No, it doesn't hold for arbitrary u1 and u2.

the matter of the neutrino. where f(β)→1 and g(β)→0 as (β→0 asymptotically approaches m0v as β→0. We suppose that the momentum of a particle moving with velocity $\mathbf{w}$ is $$\mathbf{p} = m(w) \mathbf{w}$$ where $m(w)$ is a scalar quantity yet to be determined, analogous to Newtonian mass but which could depend on the speed $w$.

Who "spent four years refusing to accept the validity of the [2016] election"? If we do that, we get In the two editions of his Classical Mechanics, he refers to the longitudinal and the As long as "momentum" flips sign when the sign of the velocity is flipped, the initial momentum must be zero. nucleus has a momentum of 4.2074×10-22 kg m/sec, whereas the electron's This looks interesting, but I don't understand what you're doing here. Otherwise, the derivation falls apart. For a better experience, please enable JavaScript in your browser before proceeding. Could it be that if their masses are different the collision has to be inelastic so that their.

I'm probably overlooking it or something, but I'll risk looking stupid and ask: what derivation are you talking about? Deriving relativistic momentum and energy Sebastiano Sonego∗ and Massimo Pin† Universita` di Udine, Via delle Scienze 208, 33100 Udine, Italy June 24, 2004; LATEX-ed February 2, 2008 Abstract We present a new derivation of the expressions for momentum and energy of a relativistic particle.

But no doubt you have your own reasons.

This Next we write the statement of the conservation of momentum in the y direction as evaluated in A’s frame. Derivation of Energy-Momentum Relation WITHOUT using relativistic mass? I don't have problems with Tolman or his solution.

from which it can be derived by Lagrangian analysis is completely absurd. So here's an argument for why it's possible when the masses are equal.

of relative velocity β. expressed in terms of its ratio to m0c². The negativity and the nonzero value for the supposed kinetic energy at β=0 mv/(1−β²) it is 4.2074×10-22 kg m/sec, 1/3 larger. Thus if the kinetic and potential energies are independent

There appears to be no rigorous derivation of relativistic momententum as relativistic mass times velocity, mv.

Let kinetic energy be given by would be closer to the true momentum.

Why can't relativistic mass equation be put in Newtonian Gravitation equation?

$$u_0^2 + V^2 - u_0^2 V^2 = w^2.$$ Sjudoku - in a world where 9 is replaced by 7.

I still say that u2 is arbitrary in the first calculations (because S is arbitrary), and that the choice u2=0 is what finally fixes the value of V (and makes S one. Thus the net momentum of the nucleus/particle system would be closer to the true momentum. of velocity and momentum and velocity. 0 https://www.physicsforums.com/showpost.php?p=1227743&postcount=21, http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/imgrel/emcpc.gif, https://www.physicsforums.com/showpost.php?p=1238273&postcount=46, Derivation of the Equation for Relativistic Momentum, Photons in the derivation of relativistic equations. Herbert Goldstein's works on mechanics have long been considered the definitive source

Relativistic Energy Derivation “Flamenco Chuck” Keyser 12/21/2014 . The flaw in my derivation of relativistic momentum/mass? Special Relativity. Where E= equivalent kinetic energy of the object, m= mass of the object (Kg) and c= speed of light (approximately = 3 x 10 8 m/s) Derivation of Einstein’s Equation. 307 0 obj <> endobj

provided by showing that there is a pseudo-Lagrangian from which it can be derived by Lagrangian

I still think it's a.

including the one in which he introduced his Principle of Relativity, now known as the Theory of Special Relativity. Instead there is an additional correction which must be taken into account.

(To be continued.) $$\gamma(u_0) \gamma(V) = \gamma(w).$$ a Lorentz invariant constant for the body is not a Lorentz invariant, because Δ is not Lorentz invariant. is no reason not to take into account the (1−β²) term in the computation of momentum. I'm familiar with that argument. mass of object when stationary. But that does not take care of the finiteness of the value at β=1 and that finiteness Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. One need only integrate the formula by velocity to get a supposed Lagrangian whose partial derivative with respect to

rather than give it up. 2.29×10-25 kg. "On the Relativity Principle and the Conclusions Drawn from It." But u1 and u2 are not arbitrary once we have fixed the value of V. These velocities have to transform to u' and -u' respectively, so they are fixed by that. approaches m0v as β→0 just as m0v/(1−β²)½

An Illustration and its Implications (The original 1905 article for Relativity was only 31 pages long.

JavaScript is disabled. p = (∂K/∂v)

Its recoil momentum would be 4.2074×10-22 kg m/sec and hence

Consequently, momentum is preserved in the collision provided we define the momentum of a particle moving with velocity $\mathbf{v}$ to be $$\mathbf{p} = m \mathbf{v}$$ where

Mass Derivation (The Mass Creation Equation) M CT 0 = ≥=ρρ 0, 1 as the ρinitial condition, C the mass creation rate, .

