Is this relativistic mass? The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)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?
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Is this relativistic mass?
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)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I have seen in a lot of places in here clearly stating that relativistic mass is outdated, that we can make do just fine with the concept of invariant mass,etc.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
edited Apr 9 at 3:10
Qmechanic♦
108k122001244
asked Apr 8 at 20:32
Achilles' AdvisorAchilles' Advisor
608
$endgroup$
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
edited Apr 9 at 3:10
Qmechanic♦
108k122001244
asked Apr 8 at 20:32
Achilles' AdvisorAchilles' Advisor
608
$endgroup$
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
edited Apr 9 at 3:10
Qmechanic♦
108k122001244
asked Apr 8 at 20:32
Achilles' AdvisorAchilles' Advisor
608
$endgroup$
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 Apr 9 at 3:10
Qmechanic♦
108k122001244
asked Apr 8 at 20:32
Achilles' AdvisorAchilles' Advisor
608
edited Apr 9 at 3:10
Qmechanic♦
108k122001244
asked Apr 8 at 20:32
Achilles' AdvisorAchilles' Advisor
608
edited Apr 9 at 3:10
Qmechanic♦
108k122001244
edited Apr 9 at 3:10
Qmechanic♦
108k122001244
edited Apr 9 at 3:10
Qmechanic♦
108k122001244
108k122001244
asked Apr 8 at 20:32
Achilles' AdvisorAchilles' Advisor
608
asked Apr 8 at 20:32
Achilles' AdvisorAchilles' Advisor
608
asked Apr 8 at 20:32
Achilles' AdvisorAchilles' Advisor
608
608
add a comment |
add a comment |
2 Answers
2
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 $m$.
answered Apr 8 at 21:07
Ben CrowellBen Crowell
54.1k6165313
$endgroup$
$begingroup$
Okay thanks and does relaivistic mass add linearly?
$endgroup$
– Achilles' Advisor
Apr 9 at 17:21
1
$begingroup$
No, that's what I mean by saying that it isn't additive.
$endgroup$
– Ben Crowell
yesterday
$begingroup$
But you said that for invariant mass. I asked if it was the same case for relativistic mass.
$endgroup$
– Achilles' Advisor
16 hours ago
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.
answered Apr 9 at 4:03
anna vanna v
162k8153455
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
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 $m$.
answered Apr 8 at 21:07
Ben CrowellBen Crowell
54.1k6165313
$endgroup$
$begingroup$
Okay thanks and does relaivistic mass add linearly?
$endgroup$
– Achilles' Advisor
Apr 9 at 17:21
1
$begingroup$
No, that's what I mean by saying that it isn't additive.
$endgroup$
– Ben Crowell
yesterday
$begingroup$
But you said that for invariant mass. I asked if it was the same case for relativistic mass.
$endgroup$
– Achilles' Advisor
16 hours ago
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 $m$.
answered Apr 8 at 21:07
Ben CrowellBen Crowell
54.1k6165313
$endgroup$
$begingroup$
Okay thanks and does relaivistic mass add linearly?
$endgroup$
– Achilles' Advisor
Apr 9 at 17:21
1
$begingroup$
No, that's what I mean by saying that it isn't additive.
$endgroup$
– Ben Crowell
yesterday
$begingroup$
But you said that for invariant mass. I asked if it was the same case for relativistic mass.
$endgroup$
– Achilles' Advisor
16 hours ago
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 $m$.
answered Apr 8 at 21:07
Ben CrowellBen Crowell
54.1k6165313
$endgroup$
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 Apr 8 at 21:07
Ben CrowellBen Crowell
54.1k6165313
answered Apr 8 at 21:07
Ben CrowellBen Crowell
54.1k6165313
answered Apr 8 at 21:07
Ben CrowellBen Crowell
54.1k6165313
answered Apr 8 at 21:07
Ben CrowellBen Crowell
54.1k6165313
54.1k6165313
$begingroup$
Okay thanks and does relaivistic mass add linearly?
$endgroup$
– Achilles' Advisor
Apr 9 at 17:21
1
$begingroup$
No, that's what I mean by saying that it isn't additive.
$endgroup$
– Ben Crowell
yesterday
$begingroup$
But you said that for invariant mass. I asked if it was the same case for relativistic mass.
$endgroup$
– Achilles' Advisor
16 hours ago
add a comment |
$begingroup$
Okay thanks and does relaivistic mass add linearly?
$endgroup$
– Achilles' Advisor
Apr 9 at 17:21
1
$begingroup$
No, that's what I mean by saying that it isn't additive.
$endgroup$
– Ben Crowell
yesterday
$begingroup$
But you said that for invariant mass. I asked if it was the same case for relativistic mass.
$endgroup$
– Achilles' Advisor
16 hours ago
$begingroup$
Okay thanks and does relaivistic mass add linearly?
$endgroup$
– Achilles' Advisor
Apr 9 at 17:21
$begingroup$
Okay thanks and does relaivistic mass add linearly?
$endgroup$
– Achilles' Advisor
Apr 9 at 17:21
1
1
$begingroup$
No, that's what I mean by saying that it isn't additive.
$endgroup$
– Ben Crowell
yesterday
$begingroup$
No, that's what I mean by saying that it isn't additive.
$endgroup$
– Ben Crowell
yesterday
$begingroup$
But you said that for invariant mass. I asked if it was the same case for relativistic mass.
$endgroup$
– Achilles' Advisor
16 hours ago
$begingroup$
But you said that for invariant mass. I asked if it was the same case for relativistic mass.
$endgroup$
– Achilles' Advisor
16 hours ago
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.
answered Apr 9 at 4:03
anna vanna v
162k8153455
$endgroup$
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.
answered Apr 9 at 4:03
anna vanna v
162k8153455
$endgroup$
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.
answered Apr 9 at 4:03
anna vanna v
162k8153455
$endgroup$
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 Apr 9 at 4:03
anna vanna v
162k8153455
answered Apr 9 at 4:03
anna vanna v
162k8153455
answered Apr 9 at 4:03
anna vanna v
162k8153455
answered Apr 9 at 4:03
anna vanna v
162k8153455
162k8153455
add a comment |
add a comment |
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