I like the way you’re approaching this, and this doesn’t take away from the point you were trying to make, but there’s one thing you said that I’m not understanding.
Why do things with energy have to have mass? Photons contain energy, and they are massless. And even more generally, if there is potential energy (say, gravitational) then the energy is in the field, which isn’t even a particle.
Photons do not have rest mass, which describes the energy they possess when stationary relative to a given frame of reference, because they’re always moving at the speed of light relative to any frame of reference, and the formula that relates rest mass to relativistic mass returns infinity for anything with finite rest mass moving at the speed of light.
They do, however, have mass equivalency. They exert a (very small) gravitational pull, can impart momentum equal to their mass equivalency times the speed of light, and if an object absorbs a photon, it gains mass equal to its mass equivalency.
If an object gains or loses potential energy, it also gains or loses relativistic mass. For instance, if you pull something out of a gravity well, its relativistic mass increases. These changes usually don’t occur on a large enough scale to be observable, but we can easily observe the relationship between potential energy and mass in high energy interactions such as nuclear fission or fusion.
Actually, to correct myself for further precision, if an object gains or loses potential energy, it’s not necessarily gaining or losing relativistic mass. The relativistic mass is the sum of all the energy in the body times the speed of light squared, including potential energy. So if you throw a ball upwards in a vacuum, it’s not gaining relativistic mass as it ascends because its kinetic energy is being converted into gravitational potential energy. Its relativistic mass was increased when you imparted energy by throwing it.
My own experience of learning physics has been a long series of discarded confusions imparted on me by imprecise instruction.
One thing that confused me when I studied special relativity in my undergraduate physics class: is all potential energy actually mass? For example, if you had a sensitive enough inertial balance, could you measure a change in mass in a spring when it is coiled and when it is uncoiled? Or between a charged capacitor and an uncharged one? E/c^2 would indeed be very tiny, but it wouldn’t be zero.
I don’t think this mass (relativistic?) could be real. Because potential energy is relative, and depends on context. For example, a marble at the bottom of a bowl doesn’t know it’s also sitting on a table … in a deep canyon … 4000 miles from the core of the Earth. These things can’t be affecting it’s actual mass?
Relativistic mass is, as the name suggests, relative. It depends on your frame of reference. If you observe a spaceship traveling at .9C, for example, then from your perspective its mass will be significantly greater than from the perspective of the passengers. This doesn’t affect its intrinsic mass, if that’s what you mean by “actual” mass, but it’s still a measurable phenomenon. Intrinsic mass and relativistic mass are interchangeable, such as when a nuclear reaction releases products with a lower rest mass than the reactants, at high atomic velocity.
Yes, a charged capacitor has more inertial and gravitational mass than a discharged one. No, I don’t think this is humanly measurable.
If you accept that one form of energy contributes to inertial and gravitational mass, you should expect all to. You can short a capacitor, converting that electrical potential energy to heat. It would be somewhat surprising if this changed the inertial or gravitational mass. Special relativity says that kinetic energy contributes to inertial mass and general relativity that it contributes to gravitational mass; thus all forms of energy should.
This actually makes potential energy less “mysterious” (if “mysterious” is the word I’m looking for) - it’s a thing that’s actually there to be measured, instead of a mathematical abstraction that depends on everything else around it that smells suspiciously like a fudge factor. ;)
I like the way you’re approaching this, and this doesn’t take away from the point you were trying to make, but there’s one thing you said that I’m not understanding.
Why do things with energy have to have mass? Photons contain energy, and they are massless. And even more generally, if there is potential energy (say, gravitational) then the energy is in the field, which isn’t even a particle.
Photons do not have rest mass, which describes the energy they possess when stationary relative to a given frame of reference, because they’re always moving at the speed of light relative to any frame of reference, and the formula that relates rest mass to relativistic mass returns infinity for anything with finite rest mass moving at the speed of light.
They do, however, have mass equivalency. They exert a (very small) gravitational pull, can impart momentum equal to their mass equivalency times the speed of light, and if an object absorbs a photon, it gains mass equal to its mass equivalency.
If an object gains or loses potential energy, it also gains or loses relativistic mass. For instance, if you pull something out of a gravity well, its relativistic mass increases. These changes usually don’t occur on a large enough scale to be observable, but we can easily observe the relationship between potential energy and mass in high energy interactions such as nuclear fission or fusion.
Ok, thanks for clearing that up for me
You’re welcome.
Actually, to correct myself for further precision, if an object gains or loses potential energy, it’s not necessarily gaining or losing relativistic mass. The relativistic mass is the sum of all the energy in the body times the speed of light squared, including potential energy. So if you throw a ball upwards in a vacuum, it’s not gaining relativistic mass as it ascends because its kinetic energy is being converted into gravitational potential energy. Its relativistic mass was increased when you imparted energy by throwing it.
My own experience of learning physics has been a long series of discarded confusions imparted on me by imprecise instruction.
One thing that confused me when I studied special relativity in my undergraduate physics class: is all potential energy actually mass? For example, if you had a sensitive enough inertial balance, could you measure a change in mass in a spring when it is coiled and when it is uncoiled? Or between a charged capacitor and an uncharged one? E/c^2 would indeed be very tiny, but it wouldn’t be zero.
I don’t think this mass (relativistic?) could be real. Because potential energy is relative, and depends on context. For example, a marble at the bottom of a bowl doesn’t know it’s also sitting on a table … in a deep canyon … 4000 miles from the core of the Earth. These things can’t be affecting it’s actual mass?
Relativistic mass is, as the name suggests, relative. It depends on your frame of reference. If you observe a spaceship traveling at .9C, for example, then from your perspective its mass will be significantly greater than from the perspective of the passengers. This doesn’t affect its intrinsic mass, if that’s what you mean by “actual” mass, but it’s still a measurable phenomenon. Intrinsic mass and relativistic mass are interchangeable, such as when a nuclear reaction releases products with a lower rest mass than the reactants, at high atomic velocity.
Yes, a charged capacitor has more inertial and gravitational mass than a discharged one. No, I don’t think this is humanly measurable.
If you accept that one form of energy contributes to inertial and gravitational mass, you should expect all to. You can short a capacitor, converting that electrical potential energy to heat. It would be somewhat surprising if this changed the inertial or gravitational mass. Special relativity says that kinetic energy contributes to inertial mass and general relativity that it contributes to gravitational mass; thus all forms of energy should.
This actually makes potential energy less “mysterious” (if “mysterious” is the word I’m looking for) - it’s a thing that’s actually there to be measured, instead of a mathematical abstraction that depends on everything else around it that smells suspiciously like a fudge factor. ;)
“Q: What’s potential energy? A: Mass.”