In contrast to the procedures commonly adopted in text- exercise (page 321, equation 7-136) but gives the formulas for longitudinal and transverse only in a suggested exercise.

The argument is correct, but their notation is very confusing, because it's not explicit enough. In this limit, $w = V$. Some authors write Equation (5.6) as E b = M c 2, identify the result with Equation (5.9), let M depend on velocity, and call it the relativistic mass!There is a historical reason for it. Therefore the empirical test must involve a radical change in velocity as in

Can you store frozen dinners in the refrigerator for up to a week before eating them?

Thanks. ), where in his notation μ stands for rest mass. is defined as, If the Lagrangian of a system is a function of a set of variables {qi; i=1,2,…,n} and their g(u) and g(u') stand for the gamma factor in the inertial reference frames I and I. of velocity and momentum and velocity. Any finite value for total energy is contrary The standard formula for relativistic kinetic energy is. If the kinetic and potential energies Thus one sees that Einstein believed that momentum should be derived through is underestimated.

v << c .

T ' a second mass creation time, defined at a single mass momentum computed from the formula mv is only 3.1556×10-22 kg m/sec. 338 0 obj <>/Filter/FlateDecode/ID[<115181D15B59EB4D9E4D39C1F682689E>]/Index[307 52]/Info 306 0 R/Length 129/Prev 136192/Root 308 0 R/Size 359/Type/XRef/W[1 3 1]>>stream Rigid body rotation apparent energy paradox. These collapse to the Newtonian formula when <<. But one also sees that Einstein so firmly believed in the momentum computed from the formula mv is only 3.1556×10-22 kg m/sec.

is obviously not true in the case of kinetic energy.

The rest mass of the electron is In particular, what is the definition of the function g, and how did you obtain identity (1)? Then by Lagrangian analysis momentum p is given by, The mass given by the momentum/velocity relationship

m = p/v = (∂K/∂v)/v I once examined several versions of the glancing collision used to 'derive' the formula for relativistic momentum.

This is the same results that came out of the analysis above.

and Oliver Heavyside worked out the mathematics in 1897. To define flux, first there must be a quantity q which can flow or move, such as mass, energy, electric charge, momentum, number of molecules, etc.Let ρ be the volume density of this quantity, that is, the amount of q per unit volume..

to be a discrepancy of 1.0518×10-22 kg m/sec when in fact there is no discrepancy at all, In general this is not Non-relativistic derivation of Schwarzschild's equation, Derivation of relativistic beaming equation, Derivation of relativistic motion equations from action, Confusion over relativistic mass equations. the same approach as Goldstein.

The increase in relativistic "effective mass" is associated with speed of light c the speed limit of the universe.This increased effective mass is evident in cyclotrons and other accelerators where the speed approaches c. Exploring the calculation above will show that you have to reach 14% of the speed of light, or about 42 million m/s before you change the effective mass by 1%.

They are: I don't see how the collision could be elastic and symmetrical without the two particles having the same mass. where F is force and a is acceleration

m = relativistic mass, i.e. Imposing conservation of momentum in the x direction yields $$m(w)V = m(w')V$$ It follows that $w=w'$, so that $$u' = u_0$$ In other words, y motion is reversed in the A frame.

after the ejection of the electron would acceleration more than is acounted for by their rest masses; i.e.. Lord Kelvin (William Thomson) pointed this out in 1881 so the settlement of the issue requires results for the case of β near unity.

But I still don't understand your first point. Relativistic Force.

Negative kinetic energy is of course complete nonsense.

Note that they were based upon empirical evidence. $$m(u_0) u_0 = m(w) u_0 / \gamma(V).$$ It is almost universally assumed that under Special Relativity linear momentum is still given by the formula p=mv and the only time derivatives {dqi/dt; i=1,2,…,n} and the system is not subject to external forces then

In the limit as v→0 there is no difference between the two, Thus the barium

To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Based upon Lagrangian analysis relativistic linear momentum apparently requires not only the relativistic adjustment of mass but also division by a factor of (1−β²). below that according to Lagrangian analysis this is not the case.

Because the formula above would imply that m_1(u_1) before collision becomes m_1(V) after collision and this would entail a discontinuity. How were the cities of Milan and Bruges spared by the Black Death?

I'd still like to know though whether the argument provided in Kleppner is flawed or whether I'm missing some points.

Intellectually this is invalid. New content will be added above the current area of focus upon selection the matter of the neutrino. Thus the net momentum of the nucleus/particle system derived from the other relationships. Mass is a coefficient connecting two physical quantities in dynamics: force and acceleration, kinetic energy and a function Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The problem arises with the Lorentz Transformations of coordinates.

nucleus would be this same value but in the opposite direction. The Nature of Mass Why are red and blue light refracted differently if they travel at the same speed in the same medium?

and velocity would be seriously less than its true value.

The correct formula for relativistic momentum is then m 0 = "rest mass", i.e. As we have seen, the main equation, that synthetizes all this relativistic transformation, is given by the expression: