# The Naked Scientists Forum

### Author Topic: Can we measure with a balance the relativistic increase of mass with velocity?  (Read 9301 times)

#### flr

• Sr. Member
• Posts: 302
• Thanked: 2 times
##### Can we measure with a balance the relativistic increase of mass with velocity?
« on: 18/03/2013 19:53:29 »
Let's suppose I heat an object and measure its mass with very accurate balance.
As I heat is, the thermal motion of atoms increases.

Will the balance indicate an increase of the mass of the heated object, as the temperature increases?

-----

In other words. The energy that goes into the heated object is:
E=sqrt [ (pc)^2+(m_rest*c^2)^2 ] = m_relativistic*c^2

What will the balance measure: the m_rest or m_relativistic ?

« Last Edit: 18/03/2013 19:57:22 by flr »

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #1 on: 18/03/2013 20:34:58 »
Let's suppose I heat an object and measure its mass with very accurate balance.
As I heat is, the thermal motion of atoms increases.

Will the balance indicate an increase of the mass of the heated object, as the temperature increases?

-----

In other words. The energy that goes into the heated object is:
E=sqrt [ (pc)^2+(m_rest*c^2)^2 ] = m_relativistic*c^2

What will the balance measure: the m_rest or m_relativistic ?

(If I remember well, the correct term should be "scale").
If the object is stationary in the scale's frame of reference, it's simply mass (not relativistic mass) which increases.
You could say that it should be relativistic mass because the particles move. But the particles' masses don't vary, actually (their relativistic masses do); the system's mass, however, *is not* the sum of the masses of the particles (mass is not additive).
« Last Edit: 18/03/2013 20:38:57 by lightarrow »

#### flr

• Sr. Member
• Posts: 302
• Thanked: 2 times
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #2 on: 19/03/2013 04:16:40 »

Quote
If the object is stationary in the scale's frame of reference, it's simply mass (not relativistic mass) which increases.

The object is stationary relative to scale's frame.
The atoms making up the whole object can move due to thermal motion.

Will the scale indicate the same value at 200K and at 900K ?

Quote
the system's mass, however, *is not* the sum of the masses of the particles (mass is not additive).
This is counter-intuitive and I have 2 more questions:
2) is there a simple intuitive reason why masses are not additive?

#### yor_on

• Naked Science Forum GOD!
• Posts: 11652
• (Ah, yes:) *a table is always good to hide under*
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #3 on: 19/03/2013 18:49:34 »
The kinetic energy of the particles increase, and as energy is a equivalence to mass you should see the (locally measured, also being 'at rest' with what you measure) weight increasing. When it comes to relativistic mass I think I can see how you think, and myself I'm wondering what 'potential energy' means in a wider perspective, and if one can use that description too, to describe a relativistic mass?

Because a 'potential energy' is a energy, not found/measured locally, although existing when colliding two objects for example. A potential energy describes a relation, does a relativistic mass do the same? Or is there a circumstance in where I can measure it locally? It becomes a quagmire when you ask yourself how to define being 'at rest' relative scales. Also relative uniform motion. I prefer Plank scale for it, but? That's a ideal definition of a 'frame of reference' relative any other. And if you use that one, how would you define something as being 'at rest' with something else?
=

Thinking of it. You have 'gravity' of course. That's a real difference, but it doesn't answer what scale I should use to ideally define a 'frame of reference' relative another. Or maybe it does?
=

Like this :)
At what scale do a gravity cease to exist for a mass, locally measured?
Does it ever?

ahem, back to your question ::))
*Sorry.
« Last Edit: 19/03/2013 19:04:35 by yor_on »

