocity squared DNE acceleration
2) The energy produced is unknown until it is measured which involves obliterating the photons making them give up their energy as momentum and re-radiating some photons at a lower energy level. The increase in momentum of the target is acceleration.
E = h.nu
3) Presumably this relies upon knowing initially both the volume and mass of 1 molecule.
Knowing the mass of 1 molecule relies upon counting the total number of protons and neutrons and knowing the weight of a proton.
“Because atoms are exceptionally small, scientists typically work with atoms in larger quantities called moles. A mole is the amount of a substance with as many atoms as there would be in 12 grams of the isotope carbon-12. This number is roughly 600 sextillion (6 times 10 to the 23rd power) atoms, and is known as Avogadro's number for the scientist who defined it.”
http://www.wikihow.com/Calculate-Atomic-Mass
This method of calculating the mass depends upon initially knowing the atomic weight of one molecule and that requires ‘weighing’ it. Weighing it requires a non-inertial (accelerating) reference frame. It’s a calculation based upon a measurement taken in an accelerating reference frame.
volume of molecule no need to know. mass of molecule is calculable as well as measurable
4) Is essentially the same answer as 3 but substituting atom for molecule.
i never mentioned molecule btw. And three is easily done - whereas 4 is v difficult
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It's not arbitrary as it is comparing an unknown mass with a known mass.
All three cases involve acceleration and acceleration costs energy. In the case of the spring and triple balance the energy comes from gravitational potential energy. It makes little difference where the energy comes from it still causes acceleration and gives "some idea of the relationship between mass and energy".
As Evan points out, the known mass is completely arbitrary, so the compared mass is also completely arbitrary. Consequently, any form of balance isn't really telling you anything about the mass.
If you use a spring type scale, or an accelerometer, you are determining weight, not mass. You could use a "known mass" to determine the intensity of a gravitational field by this method then do a comparison to determine the relative mass of another object, but then you are back to only establishing a comparitive arbitrary mass.
On the other hand, if you actually alter the momentum of an object, there are methods of directly quantifying the energy conversion.
I agree it does not tell you anything about mass itself but it is not really arbitrary if you do the comparison with a known mass. Anyway that argument is beside the point.
The question was “Do we need acceleration to define the concept of mass?"
How do you propose to "alter the momentum of an object" without accelerating it?
If you accept that it accelerates then presumably you accept that you "Do .. need acceleration to define the concept of mass?" Which is what I said in the first place and repeated in post #40 of this thread.
"For example imagine a big rock floating in space. Give it a slap with a calibrated hand so you know exactly how much energy you gave it. Now measure how fast the rock is moving."
http://education.jlab.org/qa/mass_01.html (http://education.jlab.org/qa/mass_01.html)
"That's one way of measuring the mass and it involved acceleration of the mass."
Actually, that's what I've saying all along. Please refer to Reply #2 on this thread.
My original objection was to your statement about "acceleration in space-time" which is completely irrelevant. You then you introduced "gravitational acceleration" which I have repeatedly demonstrated will only let you weigh an object, or at best, compare the relative masses of two objects.
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The Earth pushes the scale. The scale pushes the mass. This results in a change of momentum for the mass. This is acceleration.
Sorry, but that's not right either. The only change in momentum is caused by the rotation of the Earth and the rotation of the object, and the amount of the change is very small.
A tripple balance compares an unknown mass with a known mass and the difference in gravity (acceleration) on different planets is compensated for by affecting both the known and unknown mass in the same proportion. The mass remains the same but the weight changes.
Yes, mass is constant, but you are ignoring the fact that gravity on Earth is not constant, so the weight of an object on Earth varies with location.
Whether you apply acceleration to the mass by the Earth pushing it or anything else pushing it, its the same thing, acceleration.
Pushing is NOT the same as acceleration. Acceleration requires a change in velocity. In Classical Mechanics, gravity produces an accelerative force that acts on all matter, but there is only acceleration with change in velocity, hence a change in momentum.
There is no difference between accelerating a mass by applying a force to it and the Earth accelerating the same mass by applying a pseudo-force to it (gravity). They are equivalent.
But the object is not accelerating. Your argument only applies if you allow the object to free-fall, but then you will find that all objects accelerate at the same rate regardless of their mass. Treating gravity as a pseudo-force only works if you apply General Relativity. That means you have to analyze the entire problem using General Relativity.
There is no difference in measuring a force applied to a mass and the distance it travels than measuring the pseudo-force the Earth applies to the same mass and the distance it travels.
