I’ve always considered Einstein wrong about his E=mc2 equation, I’ve always thought that mass and matter were interchangeable in his formula, but every time I hear his equation spoken, they always say mass, and not matter. So- does any one know what Einstein’s understood definition of mass was. He may have been smarter than I ever gave him credit for.
I think you meant this to go to either General Questions or In My Humble Opinion. This forum is meant for the whole Forum problems of whatever kind.
I have notified this Forum’s mod and they’ll set your question where it should be asked and hopefully let you know, too.
But while we’re waiting…matter possesses mass. Mass is a property of matter. All E=mc[sup]2[/sup] says is that anything with mass has an equivalent amount of energy.
More precisely E=mc2 is a special case, simplified form for the energy of an object at rest.
For most physics programs that focus on classical m is the sum of the rest mass and kinetic mass.
That will be fine to get you past the oversimplification that increasing the velocity of an object increases it’s mass which will prep you for the next * spherical cow*.
Why is the “squared” part important? Why not E=mc?
The math wouldn’t work out with what we observe, and time travel would be easy or perhaps wouldn’t even exist at all.
E=mc^2 is the popular younger sibling to the more complete E^2= (pc)^2+( m_oc^2)^2
Where m_o is the more modern “rest mass” but that will break things in the Newtonian world if you worry about mass right now.
Since this isn’t a question about the message board itself, let’s give GQ a try.
Moving thread from ATMB to GQ.
This form is better for the why ^2.
But on the OP’s question on if
A positron or anti-electron and an electron can be converted to radiation demonstrating the simple answer for mass–energy equivalence.
The slightly longer answer is that the mass of an object does not merely depend on the amount of stuff in them but also depends on how they are arranged and the resulting energies.
An atom of gold, will have less “mass at rest” than the parts that make it up. Yet the proton from that same atom will have much more mass than the two up quarks and one down quark that make up it’s valence quarks.
Those 3 quarks separated would have a total mass of 9.4 MeV/c2, yet the proton’s mass will be around 938.3 MeV/c2.
The point is that mass and matter were interchangeable in his formula and that has been experimentally demonstrated. The problem is that those interchanges are not always practical or due to energy levels may not be available to do work.
For the OP, you get to ask what actually is “matter”. As noted above, one property mater ends to have is mass. You can measure mass, and thus it is a useful thing to use in calculating other physical properties and results. Matter can have other attributes, each of which might also have a quantifiable value. Mass is just one.
Mass means that you can talk about how a body of matter with a given mass behaves. It will have inertia, and thus obey Newtons laws of motion. It will also obey Newtons laws of gravitation. The fact that the same thing - a body’s mass governs both its inertia and its gravitational effect is little short of mind blowing - and is known as the equivalence principle. Galileo is noted for observing this.
But when it gets to Einstein and his famous equation we see something even more mind blowing. This thing mass has an equivalent energy. Which also means raw energy has mass. Which sounds ridiculous until you find out it is true.
When we talk of matter we can talk of baryonic matter - which is mostly what we consider “stuff” about us. We know atom are made up of electrons, protons and neutrons. And further that protons and neutrons are made up of various quarks. Through various observations in particle accelerators we can get an idea of the properties of quarks, and we find that the individual quarks in a proton or neutron account for only a fraction of the mass of the particle. Which is astounding. The rest of the mass of a proton or neutron comes from the force needed to hold the quarks (confinement) inside the particle. The energy held in that force accounts for the majority of the mass of ordinary matter. It does so with E=mc[sup]2[/sup].
A famous question is to ask whether a wound up clock weights the same as the clock does when run down. The answer is that is weighs more wound up. By an infinitesimal tiny amount more, that accounts for the energy stored in the wound clock spring. Same deal, add energy, the mass increses.
Mass is a measure of matter. They’re not completely synonymous (you wouldn’t say “I’m made out of mass”, or “my matter is 80 kg”), but they’re close enough concepts that swapping the words won’t lead to any confusion.
As for the c^2, we use a system of units where we have different units for space and time (meters and seconds, for instance). If we used the same units for both, then c would just equal 1, and so we could just say that E = m (or for a moving object, E^2 = m^2 + p^2).
But (typically) we don’t use those units. And so energy and mass have different units, too. Specifically, energy has units of mass times speed squared. So, in such a system of units, it would be not only wrong but nonsensical to say that “E = mc”, or “E = mc^3”, or whatever.
So “dark matter” and “dark mass” are analogous expressions ?
Things in physics are typically named before we know what they are and they often keep their names even after we do.
The terms inertial mass, gravitational mass, rest mass, invariant mass, and relativistic mass are all jargon and one must consider context and not be understood outside that context.
It is called “dark matter” because it has some effects like matter, but we can’t see it. Until we understand it don’t read anything more into that name except that the name refers to a set of phenomena.
Mass is easily defined in classical mechanics, but is problematic in more modern theories like general relativity. You have to know the specific context to even define “mass” under GR and in some cases it is simply undefined.
Even under special relativity systems have to be isolated or have no volume for mass to be Lorentz invariant.
Another way to think of this is that physics is descriptive not prescriptive. The terms “mass” and “matter” are useful for describing them under some contexts but themselves are not fundamental to the realities of the universe. That said they are fundamental to the theories that allow us to describe and predict some actions.
rat avatar - I am not sure I understand. Your post felt like a religious experience.
What’s the matter?
“Dark mass” is not a synonym for “dark matter”, because “dark mass” isn’t a term at all.
It is in radiological medicine! But, that should not confuse anybody.
“Dark mass” and “the dark mass”, though less commonly used nowadays, are synonyms for dark matter or more particularly used to describe the mass of dark matter. See for example: https://link.springer.com/chapter/10.1007/978-94-009-0221-3_45
“Matter” is a fairly loosely defined term in physics, I would say broadly it means something made of particles which have rest energy or sometimes made of particles where rest energy dominates over kinetic energy.
Ya, it is a hard nut to crack ‘relativistic mass’ is not compatible with the standard theory language and is just really a remnant of the way we teach. mess.
Too bad Rest Energy=mc^2 wasn’t what people latched on to.
If you read Einstein’s other works it is obvious that typically he meant “Rest Energy” but not in the popular papers which lead to that whole m_0 rest mass mess. The good news is that most modern textbooks seem to skip the closed system exercises in Special Relativity that require this additional complexity and confusing terms.
Unfortunately Feynman lectures papers presents mass-velocity relation and experimental fact as proving the theory…so students will still have that that problem with p=mv from Newton breaking E^2= (pc)^2+( m_oc^2)^2. The Feynman lectures aren’t going away obviouslly.
Okun expands on this topic and it even includes a copy of a letter Einstein sent explaining why this would be a problem.
Such an unfortunate collision of overloaded terms.
While I don’t know if it fits all edge cases:
Matter = particles with rest mass and volume.
Seems to work for me. Remembering mass is a property not a thing helps.