The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, it is a characteristic of the system's total energy and momentum that is the same in all frames of reference related by Lorentz transformations. If a center-of-momentum frame exists for the system, then the invariant mass of a system is equal to its total mass in that "rest frame". In other reference frames, where the system's momentum is nonzero, the total mass (a.k.a. relativistic mass) of the system is greater than the invariant mass, but the invariant mass remains unchanged.
Due to mass–energy equivalence, the rest energy of the system is simply the invariant mass times the speed of light squared. Similarly, the total energy of the system is its total (relativistic) mass times the speed of light squared.
Systems whose four-momentum is a null vector (for example a single photon or many photons moving in exactly the same direction) have zero invariant mass, and are referred to as massless. A physical object or particle moving faster than the speed of light would have space-like four-momenta (such as the hypothesized tachyon), and these do not appear to exist. Any time-like four-momentum possesses a reference frame where the momentum (3-dimensional) is zero, which is a center of momentum frame. In this case, invariant mass is positive and is referred to as the rest mass.
If objects within a system are in relative motion, then the invariant mass of the whole system will differ from the sum of the objects' rest masses. This is also equal to the total energy of the system divided by c2. See mass–energy equivalence for a discussion of definitions of mass. Since the mass of systems must be measured with a weight or mass scale in a center of momentum frame in which the entire system has zero momentum, such a scale always measures the system's invariant mass. For example, a scale would measure the kinetic energy of the molecules in a bottle of gas to be part of invariant mass of the bottle, and thus also its rest mass. The same is true for massless particles in such system, which add invariant mass and also rest mass to systems, according to their energy.
For an isolated massive system, the center of mass of the system moves in a straight line with a steady sub-luminal velocity (with a velocity depending on the reference frame used to view it). Thus, an observer can always be placed to move along with it. In this frame, which is the center-of-momentum frame, the total momentum is zero, and the system as a whole may be thought of as being "at rest" if it is a bound system (like a bottle of gas). In this frame, which exists under these assumptions, the invariant mass of the system is equal to the total system energy (in the zero-momentum frame) divided by c2. This total energy in the center of momentum frame, is the minimum energy which the system may be observed to have, when seen by various observers from various inertial frames.
Note that for reasons above, such a rest frame does not exist for single photons, or rays of light moving in one direction. When two or more photons move in different directions, however, a center of mass frame (or "rest frame" if the system is bound) exists. Thus, the mass of a system of several photons moving in different directions is positive, which means that an invariant mass exists for this system even though it does not exist for each photon.
As far as I know, something like relativistic mass is just a concept, just a trick, there is nothing like the relativistic mass. When I move faster, I have higher kinetic energy, but my mass is still the same as if I was at rest. Kinetic and potential energies do not increase object's mass.
A...
What´s really experimentally known about neutrino masses for now?
- There are two neutrino oscillation periods, each with a mass square difference, so at least two neutrino mass eigenstates of the three have nonzero masses. (Note that "imaginary" is also "nonzero"!)
- There is an upper bound on...
The experimentally measured properties of protons and neutrons are known with exquisite detail. Our data is not quite as extremely precise, but still very good more other baryons and mesons with light quarks (u, d, and s) as valence quarks, such as pions and kaons.
Yet, on a percentage basis...
The mass (rest mass) of an atom, for example, depends on the kinetic and potential energy of the particles and their individual masses. Kinetic and potential energy are relative. Why is the mass not relative, but the same for all reference frames?
The answer is 3.079*10^-26 kg
I tried doing E=mc^2
20*10^9*1.602*10^-19=m*(3*10^8)^2
m=3.56*10^-26 kg
However when I do E=γmc^2 I get the correct answer.
Is the question wrong, because isn't it 20 GeV of kinetic energy, not total energy?
Ugh ... I remember there was a reason ... but forgot what it was.
So here's 3 bits of information gathered from dozens of sources, textbooks, official sites:
Alpha particles are identical to Helium nuclei.
Alpha particle mass = 4.001506 u
helium-4 nuclei mass = 4.0026032 u
OK, so ... why...
I'd like to ask an specific question. If c changes (for whatever reason*), does the rest mass of a given particle changes, asuming E is conserved?
Let's say, for a given particle, the following initial condition:
Placed in a vacuum**.
Rest mass m0.
Particle's energy E.
Propagation speed of...
Dirac's rest mass seems to be expressed as a fourth dimension. If we were to try to include this rest-mass dimension into Minowski space time, could it be expressed as a distance in space? S^2=x^2+y^2+z^2+(rest-mass dimension)^2-(ct)^2?
In all the derivations of E2=p2c2+m2c4 ,that I've stumbled on, it's assumed that the rest mass energy is m*c2 just because kinetic energy is mc2λ-mc2. Was it originally assumed? If so, can someone explain me why is it a logical assumption? Are there any derivations without such assumptions?