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #4 on: 19/03/2013 19:00:05 »
Quote
If the object is stationary in the scale's frame of reference, it's simply mass (not relativistic mass) which increases.
The object is stationary relative to scale's frame.
The atoms making up the whole object can move due to thermal motion.
If the object (centre of mass) is stationary with respect to the scale's frame, it doesn't matter if the atoms inside move or not: any increase in the object's energy will be measured as an increase in its mass (the one you call "rest" mass but it's simply called "mass"; if you want to compare it to relativistic mass, I prefer the term "invariant mass" instead of "rest mass", because, for example, photons don't have any frame of reference in which they are "at rest", but they however have an invariant mass).
Quote
Will the scale indicate the same value at 200K and at 900K ?
No, as I wrote, the scale will indicate a greater mass at 900 K
Quote

Quote
the system's mass, however, *is not* the sum of the masses of the particles (mass is not additive).
This is counter-intuitive and I have 2 more questions:
I wrote it. It's *not* additive.
Quote
2) is there a simple intuitive reason why masses are not additive?
Example: you have an electron and a proton in a stationary hydrogen atom at the fundamental level. You measure the atom's mass and you find the value Ma. Then you separate the electron from the proton, you measure the electron's mass when it's at rest and you find the value me, the same with the proton and you find Mp, but Ma is not equal to Mp + me, because in the atom there is also the binding energy (in this context it's not important if this binding energy is positive or negative).

The total mass of the atom Ma is its total energy Ea divided c2: Ma = Ea/c2, but in the compute of its total energy Ea there are *not only* the rest energies of the masses me and Mp, there also is the binding energy.

Every time two particles (or bodies, or objects) A and B can form a bound state AB, the mass of the system AB is not equal to mass(A) + mass(B).

In chemistry these differences are actually very small and irrelevant; in nuclear and subatomic physics, not, because the binding energies are greater.

« Last Edit: 19/03/2013 19:18:04 by lightarrow »

#### yor_on

• Naked Science Forum GOD!
• Posts: 11652
• (Ah, yes:) *a table is always good to hide under*
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #5 on: 19/03/2013 19:46:54 »
You know Lightarrow, if I define mass (rest mass) as a property being invariant, intrinsically belonging to a rest mass, unchanging although I may change its frame of reference from where I, for example, measure its weight. Can I really state that I by heating it up change its rest mass? Also :) photons and rest mass? I think I know what you are referring to, but?

#### Pmb

• Neilep Level Member
• Posts: 1838
• Physicist
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #6 on: 19/03/2013 22:31:47 »
Quote from: flr
The object is stationary relative to scale's frame.
The atoms making up the whole object can move due to thermal motion.
The increase in energy will cause an increase in the rest mass of the body. If the body was moving then the weight of the body would be W = Mg where M = relativistic mass.

Now consider an air hockey table. First let the pucks be at rest and measure the weight of the table. Call that weight w = mg where m = intial rest mass of table. Now add energy to the table such that the energy goes into the kinetic energy of the now moving hockey pucks which we'll consider to be part of the table. The moving pucks weigh more than the same pucks at rest so that the entire weight of the table increases. The new weight will be W = Mg where M is the new mass of the table/hockey puck system. M > m.

#### simplified

• Sr. Member
• Posts: 428
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #7 on: 20/03/2013 09:36:57 »
Kinetic energy without counteraction doesn't create additional gravitation.

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #8 on: 20/03/2013 19:24:45 »
You know Lightarrow, if I define mass (rest mass) as a property being invariant, intrinsically belonging to a rest mass, unchanging although I may change its frame of reference from where I, for example, measure its weight. Can I really state that I by heating it up change its rest mass? Also :) photons and rest mass? I think I know what you are referring to, but?
What you can do is to prove that the quantity:

sqrt[(E/c2)2 - (p/c)2]

is invariant...

#### yor_on

• Naked Science Forum GOD!
• Posts: 11652
• (Ah, yes:) *a table is always good to hide under*
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #9 on: 21/03/2013 13:24:36 »
There is a time component to the definition of a invariant mass, to me that is. If it is invariant, it should be so under time too? It's not so much the question of if it really will weight more that confuse me, but how that time component are used.

Mass in special relativity uses this definition.