Except that you don't know what the gravitational force actually is, and there isn't any "travel".
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The Earth pushes the scale. The scale pushes the mass. This results in a change of momentum for the mass. This is acceleration.
Sorry, but that's not right either. The only change in momentum is caused by the rotation of the Earth and the rotation of the object, and the amount of the change is very small.
A tripple balance compares an unknown mass with a known mass and the difference in gravity (acceleration) on different planets is compensated for by affecting both the known and unknown mass in the same proportion. The mass remains the same but the weight changes.
Yes, mass is constant, but you are ignoring the fact that gravity on Earth is not constant, so the weight of an object on Earth varies with location.
Whether you apply acceleration to the mass by the Earth pushing it or anything else pushing it, its the same thing, acceleration.
Pushing is NOT the same as acceleration. Acceleration requires a change in velocity. In Classical Mechanics, gravity produces an accelerative force that acts on all matter, but there is only acceleration with change in velocity, hence a change in momentum.
There is no difference between accelerating a mass by applying a force to it and the Earth accelerating the same mass by applying a pseudo-force to it (gravity). They are equivalent.
But the object is not accelerating. Your argument only applies if you allow the object to free-fall, but then you will find that all objects accelerate at the same rate regardless of their mass. Treating gravity as a pseudo-force only works if you apply General Relativity. That means you have to analyze the entire problem using General Relativity.
There is no difference in measuring a force applied to a mass and the distance it travels than measuring the pseudo-force the Earth applies to the same mass and the distance it travels.
Except that you don't know what the gravitational force actually is, and there isn't any "travel".
That's not true. According to Einstein, gravity and acceleration are equivalent. It is the acceleration of the Earth that endows us with weight.
True but irrelevant to the discussion.
It is when talking about the acceleration of a massive body like the Earth. A steady push is the steady application of energy. The steady application of energy (as in a rocket for example) causes a steady acceleration. A 'push' changes the velocity of the object. That change in velocity is acceleration.
If you choose to ignore General Relativity then there is little point in discussing gravity.
We do know what the acceleration is it's 1 g. There must be travel as the Earth is travelling through space-time. Because we do not understand how to take the measurements does not make it any the less true.
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It is when talking about the acceleration of a massive body like the Earth. A steady push is the steady application of energy. The steady application of energy (as in a rocket for example) causes a steady acceleration. A 'push' changes the velocity of the object. That change in velocity is acceleration.
We do know what the acceleration is it's 1 g. There must be travel as the Earth is travelling through space-time. Because we do not understand how to take the measurements does not make it any the less true.
Mike, if you are going to argue using GR, I strongly suggest you study Classical Mechanics and basic Thermodynamics first. What you are suggesting here is that there is a continuous transfer of energy from the Earth to your backside when you are sitting in a chair. That is patently ridiculous. There is no change in energy of the Earth, you, or the chair, and even String Theory won't support the idea that there is.
Standard Gravity on Earth is an approximation. It is not constant with location which is why weight varies depending on where you are on the Earth.
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Mike - if you continue to promulgate your personal ideas of gravity/time/light etc in the main forums you will be suspended or banned. Please do not continue this line of argument or theory anywhere other than in the New Theories. Whilst we appreciate your enthusiasm we cannot tolerate the continued stream of mis-information and misguided posts; the next post in the main fora that you make that argues non-mainstream physics will lead to sanctions.
imatfaal \ moderator
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Dude! :)
Velocity and acceleration are interrelated... acceleration is nothing but the rate of change of velocity.. i.e., a=dv/dt
and also i would say, when an object's velocity or acceleration increases, thus the mass of the object indeed increases! ;)
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mass is only a function of speed (magnitude of velocity), not of acceleration.
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1) The increase in heat of the water is equivalent to the loss of mass. So presumably you are referring to the equivalence principle E=mc2. The 2 in c2 represents acceleration.
velocity squared DNE acceleration
2) The energy produced is unknown until it is measured which involves obliterating the photons making them give up their energy as momentum and re-radiating some photons at a lower energy level. The increase in momentum of the target is acceleration.
E = h.nu
3) Presumably this relies upon knowing initially both the volume and mass of 1 molecule.
Knowing the mass of 1 molecule relies upon counting the total number of protons and neutrons and knowing the weight of a proton.
“Because atoms are exceptionally small, scientists typically work with atoms in larger quantities called moles. A mole is the amount of a substance with as many atoms as there would be in 12 grams of the isotope carbon-12. This number is roughly 600 sextillion (6 times 10 to the 23rd power) atoms, and is known as Avogadro's number for the scientist who defined it.”
http://www.wikihow.com/Calculate-Atomic-Mass
This method of calculating the mass depends upon initially knowing the atomic weight of one molecule and that requires ‘weighing’ it. Weighing it requires a non-inertial (accelerating) reference frame. It’s a calculation based upon a measurement taken in an accelerating reference frame.
volume of molecule no need to know. mass of molecule is calculable as well as measurable
4) Is essentially the same answer as 3 but substituting atom for molecule.
i never mentioned molecule btw. And three is easily done - whereas 4 is v difficult
What does that mean?
To know the frequency or wavelength involves obliterating the photon which gives up its momentum by transferring it to something else. That transfer involves a change in velocity which is acceleration.
How do you calculate it without first knowing the weight of either one molecule or constituent parts? Weighing involves using a non-inertial (accelerating) reference frame.
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It is when talking about the acceleration of a massive body like the Earth. A steady push is the steady application of energy. The steady application of energy (as in a rocket for example) causes a steady acceleration. A 'push' changes the velocity of the object. That change in velocity is acceleration.
We do know what the acceleration is it's 1 g. There must be travel as the Earth is travelling through space-time. Because we do not understand how to take the measurements does not make it any the less true.
Mike, if you are going to argue using GR, I strongly suggest you study Classical Mechanics and basic Thermodynamics first. What you are suggesting here is that there is a continuous transfer of energy from the Earth to your backside when you are sitting in a chair. That is patently ridiculous. There is no change in energy of the Earth, you, or the chair, and even String Theory won't support the idea that there is.
Standard Gravity on Earth is an approximation. It is not constant with location which is why weight varies depending on where you are on the Earth.
Is it ridiculous? Let me see if I understand you correctly. What you are saying is if You are sitting in a chair in a rocket accelerating at one g and approaching the speed of light you will not have gained mass?
My point was a push causes a change in velocity which involves acceleration.
It costs the Earth nothing extra to accelerate anything on its surface (other than maybe meteorites) as everything is part of the Earths mass.
Whether or not the Earths acceleration in space-time (gravity) involves the expenditure or energy we simply do not know. We do know that the Earth warps or bends space-time locally. Maybe the Earth extracts energy from that. I am not postulating that it does, I am simply saying it remains a possibility until proven otherwise.
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mass is only a function of speed (magnitude of velocity), not of acceleration.
How does that relate to
quote lightarrow
Reply #2 on: 24/05/2012 21:52:40
Quote
"The best way is to consider the object...still
An oject's mass is its energy (divided c2) when the object is still."
and
The question was not about what mass is a function of but "Do we need acceleration to define the concept of mass?"
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Going back to basics and the original question
Do we need acceleration to define the concept of mass?
"The kilogram or kilogramme (SI symbol: kg), also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram (IPK), which is almost exactly equal to the mass of one liter of water."
The IPK is made of a platinum–iridium alloy and is stored in a vault at the International Bureau of Weights and Measures in Sèvres, France. It is known as Le Grand K.
http://en.wikipedia.org/wiki/Kilogram
The kilogram is by definition what the IPK weighs and is not a constant in the sense that the speed of light is a constant.
Weight
From Wikipedia, the free encyclopedia
"A spring scale measures the weight of an object (according to the operational definition)
In science and engineering, the weight of an object is the force on the object due to gravity.[2][3] Its magnitude (a scalar quantity), often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g;[4] thus: W = mg. When considered a vector, weight is often denoted by a bold letter W. The unit of measurement for weight is that of force, which in the International System of Units (SI) is the newton. For example, an object with a mass of one kilogram has a weight of about 9.8 newtons on the surface of the Earth, about one-sixth as much on the Moon, and very nearly zero when in deep space far away from all bodies imparting gravitational influence."
http://en.wikipedia.org/wiki/Weight
The Newton
"Definition
The newton is the SI unit for force; it is equal to the amount of net force required to accelerate a mass of one kilogram at a rate of one metre per second squared. Newton's second law of motion states: F = ma, multiplying m (kg) by a (m/s2), The newton is therefore:[1]
N=kg x m/s2
Units used:
N = newton
kg = kilogram
m = metre
s = second
http://en.wikipedia.org/wiki/Newton_(unit)
“Le Grand K has been losing weight — or, by the definition of mass under the metric system, the rest of the universe has been getting fatter. The most recent comparison, in 1988, found a discrepancy as large as five-hundredths of a milligram, a bit less than the weight of a dust speck, between Le Grand K and its official underlings.