So from what I've heard, the rest mass of a object increases when the object's internal energy increases.
So a clock that is ticking has increased rest mass vs the same clock that is completely still.
But doesn't the clock have moving parts that give kinetic and thermal energy? Then in what...
Homework Statement
A particle is accelerated so it has a total energy of 10GeV measured in the accelerator’s rest frame. The particle's momentum is 8GeV/c in the same frame. Calculate...
a.) Rest mass of the particle
b.) Energy in an inertial frame in which its momentum is 6GeV/c
c.) The speed...
Homework Statement
Good day all!
Quick question:
As part of a problem statement, I'm asked to verify if the trajectory: \frac{dx}{dt}=\frac{cgt}{\sqrt{1+g^2t^2}}
Is "consistent".
Homework Equations
None
The Attempt at a Solution
Im not sure what "consistent" means. Does it mean, \frac...
The energy associated with the mass of a free proton in the center of momentum frame where the proton’s momentum is zero is 938.272 (with more decimals).
What is the rest energy of a single proton inside a Uranium atom? (It could be any other radioactive or fissionable element but I took...
Does the rest mass of an object increase when it acquires gravitational potential energy, and if so, is this the reason why Einstein believed that the inertia of a mass increases in the presence of other masses?
Hello.
The speed of an elementary particle, for example an electron, in Zitterbewegung motion is c. So theory of relativity should say electron is massless particle ? Is Zitterbewegung not considered in theory in relativity ? Thanks.
The Electron Rest Mass is considered as a fundamental constant of nature.
In relativistic Quantum Field Theory, in contrast, divergences arise. In order to deal with these divergences, one uses renormalization. According to this renormalization, the 'macroscopic' parameters of the lagrangian...
About 40 years ago, someone told me that free neutrons decay with a half life of around 14 minutes.
About 10 years ago, I discovered that W bosons were involved, and that they are about 100 times as massive as a proton.
Do W bosons really exist as "massive" particles for their very brief...
Using these equations I am about to prove that photons have a rest mass of zero (mathematically)
________________________________________________________________________________________
E=hc/λ Photon Energy Equation
E2=(pc+mc2)2 Mass-Energy Equivalence with Momentum Equation
p=h/λ Momentum...
Homework Statement
A meteorite is approaching Earth at very high speed. In order to avoid an impact on earth, the world space agency has launched two space missions: one mission sends the astronaut Albert to the meteorite approaching earth. The other mission, lead by the space commander Trebla...
Title should be: Does rest mass increase in the FRW metric?
The flat FRW metric can be written in conformal co-ordinates:
$$ds^2=a^2(\eta)(d\eta^2-dx^2-dy^2-dz^2)$$
where ##\eta## is conformal time. Let us assume that ##a(\eta_0)=1## where ##\eta_0## is the present conformal time.
Now the...
I have seen this before, and just saw a thread about the sped of light. The problem is that they say, "light has no mass" then conclude incorrectly on a number of issues. What may be worse is that no replies seem to address the source of confusion, light does have mass, zero rest mass yes, but...
I was wondering... can the rest mass of an object be time dependent? Like in a scenario where the body is losing mass?
(Sorry I meant for a title "rest mass time dependent?")
Hi there,
I'm trying to get a better intuitive handle on the concept of rest mass and rest energy - the energy term associated with rest mass. Introductory Physics textbooks often give statements along the lines of "mass is a form of energy" or "mass can be converted to energy" to explain...
Homework Statement
A particle of rest mass m0 collides elastically with a stationary particle of equal mass and scatters at angle θ. The incident particle has kinetic energy T0 before the collision and T1 after the collision. (a) Show that T12 (2m0c 2 + T0) 2 = p02 p12 c4 cos2 θ. (b) Using the...
Hello, my problem is as follows
I've tried finding the invariant mass of the positron and pion as follows
M^2=(E_e+E_{\pi})^2-(\mathbf{p_e}+\mathbf{p_{\pi}})\\
=E_e^2+E_{\pi}^2+2E_eE_{\pi}-p_e^2-p_{\pi}^2-2\mathbf{p_ep_{\pi}}\\
=m_e^2+m_{\pi}^2-2(E_eE_{\pi}+\mathbf{p_ep_{\pi}})\\...
Suppose you have a source of electron antineutrinos, and you arrange your apparatus so that a billion billion billion of them collide directly with a black hole. In principle, you could measure the change in momentum and energy from that occurrence.
Suppose you did that the next day. According...
Wasnt it ?
So I stumbled upon this fragment from wikipedia's photon page
"Current commonly accepted physical theories imply or assume the photon to be strictly massless, but this should be also checked experimentally. If the photon is not a strictly massless particle, it would not move at the...
