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Is this relativistic mass?
Does relativistic mass exhibit gravitiational effects?Would an object lose physical mass if it accelerated to a relativistic speed (would an object burn it's own mass)?If rest mass does not change with $v$ then why is infinite energy required to accelerate an object to the speed of light?Will objects heat up and become hidden at relativistic speed?Can relativistic mass be treated as rest mass?Questions on MassProper mass and space-time wrap questionGravitational Field of a Photon compared to that of Massive MatterDoes the mass of object really increase?Are relativistic momentum and relativistic mass conserved in special relativity?
$begingroup$
I have seen in a lot of places in here clearly stating that relativistic mass is outdated, that we can make do just fine with the concept of invariant mass,etc. But I've also seen people saying that a hotter object is heavier than a colder object. Where they say that the internal energy of the constituent atoms contribute to the mass of the object. This confuses me. Doesn't relativistic mass imply that I should observe your mass to increase as your velocity increases? Doesn't an increase in internal energy mean an increase in the constituent atom's velocity?
special-relativity mass inertial-frames mass-energy
$endgroup$
add a comment |
$begingroup$
I have seen in a lot of places in here clearly stating that relativistic mass is outdated, that we can make do just fine with the concept of invariant mass,etc. But I've also seen people saying that a hotter object is heavier than a colder object. Where they say that the internal energy of the constituent atoms contribute to the mass of the object. This confuses me. Doesn't relativistic mass imply that I should observe your mass to increase as your velocity increases? Doesn't an increase in internal energy mean an increase in the constituent atom's velocity?
special-relativity mass inertial-frames mass-energy
$endgroup$
add a comment |
$begingroup$
I have seen in a lot of places in here clearly stating that relativistic mass is outdated, that we can make do just fine with the concept of invariant mass,etc. But I've also seen people saying that a hotter object is heavier than a colder object. Where they say that the internal energy of the constituent atoms contribute to the mass of the object. This confuses me. Doesn't relativistic mass imply that I should observe your mass to increase as your velocity increases? Doesn't an increase in internal energy mean an increase in the constituent atom's velocity?
special-relativity mass inertial-frames mass-energy
$endgroup$
I have seen in a lot of places in here clearly stating that relativistic mass is outdated, that we can make do just fine with the concept of invariant mass,etc. But I've also seen people saying that a hotter object is heavier than a colder object. Where they say that the internal energy of the constituent atoms contribute to the mass of the object. This confuses me. Doesn't relativistic mass imply that I should observe your mass to increase as your velocity increases? Doesn't an increase in internal energy mean an increase in the constituent atom's velocity?
special-relativity mass inertial-frames mass-energy
special-relativity mass inertial-frames mass-energy
edited 1 hour ago
Qmechanic♦
107k121991239
107k121991239
asked 7 hours ago
Achilles' AdvisorAchilles' Advisor
538
538
add a comment |
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
But I've also seen people saying that a hotter object is heavier than a colder object. Where they say that the internal energy of the constituent atoms contribute to the mass of the object.
Yes, and this is not in contradiction with the convention of invariant mass. Mass is defined by the identity $m^2=E^2-p^2$ (in units where $c=1$), which implies that it isn't additive. So say I have two electrons, each with mass $m$. If one is moving to the right at $0.9c$, and the other is moving to the left at $-0.9c$, then the mass of the whole system is greater than $2m$. However, each electron individually still has mass $m$.
$endgroup$
add a comment |
$begingroup$
Doesn't relativistic mass imply that I should observe your mass to increase as your velocity increases?
Outdated does not mean wrong. It means confusing, since we have much better tools to study the microcosm of atoms, since it was realized that special relativity in the motion of particles is completely and cleanly described by defining the relativistic four vectors, which obey vector equations.
Here is the energy momentum four vector :
and to the right the definition of the invariant mass:
The length of this 4-vector is the rest energy of the particle. The invariance is associated with the fact that the rest mass is the same in any inertial frame of reference.
As with the everyday length of vectors, lengths are not addivive, one has to use vector addition, in the special relativity case as defined on the right.
Doesn't an increase in internal energy mean an increase in the constituent atom's velocity?
Note what you said:
Doesn't relativistic mass imply that I should observe your mass to increase as your velocity increases?
bold mine.
When you hold a solid, is the solid moving with respect to your observation? The statement holds mathematically for each individual electron and atom with respect to the other, but statistically there is no motion that an external observer can measure.
The four vector formalism simplifies this. The addition of all the four vectors in a solid will give the total four vector whose length is the mass you can measure in the laboratory. Hotter items have higher momenta and the total addition of four vectors will give higher invariant mass for a hot object than it has when cold.