This state of affairs is intolerable to the guardians of weights and measures. “Something must be done,” says Terry Quinn, director emeritus of the International Bureau of Weights and Measures, the governing body of the metric system. Since the early 1990s, Quinn has campaigned to redefine the kilogram based not on a physical prototype but on a constant of nature, something hardwired into the circuitry of the universe. In fact, of the seven fundamental metric units — the kilogram, meter, second, ampere, kelvin, mole, and candela — only the kilogram is still dependent on a physical artifact. (The meter, for example, was redefined 30 years ago as the distance traveled by light in a given fraction of a second.)”
http://www.wired.com/magazine/2011/09/ff_kilogram/all/1
What is the point of the above? The point is the "The kilogram or kilogramme (SI symbol: kg), also known as the kilo, is the base unit of mass in the International System of Units” is defined by measuring its acceleration (weighing it). “Its magnitude (a scalar quantity), often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g;[4] thus: W = mg.” “ The unit of measurement for weight is that of force, which in the International System of Units (SI) is the newton.” “The newton is the SI unit for force; it is equal to the amount of net force required to accelerate a mass of one kilogram at a rate of one metre per second squared.” “In science and engineering, the weight of an object is the force on the object due to gravity.[2][3] Its magnitude (a scalar quantity), often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g;[4] thus: W = mg.” So, going back to the original question “Do we need acceleration to define the concept of mass?” From the above it is obvious that we do.
As Le Grand K has been loosing weight in comparison to the rest of the Universe it is necessary to find a way of defining mass by using some constant of nature as opposed to using an artifact. “So two decades ago, as Quinn’s campaign to switch the kilo to a physical constant began to gain traction, Becker and his colleagues decided to tackle the problem from the opposite direction. Building upon their earlier work, they decided to create a 1-kilogram sphere, not from hydrogen, but from silicon. The sphere would be identical in mass to the international prototype. Then, because Becker’s x-ray experiments had shown that the atoms were arranged in a regular pattern, they could use basic geometry to deduce how many silicon atoms the crystalline sphere contained. Once the number of atoms was determined with sufficient precision, that figure would forever define the mass of the kilogram. In other words, they set out to make a new artifact superior to Le Grand K — but only so that they could count its atoms and then eliminate all kilogram artifacts in perpetuity.”
The other approach is to use an apparatus called a watt balance, which compares electrical and mechanical power. “On the upper floor is a room-sized scale dominated by a wheel fabricated of milled aluminum. Below the wheel is a hand-sized pan supporting a platinum-iridium mass positioned like an apple on a produce scale. One floor below, superconducting electromagnets counteract the downward tug of the platinum-iridium. In other words, the gravitational force on the mass is balanced with the electrical force produced by current in the copper coil. Once calibrated against the international prototype, the electronic kilogram can be defined in terms of the voltage required to levitate Le Grand K — a numerical value, governed by a natural constant, that can be used to calibrate any future watt balance — and the international prototype can at last be sent into retirement.”
http://www.wired.com/magazine/2011/09/ff_kilogram/all/1
Both of the above alternatives of defining a kg of mass require weighing the object. In the first case knowing the weight of a silicon atom and counting (calculating) the number of atoms. In the second case weighing the object by knowing the amount of energy required to levitate it. Both scenarios require weighing the object and that requires the use of a non-inertial (accelerating) reference frame.
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Whether or not the Earths acceleration in space-time (gravity) involves the expenditure or energy we simply do not know. We do know that the Earth warps or bends space-time locally. Maybe the Earth extracts energy from that. I am not postulating that it does, I am simply saying it remains a possibility until proven otherwise.
Whether or not you're postulating your new theories or just stating them while not postulating them, I am postulating that you're banned for ignoring repeated moderator warnings to stop posting new theories in the mainstream fora.
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How does that relate to
quote lightarrow
Reply #2 on: 24/05/2012 21:52:40
Quote
"The best way is to consider the object...still
An oject's mass is its energy (divided c2) when the object is still."
and
The question was not about what mass is a function of but "Do we need acceleration to define the concept of mass?"
Lightarrows comment works under certain situations. Under certain situations it fails, such as when a macroscopic body is under stress.
The inertia mass for a free point particle moving at speed v is
m = m_0/sqrt(1-(v/c)^2)
Notice that it depends only on v, not a = dv/dt. The acceleration could be arbitrarily high but if v = 0 m = m_0.