1. is there a difference between 'rest mass' and 'invariant mass'?
I thought there wasn't...
To put it another way (or maybe this next question is a different question):
2. Is there a difference between the rest mass of a positron/electron pair, and the rest massa of a system containing two...
Homework Statement
Could someone please let me know if this is correct? I'm unsure about matter always being conserved, does it change whether we're talking about Newtonian physics or special relativity? To me, matter is conserved regardless but maybe there is something I don't know...
Homework Statement
Suppose that a certain accelerator can give protons a kinetic energy of 200 GeV. The rest mass of a proton is 0.938 Gev/c^2. Calculate the largest possible rest mass M0 of a particle that could be produced by the impact of one of the high-energy protons on a stationary...
I'm a high school chem and physics teacher, participating in a recreational online chem course hosted by MIT.
One of the practice questions in this course asked how many atoms a certain mass would contain at 300K. This got me thinking about mass-energy equivalence, and whether the atomic...
Hi all. we know that the rest is the mass of an object within a coordinate system which has zero velocity, but how does it exist for an electron inside a crystal, which we call rest mass of electron, how electron exist with zero velocity.or we mean by zero velocity of electron with respect to...
Hi PF. This a fact well aware to just about anyone that has had even basic chemistry, but I'm having a hard time coming to an understanding as to why this must be true. So why?
Also, if I knew that some box contained, say, a proton and an electron, could I ever know whether or not, inside...
I, like many others, have always wondered whether photons truly massless or if their mass is just so small that its irrelevant? And of course, if they truly are massless, then how can black holes attract them?
http://cosmoquest.org/forum/showthread.php?98056-Upper-limit-to-photon-mass <--...
The TOTAL energy of a pion is given, no other information is given so we don't know how fast it is moving, is it possible to calculate its mass? I'm assuming it's relativistic and we need GAMMA (the lorentz factor)
Also if E is it's total energy what would it's kinetic energy be? wouldn't its...
Electrons emit and absorb photons all the time. I heard that each electron is surrounded by a cloud of 10^{20} photons. That suggests to me that the rest mass of an electron must fluctuate, and that raises the prospect of uncertainty.
My questions:
Is the rest mass of an electron really...
The velocity of an object can, theoretically, only be measured relative to the velocity of another object. If I understand the concept of rest mass correctly, it is the mass of a particle with zero velocity; if my understanding is correct, what is 'zero velocity' relative to? Is it relative to...
A nucleus of rest mass m initially at rest in the lab absorbs a photon such that its total energy becomes 1.01mc^2.
I've calculated the energy of the photon to be greater than the change in rest mass of the nucleus this is on track because the follow up question is why is the required energy...
If we use only rest mass as the source of gravity, but use the rest of general relativity. What are the differences with observations. Excluding cosmology and dark energy.
I mean real observations, not just theory. I exclude from the question, cosmology, dark matter and dark energy. In my...
I am confused on an issue relating to gluons and mass. As I understand it, quarks don't actually have a lot of rest mass. In fact, most of the rest mass found in Hadrons arises from the interactions and energy of the Gluon field between quarks(??). This sounds like GR to me, meaning that the...
My question concerns the delta++ baryon.
I understand that the rest mass of quarks makes up a very small percentage of the total mass of a baryon, but I don't understand exactly what it is about delta ++ (uuu) which makes it have greater rest mass than a proton (uud).
If anyone can explain...
My understanding is that the presence of energy and matter curve spacetime.
Is a photon considered energy?
If so, how can it curve spacetime while having zero rest mass?
Hello all .
Rest mass of Hydrogen is more than rest mass of one proton and one electron ?
I mean virtual photon between electron and proton give extra mass to Hydrogen ?
Like gluon between quarks ?
and another example : mass of solar system is more than mass of One to One planets and sun...
Homework Statement
An unstable particle, initially at rest, decays into a pro-
ton (rest energy 938.3 MeV) and a negative pion (rest
energy 139.5 MeV). A uniform magnetic ﬁeld of
0.250 T exists perpendicular to the velocities of the cre-
ated particles. The radius of curvature of each...
I was reading the Wikipedia page on "Mass in Special Relativity" (http://en.wikipedia.org/wiki/Mass_in_special_relativity) and I came across two equations:
M = m/sqrt(1-v2/c2)
and
p = mv/sqrt(1-v2/c2)
along with the following quote:
Einstein's comment seems to suggest that the...
Homework Statement
A particle of rest mass m_0 and kinetic energy 2m_0c^2 and sticks to a stationary particle with rest mass 2m_0. Find the rest mass of the composite particle.
Homework Equations
Conservation of momentum and thus energy.
E_{bef} = E_r + E_k = E_{aft} where Er is...