$endgroup$
add a comment |
$begingroup$
Yes, you can obtain alternatives to the ordinary Einstein equivalence relation, for instance, Max Planck suggested a correction of the form
$E = mc^2 + PV$
Which would take into account internal thermal contributions to the rest mass. The constituent particles which a system is also subject to kinetic energy (they are in motion) and as predicted from the theory of systems being heated, the particles gain energy and so contribute to rest mass. It's sort of similar to when a photon enters a box, the box's mass will increase according to the energy gained. In the same way, kinetic theory of heat involves the excitation of many particles and so contribute to larger mass. But it certainly is not a relativistic mass for the system contribution.
$endgroup$
2
$begingroup$
This seems obscure, historical, or speculative. The OP isn't asking anything obscure. They're just asking a question about how mass behaves in standard SR.
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
This isn't obscure, or speculative. Give some reasons why?
$endgroup$
– Gareth Meredith
7 hours ago
$begingroup$
And no they are not, they are asking how thermal contributions from the constituent particles of a system, may contribute to the rest mass of a system, including also if this is a case of relativistic mass, which I explained it wasn't. This is good old classical physics and equipartition.
$endgroup$
– Gareth Meredith
7 hours ago
add a comment |
Your Answer
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
But I've also seen people saying that a hotter object is heavier than a colder object. Where they say that the internal energy of the constituent atoms contribute to the mass of the object.
Yes, and this is not in contradiction with the convention of invariant mass. Mass is defined by the identity $m^2=E^2-p^2$ (in units where $c=1$), which implies that it isn't additive. So say I have two electrons, each with mass $m$. If one is moving to the right at $0.9c$, and the other is moving to the left at $-0.9c$, then the mass of the whole system is greater than $2m$. However, each electron individually still has mass $m$.
$endgroup$
add a comment |
$begingroup$
But I've also seen people saying that a hotter object is heavier than a colder object. Where they say that the internal energy of the constituent atoms contribute to the mass of the object.
Yes, and this is not in contradiction with the convention of invariant mass. Mass is defined by the identity $m^2=E^2-p^2$ (in units where $c=1$), which implies that it isn't additive. So say I have two electrons, each with mass $m$. If one is moving to the right at $0.9c$, and the other is moving to the left at $-0.9c$, then the mass of the whole system is greater than $2m$. However, each electron individually still has mass $m$.
$endgroup$
add a comment |
$begingroup$
But I've also seen people saying that a hotter object is heavier than a colder object. Where they say that the internal energy of the constituent atoms contribute to the mass of the object.
Yes, and this is not in contradiction with the convention of invariant mass. Mass is defined by the identity $m^2=E^2-p^2$ (in units where $c=1$), which implies that it isn't additive. So say I have two electrons, each with mass $m$. If one is moving to the right at $0.9c$, and the other is moving to the left at $-0.9c$, then the mass of the whole system is greater than $2m$. However, each electron individually still has mass $m$.
$endgroup$
But I've also seen people saying that a hotter object is heavier than a colder object. Where they say that the internal energy of the constituent atoms contribute to the mass of the object.
Yes, and this is not in contradiction with the convention of invariant mass. Mass is defined by the identity $m^2=E^2-p^2$ (in units where $c=1$), which implies that it isn't additive. So say I have two electrons, each with mass $m$. If one is moving to the right at $0.9c$, and the other is moving to the left at $-0.9c$, then the mass of the whole system is greater than $2m$. However, each electron individually still has mass $m$.
answered 7 hours ago
Ben CrowellBen Crowell
53.9k6165313
53.9k6165313
add a comment |
add a comment |
$begingroup$
Doesn't relativistic mass imply that I should observe your mass to increase as your velocity increases?
Outdated does not mean wrong. It means confusing, since we have much better tools to study the microcosm of atoms, since it was realized that special relativity in the motion of particles is completely and cleanly described by defining the relativistic four vectors, which obey vector equations.
Here is the energy momentum four vector :
and to the right the definition of the invariant mass:
The length of this 4-vector is the rest energy of the particle. The invariance is associated with the fact that the rest mass is the same in any inertial frame of reference.
As with the everyday length of vectors, lengths are not addivive, one has to use vector addition, in the special relativity case as defined on the right.
Doesn't an increase in internal energy mean an increase in the constituent atom's velocity?
Note what you said:
Doesn't relativistic mass imply that I should observe your mass to increase as your velocity increases?
bold mine.
When you hold a solid, is the solid moving with respect to your observation? The statement holds mathematically for each individual electron and atom with respect to the other, but statistically there is no motion that an external observer can measure.
The four vector formalism simplifies this. The addition of all the four vectors in a solid will give the total four vector whose length is the mass you can measure in the laboratory. Hotter items have higher momenta and the total addition of four vectors will give higher invariant mass for a hot object than it has when cold.
$endgroup$
add a comment |
$begingroup$
Doesn't relativistic mass imply that I should observe your mass to increase as your velocity increases?