"The term mass in special relativity usually refers to the rest mass of the object, which is the Newtonian mass as measured by an observer moving along with the object. The invariant mass is another name for the rest mass of single particles. The more general invariant mass (calculated with a more complicated formula) loosely corresponds to the "rest mass" of a "system". Thus, invariant mass is a natural unit of mass used for systems which are being viewed from their center of momentum frame (COM frame), as when any closed system ..... (for example a bottle of hot gas) ...... is weighed, which requires that the measurement be taken in the center of momentum frame where the system has no net momentum. Under such circumstances the invariant mass is equal to the relativistic mass (discussed below), which is the total energy of the system divided by c (the speed of light) squared.

The concept of invariant mass does not require bound systems of particles, however. As such, it may also be applied to systems of unbound particles in high-speed relative motion. Because of this, it is often employed in particle physics for systems which consist of widely separated high-energy particles. If such systems were derived from a single particle, then the calculation of the invariant mass of such systems, which is a never-changing quantity, will provide the rest mass of the parent particle (because it is conserved over time)."

But I'm not sure, as always :) Because, although a definition using a idea of invariant mass, as stating that it must be invariant under time, works splendidly for me it then seems to come down to QM.s definitions of particles and their 'life times' too?

"Updated by Don Koks, 2012.
Original by Philip Gibbs and Jim Carr, late 1990s."

comment on it this way.

"When particles are moving, relativistic mass provides a very economical description that absorbs the particles' motion naturally.  For example, suppose we put an object on a set of scales that are capable of measuring incredibly small increases in weight.  Now heat the object.  As its temperature rises causing its constituents' thermal motion to increase, the reading on the scales will increase.  If we prefer to maintain the usual idea that mass is proportional to weight—assuming we don't step into an elevator or change planets midway through the experiment—then it follows that the object's mass has increased.  If we define mass in such a way that the object's mass does not increase as it heats up, then we will have to give up the idea that mass is proportional to weight."

What is relativistic mass?

#### yor_on

• Naked Science Forum GOD!
• Posts: 11652
• (Ah, yes:) *a table is always good to hide under*
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #10 on: 21/03/2013 13:40:29 »
This one "The concept of invariant mass does not require bound systems of particles, however. As such, it may also be applied to systems of unbound particles in high-speed relative motion. Because of this, it is often employed in particle physics for systems which consist of widely separated high-energy particles. If such systems were derived from a single particle, then the calculation of the invariant mass of such systems, which is a never-changing quantity, will provide the rest mass of the parent particle (because it is conserved over time)"

Seems as a circular logic, to me? It assumes a invariant mass to exist, and as all particles then by definition have it, we can presume that any 'system', no matter how separated in time and space must, by definition, have it too?

I like invariant mass, it makes sense to assume that a particle have a defined 'rest mass' even under translations by 'gravity' 'motion', as well as 'energy' in general. But 'relativistic mass' do make sense to me too.

#### yor_on

• Naked Science Forum GOD!
• Posts: 11652
• (Ah, yes:) *a table is always good to hide under*
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #11 on: 21/03/2013 14:07:12 »
Maybe you could define it such as a 'invariant rest mass' indeed is a invariant, even to time? Although a relativistic 'rest mass' use the notion, indirectly, when for example defining a acceleration, or 'uniform motion'? Einsteins definition isn't one of three spatial dimensions being separated from a temporal. To me it's a whole expression, where the spatial and temporal parameters have a balance relative each other. So for example, imagining a 'space' without a arrow shouldn't be possible from such a definition.

