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.
a) Two particles have energies E1 and E2, and momenta p1 and p2. Write down an expression for the invariant mass of this two-particle system. Leave your answer in terms of E1 and E2, and p1 and p2.
b) A typical photon (γ) in the Cosmic Microwave Background (CMB) has an energy of kBTCMB, where...
I think since Esystem=(PsystemC)^2 + (Minvariant C^2)^2. Then the invariant mass of the system should be zero, but I am hesitated with this is it always the case that photon that travels perpendicular to each other have zero invariant mass
So I know that since we are ignoring the mass of the electron, and the proton starts at rest, the proton has no KE and the electron has no rest energy.
So the initial total energy of the system would be
rest energy of proton + KE of electron = 2GeV + .938GeV = 2.938 GeV
and since energy is...
In Special Relativity, you learn that invariant mass is computed by taking the difference between energy squared and momentum squared. (For simplicity, I'm saying c = 1).
m^2 = E^2 - \vec{p}^2
This can also be written with the Minkowski metric as:
m^2 = \eta_{\mu\nu} p^\mu p^\nu
More...
A question of invariable mass.
In a inertial system, the invariable mass of a system never change with time. This system may not be an isolated system.
Whether in any inertial system, the invariant mass of the system remains unchanged.Or, in a certain inertial system, what is the necessary and...
The interaction p + π- → n + π- + π + may proceed by the creation of an intermediate 'particle' or resonance called a rho. This can be detected as a peak in the plot of invariant rest mass energy of the emergent pions versus frequency of pions observed. My question is quite simply, invariant...
fHomework Statement
Question b:
Homework Equations
E2=c2p2+m2c4
The Attempt at a Solution
We have c2pinitial2=E02-m2c4, and Ef2=c2p2+m2c4 for each outgoing proton. Combining those equations we get c2p2=Ef2-E02+c2pinitial2. I don't know where to go from here.
Dear all,
We were trying to solve the following question but did not quite understand what to do. The question is as follows:
The reconstructed invariant mass is usually described by a Gaussian (or Normal) distribution. However, the resolution σ (the width of the distribution) is found to...
Considering a D0->π+K- where the D meson decays from rest.
If one was to want to calculate the invariant mass of the D meson by measuring the momenta of the pion and kaon, following from conservation of momentum:
m2=(Eπ+EK)2-(pπ+pK)2
However by inputting numerical data
Eπ=137MeV
EK=493MeV...
Hello.
Suppose you were to assemble a sphere of negative charges. When you are done, the rest mass of the sphere is larger than that of the negative charges because they gain energy in forming the sphere. But the invariant mass of the electrons can't change and apparently gaining energy doesn't...
Homework Statement
At the LHC at CERN protons with an energy of 6.5 TeV (= 6.5·1012eV) each are collided with each other.To achieve the same invariant mass in a ﬁxed target experiment, what would the energy of the proton beam have to be?
Homework Equations
E2 - p2c2 = m2c4
E2 - p2c2=...
I'm reading the Wiki article below to say the invariant mass of photons in an expanding volume of space will decrease. I thought invariant mass of a photon was always zero and the energy of photon changed due to the expansion of space. So where did I go wrong?
Quote from Wiki
General...
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}})\\...
What can we learn from Invariant Mass Spectrum?How to measure it?So,how to read it?
Mass measurement is converted into energy measurement,but how could we make the quantity change continuously in order to form the horizontal axis?
How to divide different particles to measure them...
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...
The invariant mass of special relativity:
m_0{^2} = E^2 – p^2
There doesn't seem to be any quantity with units of mass that is invariant in general relativity. Invariant mass loses significance, as other than an approximation where space-time is sufficient flat.
But at the same time, mass is...
A friend of mine was reading Penrose's new book on CCC; I do not want to discuss this story here but a rather interesting detail which could be relevant w/o the whole CCC stuff.
SR and GR rely on (global and local) Lorentz invariance. From these symmetries one can derive invariant mass M² and...
Hey all, I'm quite confused on this and am curious to be put straight. Now I understand the basic principles of relativity, this one just bugs me.
Now I have always been taught that the famous E=MC^2 formula was proof that mass would reach toward infinity as it neared the speed of light...
Homework Statement
so I'm doing some proof-of-concept data analysis this summer and I've never taken a relativistic mechanics class and I'm a bit stuck. i need to figure out if there was a rho0 decay to pi+/pi- in some hypothetical 900GeV collision data. If there is, there should be a spike...
Hi, hopefully this isn't a dumb question. I've read essentially that in the center of mass/momentum frame an object has invariant mass, and that the system's total mass will be composed of the constituent particles' masses and any other kinetic and potential energies within the system. I also...
We have a collision involving a Kaon plus and proton initially resulting in the same plus a neutral pion (ie. Kp to Kp(pi)). The question asks to calculate the invariant mass of just the outgoing kaon and pion, given the outgoing momenta of the particles, the angle between them and their masses...
Homework Statement
At HERA 30 GeV electrons collided head on with 820 GeV protons. Calculate the invariant mass of ep collisions.
(masses: e=0.0005GeV, p=0.938GeV)
Homework Equations
M^2 = (E1 + E2)^2 - (p1 + p2)^2 ?
The Attempt at a Solution
I know the numerical answer to...
Hello,
I'm working on this problem and I'd like to know how to find the invariant mass using just the lab-frame momentum and rest mass.
I've found a lot of equations that deal with E, and I'm not completely sure what that is either.
Thanks
An photon has mass zero by virtue of its momentum canceling its energy in
m^2c^4 = E^2-p^2c^2
But in electromagnetism a field configution only has momentum when both a magnetic field and an electric field are present, e.g. in an electromagnetic wave. Now when there is only an electric or...
Ok, when you use positrons to shoot at stationary electrons in a collider with enough energy so that you make a pair of proton and antiproton. The total energy of the pair would be E = T + MC^2, where M is the total invariance mass of the pair, namely 2*938Mev, or I can use E^2 = (pc)^2 +...
In some cases, inertial mass does not equal invariant mass? What is the relation between the two?
So the photon can have non zero inertial mass but always 0 invariant mass?
"Invariant Mass" vs "Proper Mass"
I see that there are many people here who prefer the idea that the mass of a particle is the magnitude of the the particle's 4-momentum.
However that is known as "Proper Mass" and some simply say "mass." However that idea is limited in use. It can't be...