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Author Topic: Do we need acceleration to define the concept of mass?  (Read 15951 times)

flr

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Do we need acceleration to define the concept of mass?
« on: 24/05/2012 20:44:36 »
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?

« Last Edit: 29/05/2012 18:57:52 by Geezer »

Geezer

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Re: Do we need acceleration de define the concept of mass?
« Reply #1 on: 24/05/2012 20:59:05 »
Its only by changing momentum that you can evaluate mass, and that means the velocity changed, so there had to be acceleration - I think :)

lightarrow

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Re: Do we need acceleration de define the concept of mass?
« Reply #2 on: 24/05/2012 22:52:40 »
The best way is to consider the object...still
An oject's mass is its energy (divided c2) when the object is still.

Pmb

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Re: Do we need acceleration de define the concept of mass?
« Reply #3 on: 24/05/2012 23:34:46 »
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

flr

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Re: Do we need acceleration de define the concept of mass?
« Reply #4 on: 25/05/2012 05:19:24 »
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".

MikeS

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Re: Do we need acceleration de define the concept of mass?
« Reply #5 on: 25/05/2012 08:01:05 »
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.
« Last Edit: 26/05/2012 09:50:42 by MikeS »

Phractality

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Re: Do we need acceleration de define the concept of mass?
« Reply #6 on: 25/05/2012 18:59:56 »
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.

Pmb

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Re: Do we need acceleration de define the concept of mass?
« Reply #7 on: 25/05/2012 21:34:58 »
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.
« Last Edit: 25/05/2012 23:50:18 by Pmb »

lightarrow

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Re: Do we need acceleration de define the concept of mass?
« Reply #8 on: 25/05/2012 21:44:29 »
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 heating it, then you weigh it again: 1 + E/c2 kg.

You don't need to move or to accelerate the object...
« Last Edit: 26/05/2012 19:40:01 by lightarrow »

MikeS

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Re: Do we need acceleration de define the concept of mass?
« Reply #9 on: 26/05/2012 08:50:44 »
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.
« Last Edit: 26/05/2012 09:40:14 by MikeS »

Geezer

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Re: Do we need acceleration de define the concept of mass?
« Reply #10 on: 26/05/2012 17:45:46 »

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

Err, I don't think so. Perhaps you are confusing mass with weight?

lightarrow

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Re: Do we need acceleration de define the concept of mass?
« Reply #11 on: 26/05/2012 19:41:17 »
But anything that has mass IS accelerating in space-time.
In which sense?

MikeS

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Re: Do we need acceleration de define the concept of mass?
« Reply #12 on: 27/05/2012 06:22:41 »

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.
« Last Edit: 27/05/2012 06:53:20 by MikeS »

Geezer

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Re: Do we need acceleration de define the concept of mass?
« Reply #13 on: 27/05/2012 07:02:58 »
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.

Pmb

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Re: Do we need acceleration de define the concept of mass?
« Reply #14 on: 27/05/2012 12:23:32 »
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.

MikeS

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Re: Do we need acceleration de define the concept of mass?
« Reply #15 on: 27/05/2012 13:11:15 »
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.
« Last Edit: 27/05/2012 13:13:44 by MikeS »

MikeS

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Re: Do we need acceleration de define the concept of mass?
« Reply #16 on: 27/05/2012 13:51:17 »
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.

Geezer

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Re: Do we need acceleration de define the concept of mass?
« Reply #17 on: 27/05/2012 21:06:08 »

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?

MikeS

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Re: Do we need acceleration de define the concept of mass?
« Reply #18 on: 28/05/2012 12:48:27 »

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.
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.

« Last Edit: 29/05/2012 11:31:19 by MikeS »

MikeS

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Re: Do we need acceleration de define the concept of mass?
« Reply #19 on: 29/05/2012 11:06:10 »
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?

Geezer

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Re: Do we need acceleration de define the concept of mass?
« Reply #20 on: 29/05/2012 17:14:24 »

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.

MikeS

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Re: Do we need acceleration to define the concept of mass?
« Reply #21 on: 30/05/2012 09:52:04 »

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?

Geezer

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Re: Do we need acceleration to define the concept of mass?
« Reply #22 on: 30/05/2012 17:15:56 »

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?

MikeS

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Re: Do we need acceleration to define the concept of mass?
« Reply #23 on: 01/06/2012 16:23:51 »

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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Re: Do we need acceleration to define the concept of mass?
« Reply #24 on: 02/06/2012 01:59:04 »
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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Re: Do we need acceleration to define the concept of mass?
« Reply #24 on: 02/06/2012 01:59:04 »