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The concept of mass can be understood as the resistance of an object to change its constant velocity motion.

I use the term motion in the Newtonian sense, i.e. as This is obvious from the well known formula: F=ma

On the other hand mass can also be introduced via formula: p=mv

I am a bit confused: Can we actually understand mass without acceleration?

The best way is to consider the object...still []An oject's mass is its energy (divided c^{2}) when the object is still.

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=maOn the other hand mass can also be introduced via formula: p=mvwhere 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?

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.

Quote from: lightarrow on 24/05/2012 22:52:40The best way is to consider the object...still []An oject's mass is its energy (divided c^{2}) when the object is still."By "still" I guess you mean "proper frame".

The best way is to consider the object...still []An oject's mass is its energy (divided c^{2}) when the object is still."

Quote from: flr on 25/05/2012 05:19:24Quote from: lightarrow on 24/05/2012 22:52:40The best way is to consider the object...still []An oject's mass is its energy (divided c^{2}) 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 c^{2}). 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/c^{2} kg.You don't need to move or to accelerate the object...

But anything that has mass IS accelerating in space-time.

Quote from: MikeS on 26/05/2012 08:50:44But anything that has mass IS accelerating in space-time.Err, I don't think so. Perhaps you are confusing mass with weight?

Quote from: MikeS on 26/05/2012 08:50:44But anything that has mass IS accelerating in space-time.In which sense?

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.

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.

Quote from: MikeS on 27/05/2012 06:22:41But 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 ...sorry, you cannot view external links. To see them, please REGISTER or LOGINAnd there exist zero acceleration of any sense in a the word in flat spacetime in a uniform gravitational field.

Quote from: MikeS on 26/05/2012 08:50:44But 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?

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.

Quote from: MikeS on 29/05/2012 11:06:10Local 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 world line only points forward. The Earth at any instant is about to enter the next instant of time, not the last.

Quote from: MikeS on 30/05/2012 09:52:04The 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?

Quote from: Geezer on 30/05/2012 17:15:56Quote from: MikeS on 30/05/2012 09:52:04The 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?

Quote from: MikeS on 01/06/2012 16:23:51Quote from: Geezer on 30/05/2012 17:15:56Mass 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.”...sorry, you cannot view external links. To see them, please REGISTER or LOGIN_{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.

Quote from: Geezer on 30/05/2012 17:15:56Mass 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.”...sorry, you cannot view external links. To see them, please REGISTER or LOGIN_{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.

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.

I am talking about the acceleration due to gravity of a massive object like the Earth, not acceleration of an object in free fall.

Quote from: MikeS on 05/06/2012 10:24:31I 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.

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.

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.

Quote from: MikeS on 06/06/2012 10:54:23The 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.

Quote from: Geezer on 06/06/2012 19:07:33Quote from: MikeS on 06/06/2012 10:54:23The 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?

Quote from: MikeS on 06/06/2012 21:28:55Quote from: Geezer on 06/06/2012 19:07:33Quote from: MikeS on 06/06/2012 10:54:23The 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.

which was acceleration and gravity are equivalent.

Quote from: MikeS on 07/06/2012 13:53:03which was acceleration and gravity are equivalent.Who cares! It doesn't help answer the question.

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.

Yes it does.

Quote from: MikeS on 08/06/2012 12:56:10Yes it does. Other than the fact that you assert that it does, why does it help answer the question?

1. Put super-critical lump of mixed radioactive Pu and U in large water pool - measure rise in temperature - do maths - get mass lost.

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.

Quote from: MikeS on 09/06/2012 10:27:21it 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.

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 mass4. 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)

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".

Quote from: MikeS on 10/06/2012 11:38:07It'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.

Quote from: MikeS on 10/06/2012 11:38:07If 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.

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.