Outdated does not mean wrong. It means confusing, since we have much better tools to study the microcosm of atoms, since it was realized that special relativity in the motion of particles is completely and cleanly described by defining the relativistic four vectors, which obey vector equations.
Here is the energy momentum four vector :
and to the right the definition of the invariant mass:
The length of this 4-vector is the rest energy of the particle. The invariance is associated with the fact that the rest mass is the same in any inertial frame of reference.
As with the everyday length of vectors, lengths are not addivive, one has to use vector addition, in the special relativity case as defined on the right.
Doesn't an increase in internal energy mean an increase in the constituent atom's velocity?
Note what you said:
Doesn't relativistic mass imply that I should observe your mass to increase as your velocity increases?
bold mine.
When you hold a solid, is the solid moving with respect to your observation? The statement holds mathematically for each individual electron and atom with respect to the other, but statistically there is no motion that an external observer can measure.
The four vector formalism simplifies this. The addition of all the four vectors in a solid will give the total four vector whose length is the mass you can measure in the laboratory. Hotter items have higher momenta and the total addition of four vectors will give higher invariant mass for a hot object than it has when cold.
$endgroup$
add a comment |
$begingroup$
Doesn't relativistic mass imply that I should observe your mass to increase as your velocity increases?
Outdated does not mean wrong. It means confusing, since we have much better tools to study the microcosm of atoms, since it was realized that special relativity in the motion of particles is completely and cleanly described by defining the relativistic four vectors, which obey vector equations.
Here is the energy momentum four vector :
and to the right the definition of the invariant mass:
The length of this 4-vector is the rest energy of the particle. The invariance is associated with the fact that the rest mass is the same in any inertial frame of reference.
As with the everyday length of vectors, lengths are not addivive, one has to use vector addition, in the special relativity case as defined on the right.
Doesn't an increase in internal energy mean an increase in the constituent atom's velocity?
Note what you said:
Doesn't relativistic mass imply that I should observe your mass to increase as your velocity increases?
bold mine.
When you hold a solid, is the solid moving with respect to your observation? The statement holds mathematically for each individual electron and atom with respect to the other, but statistically there is no motion that an external observer can measure.
The four vector formalism simplifies this. The addition of all the four vectors in a solid will give the total four vector whose length is the mass you can measure in the laboratory. Hotter items have higher momenta and the total addition of four vectors will give higher invariant mass for a hot object than it has when cold.
$endgroup$
Doesn't relativistic mass imply that I should observe your mass to increase as your velocity increases?
Outdated does not mean wrong. It means confusing, since we have much better tools to study the microcosm of atoms, since it was realized that special relativity in the motion of particles is completely and cleanly described by defining the relativistic four vectors, which obey vector equations.
Here is the energy momentum four vector :
and to the right the definition of the invariant mass:
The length of this 4-vector is the rest energy of the particle. The invariance is associated with the fact that the rest mass is the same in any inertial frame of reference.
As with the everyday length of vectors, lengths are not addivive, one has to use vector addition, in the special relativity case as defined on the right.
Doesn't an increase in internal energy mean an increase in the constituent atom's velocity?
Note what you said:
Doesn't relativistic mass imply that I should observe your mass to increase as your velocity increases?
bold mine.
When you hold a solid, is the solid moving with respect to your observation? The statement holds mathematically for each individual electron and atom with respect to the other, but statistically there is no motion that an external observer can measure.
The four vector formalism simplifies this. The addition of all the four vectors in a solid will give the total four vector whose length is the mass you can measure in the laboratory. Hotter items have higher momenta and the total addition of four vectors will give higher invariant mass for a hot object than it has when cold.
answered 22 mins ago
anna vanna v
161k8153453
161k8153453
add a comment |
add a comment |
$begingroup$
Yes, you can obtain alternatives to the ordinary Einstein equivalence relation, for instance, Max Planck suggested a correction of the form
$E = mc^2 + PV$
Which would take into account internal thermal contributions to the rest mass. The constituent particles which a system is also subject to kinetic energy (they are in motion) and as predicted from the theory of systems being heated, the particles gain energy and so contribute to rest mass. It's sort of similar to when a photon enters a box, the box's mass will increase according to the energy gained. In the same way, kinetic theory of heat involves the excitation of many particles and so contribute to larger mass. But it certainly is not a relativistic mass for the system contribution.
$endgroup$
2
$begingroup$
This seems obscure, historical, or speculative. The OP isn't asking anything obscure. They're just asking a question about how mass behaves in standard SR.
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
This isn't obscure, or speculative. Give some reasons why?
$endgroup$
– Gareth Meredith
7 hours ago
$begingroup$
And no they are not, they are asking how thermal contributions from the constituent particles of a system, may contribute to the rest mass of a system, including also if this is a case of relativistic mass, which I explained it wasn't. This is good old classical physics and equipartition.