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #12 on: 21/03/2013 18:51:37 »
There is a time component to the definition of a invariant mass, to me that is. If it is invariant, it should be so under time too?
No. If it is also "time-invariant" = constant, it means the rest energy is conserved. But this can be or not, in general, depending on the situation; for example, if you heat a stationary piece of iron, its mass is not constant and so it's not time-invariant.
Quote
It's not so much the question of if it really will weight more that confuse me, but how that time component are used.
Mass in special relativity uses this definition.
"The term mass in special relativity usually refers to the rest mass of the object, which is the Newtonian mass as measured by an observer moving along with the object. The invariant mass is another name for the rest mass of single particles. The more general invariant mass (calculated with a more complicated formula) loosely corresponds to the "rest mass" of a "system". Thus, invariant mass is a natural unit of mass used for systems which are being viewed from their center of momentum frame (COM frame), as when any closed system ..... (for example a bottle of hot gas) ...... is weighed, which requires that the measurement be taken in the center of momentum frame where the system has no net momentum. Under such circumstances the invariant mass is equal to the relativistic mass (discussed below), which is the total energy of the system divided by c (the speed of light) squared.
The concept of invariant mass does not require bound systems of particles, however. As such, it may also be applied to systems of unbound particles in high-speed relative motion. Because of this, it is often employed in particle physics for systems which consist of widely separated high-energy particles. If such systems were derived from a single particle, then the calculation of the invariant mass of such systems, which is a never-changing quantity, will provide the rest mass of the parent particle (because it is conserved over time)."
What it says here is simply this: if the system's centre of mass (or, more generally, the "centre of momentum") is *always zero*, whatever happens (for example a set of some particles could disintegrate in another set of totally different particles) then the system's energy can always be identified with its invariant mass (do you remember when E = mc2 is valid?).
Now, since the system's energy is conserved, because we assume an isolated system, then its invariant mass is conserved too. "Conserved" means that it doesn't vary after the reaction, so it doesn't vary with time. But "invariant" and "conserved/constant" are different concepts, in general.

--
lightarrow

« Last Edit: 21/03/2013 18:54:42 by lightarrow »

#### yor_on

• Naked Science Forum GOD!
• Posts: 11652
• (Ah, yes:) *a table is always good to hide under*
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #13 on: 22/03/2013 04:33:23 »
Let me think about it for a time Lightarrow, and I may misstate it. What you seem to say is that the 'energy', of any 'closed' system defined, is invariant under transformations? But not that it is invariant under time? If that is how you see it I think I agree. My own thoughts on it is that no systems go free from time in this universe, also that I find it very hard to find any closed systems anywhere in nature, and the universe. But as I said :) I may miss your point there.

#### Pmb

• Neilep Level Member
• Posts: 1838
• Physicist
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #14 on: 22/03/2013 18:37:20 »
Kinetic energy without counteraction doesn't create additional gravitation.
I don't understand what you mean by "counteraction." Kinetic energy DOES generate a gravitational field though. That's quite a well-known fact.

Regarding the term "invariant." Invariant does sound like it means "does not change with time" but this is not the case.  It gets its name from the fact that it remains inchanged upon applying a Lorentz transformation.

I want to remind you that invariant mass only applies to closed systems. It's meaningless in more general cases.
« Last Edit: 22/03/2013 18:48:00 by Pmb »

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #15 on: 22/03/2013 18:53:04 »
Let me think about it for a time Lightarrow, and I may misstate it. What you seem to say is that the 'energy', of any 'closed' system defined, is invariant under transformations?
*Which* trasformation? Certainly not Lorentz transformation.
Quote
But not that it is invariant under time?
It would be simpler if you used, as it's usually used in physics, the term "invariant" only for Lorentz transformations and the term "constant" to mean that it doesn't vary with time. As "subset" of the concept "constant", physicists sometimes use the term "conserved" to mean that it doesn't vary afyer a reaction; for exampe: "momentum is conserved in particles collisions".

#### flr

• Sr. Member
• Posts: 302
• Thanked: 2 times
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #16 on: 22/03/2013 21:41:26 »
Many thanks for so insightful answers.

Let me ask this question, because it seems inevitable:
In a box with fictitious zero-rest-mass walls we 'trap' some light.
The photos can move back and forth inside this fictitious box. They cannot tunnel (assume for the sake or argument they cannot).

If I put this imaginary box on a scale, I should get a non-zero reading right?
The imaginary box is at rest relative to scale, but the photons inside the box are not because they are going back and forth at c.