$endgroup$
– Gareth Meredith
7 hours ago
add a comment |
$begingroup$
Yes, you can obtain alternatives to the ordinary Einstein equivalence relation, for instance, Max Planck suggested a correction of the form
$E = mc^2 + PV$
Which would take into account internal thermal contributions to the rest mass. The constituent particles which a system is also subject to kinetic energy (they are in motion) and as predicted from the theory of systems being heated, the particles gain energy and so contribute to rest mass. It's sort of similar to when a photon enters a box, the box's mass will increase according to the energy gained. In the same way, kinetic theory of heat involves the excitation of many particles and so contribute to larger mass. But it certainly is not a relativistic mass for the system contribution.
$endgroup$
2
$begingroup$
This seems obscure, historical, or speculative. The OP isn't asking anything obscure. They're just asking a question about how mass behaves in standard SR.
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
This isn't obscure, or speculative. Give some reasons why?
$endgroup$
– Gareth Meredith
7 hours ago
$begingroup$
And no they are not, they are asking how thermal contributions from the constituent particles of a system, may contribute to the rest mass of a system, including also if this is a case of relativistic mass, which I explained it wasn't. This is good old classical physics and equipartition.
$endgroup$
– Gareth Meredith
7 hours ago
add a comment |
$begingroup$
Yes, you can obtain alternatives to the ordinary Einstein equivalence relation, for instance, Max Planck suggested a correction of the form
$E = mc^2 + PV$
Which would take into account internal thermal contributions to the rest mass. The constituent particles which a system is also subject to kinetic energy (they are in motion) and as predicted from the theory of systems being heated, the particles gain energy and so contribute to rest mass. It's sort of similar to when a photon enters a box, the box's mass will increase according to the energy gained. In the same way, kinetic theory of heat involves the excitation of many particles and so contribute to larger mass. But it certainly is not a relativistic mass for the system contribution.
$endgroup$
Yes, you can obtain alternatives to the ordinary Einstein equivalence relation, for instance, Max Planck suggested a correction of the form
$E = mc^2 + PV$
Which would take into account internal thermal contributions to the rest mass. The constituent particles which a system is also subject to kinetic energy (they are in motion) and as predicted from the theory of systems being heated, the particles gain energy and so contribute to rest mass. It's sort of similar to when a photon enters a box, the box's mass will increase according to the energy gained. In the same way, kinetic theory of heat involves the excitation of many particles and so contribute to larger mass. But it certainly is not a relativistic mass for the system contribution.
edited 7 hours ago
answered 7 hours ago
Gareth MeredithGareth Meredith
1
1
2
$begingroup$
This seems obscure, historical, or speculative. The OP isn't asking anything obscure. They're just asking a question about how mass behaves in standard SR.
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
This isn't obscure, or speculative. Give some reasons why?
$endgroup$
– Gareth Meredith
7 hours ago
$begingroup$
And no they are not, they are asking how thermal contributions from the constituent particles of a system, may contribute to the rest mass of a system, including also if this is a case of relativistic mass, which I explained it wasn't. This is good old classical physics and equipartition.
$endgroup$
– Gareth Meredith
7 hours ago
add a comment |
2
$begingroup$
This seems obscure, historical, or speculative. The OP isn't asking anything obscure. They're just asking a question about how mass behaves in standard SR.
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
This isn't obscure, or speculative. Give some reasons why?
$endgroup$
– Gareth Meredith
7 hours ago
$begingroup$
And no they are not, they are asking how thermal contributions from the constituent particles of a system, may contribute to the rest mass of a system, including also if this is a case of relativistic mass, which I explained it wasn't. This is good old classical physics and equipartition.
$endgroup$
– Gareth Meredith
7 hours ago
2
2
$begingroup$
This seems obscure, historical, or speculative. The OP isn't asking anything obscure. They're just asking a question about how mass behaves in standard SR.
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
This seems obscure, historical, or speculative. The OP isn't asking anything obscure. They're just asking a question about how mass behaves in standard SR.
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
This isn't obscure, or speculative. Give some reasons why?
$endgroup$
– Gareth Meredith
7 hours ago
$begingroup$
This isn't obscure, or speculative. Give some reasons why?
$endgroup$
– Gareth Meredith
7 hours ago
$begingroup$
And no they are not, they are asking how thermal contributions from the constituent particles of a system, may contribute to the rest mass of a system, including also if this is a case of relativistic mass, which I explained it wasn't. This is good old classical physics and equipartition.
$endgroup$
– Gareth Meredith
7 hours ago
$begingroup$
And no they are not, they are asking how thermal contributions from the constituent particles of a system, may contribute to the rest mass of a system, including also if this is a case of relativistic mass, which I explained it wasn't. This is good old classical physics and equipartition.
$endgroup$
– Gareth Meredith
7 hours ago
add a comment |
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