In this experiment, the energy of the trapped photons E=pc should be 'seen' by my scale as a rest mass of the box, right?

#### Pmb

• Neilep Level Member
• Posts: 1838
• Physicist
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #17 on: 22/03/2013 23:39:47 »
Many thanks for so insightful answers.

Let me ask this question, because it seems inevitable:
In a box with fictitious zero-rest-mass walls we 'trap' some light.
The photos can move back and forth inside this fictitious box. They cannot tunnel (assume for the sake or argument they cannot).

If I put this imaginary box on a scale, I should get a non-zero reading right?
Yes. There is an interesting article on this in the American Journal of Physics. The mass of a gas of massless photons, H. Kolbenstvedt, Am. J. Phys. 63(1), January 1995.

Would you like to read it? I can e-mail you a copy. I have permission to do so from the editor of that journal.

#### flr

• Sr. Member
• Posts: 302
• Thanked: 2 times
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #18 on: 23/03/2013 00:41:09 »
The abstract is interesting. Unfortunately, I don't have full access to it.

#### flr

• Sr. Member
• Posts: 302
• Thanked: 2 times
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #19 on: 23/03/2013 00:50:48 »
Many thanks for so insightful answers.

Let me ask this question, because it seems inevitable:
In a box with fictitious zero-rest-mass walls we 'trap' some light.
The photos can move back and forth inside this fictitious box. They cannot tunnel (assume for the sake or argument they cannot).

If I put this imaginary box on a scale, I should get a non-zero reading right?
Yes.

Then my question is: The mass measured by the scale is the rest mass of the box trapping photons, is that so?

#### simplified

• Sr. Member
• Posts: 428
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #20 on: 23/03/2013 06:22:14 »
Kinetic energy without counteraction doesn't create additional gravitation.
I don't understand what you mean by "counteraction." Kinetic energy DOES generate a gravitational field though. That's quite a well-known fact.

Regarding the term "invariant." Invariant does sound like it means "does not change with time" but this is not the case.  It gets its name from the fact that it remains inchanged upon applying a Lorentz transformation.

I want to remind you that invariant mass only applies to closed systems. It's meaningless in more general cases.
You can't explain something without counteraction.Energy of satellite creates gravitation to stranger.You can add much energy to the satellite, but additional energy doesn't create gravitation,because it have no counteraction. :P

#### flr

• Sr. Member
• Posts: 302
• Thanked: 2 times
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #21 on: 23/03/2013 07:21:19 »
If the object is stationary in the scale's frame of reference, it's simply mass (not relativistic mass) which increases.

So, if I keep heating it, it will eventually form a black hole?

#### simplified

• Sr. Member
• Posts: 428
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #22 on: 23/03/2013 08:00:14 »
If the object is stationary in the scale's frame of reference, it's simply mass (not relativistic mass) which increases.

So, if I keep heating it, it will eventually form a black hole?
Can you create counteraction to the energy?

#### CD13

• Jr. Member
• Posts: 13
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #23 on: 23/03/2013 08:23:09 »
Can anyone explain what exactly attraction and repulsion are? Whether it's charge or gravity. Why should what we call a positive charge move towards a negative charge?

#### yor_on

• Naked Science Forum GOD!
• Posts: 11652
• (Ah, yes:) *a table is always good to hide under*
##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #24 on: 23/03/2013 10:55:30 »
No, transformations of energy, inside a 'system' labeled 'closed', or in any way 'constricted' by your premises, limits and simplifications for getting that clean presentation. Lorentz transformations is not what I had in mind there :) I mean, the universe has to build on some simple concepts, to please me at least :) And conservation of energy makes sense from that view, although you can discuss it from GR. But from a view of locality, defining it such as you always have a measurable reality making sense, I think it should hold, although I'm never sure :)

#### The Naked Scientists Forum

##### Re: Can we measure with a balance the relativistic increase of mass with velocity?
« Reply #24 on: 23/03/2013 10:55:30 »