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If rest mass does not change with $v$ then why is infinite energy required to accelerate an object to the speed of light?

Let's write the well known equations that are involved in this discussion: The energy-momentum relation: $$E^2=p^2c^2+m_{0}^2c^4$$ The relation between energy and mass: $$E_{0}=m_{0}c^2\quad\quad\quad ...
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If rest mass does not change with $v$ then why is infinite energy required to accelerate an object to the speed of light?

The answer is that velocities don't add up straightforwardly in SR. If you were in a car on clone of the Earth which was travelling at a metre per second less than c relative to Earth, you could still ...
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If rest mass does not change with $v$ then why is infinite energy required to accelerate an object to the speed of light?

In order to apply a force to an object to make it move faster (or slower), the force must be moving at the same velocity as the object. In an H2-O2 rocket engine, the fuel does travel at the same ...
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3 votes

Why using incorrect formula results in a correct formula?

It's a good question and one that has puzzled generations of students. It seems puzzling because you are coming at it from a Newtonian viewpoint but a photon is an inherently relativistic particle so ...
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2 votes

Do massless particles have gravity?

It is not strictly true that the curvature of space-time is due to massive objects. The curvature of spacetime depends on the stress-energy tensor, which includes both mass-energy and momentum. The ...
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4 votes
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Do massless particles have gravity?

And the curvature of space-time is due to massive objects. This is not exactly correct. The source of space-time curvature is the stress-energy tensor. The stress-energy tensor includes energy ...
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4 votes

Do massless particles have gravity?

Any energy or momentum-containing particle generates curvature in space-time. This is due to the fact that Einstein's field equation depends on the energy-momentum tensor $T_{\mu \nu}$ as $$ G_{\mu \...
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1 vote

Electromagnetic contribution to the mass of proton

The electromagnetic contribution to the proton-neutron mass difference is a tiny effect of $0.58 \pm 0.16$ MeV. The main contribution to $m_p-m_n$ is a QCD effect (due to the mass difference of up and ...
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How do I calculate the mass of a moving proton?

Relativistic mass $= m_{rest}+ \frac{E_{kin}}{c^2}$ Relativistic mass$ = \frac{1}{\sqrt{ 1-v^2/c^2 }} * m_{rest}$ Relativistic mass of proton is good for: Calculating force needed to steer the ...
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6 votes
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How do I calculate the mass of a moving proton?

Suppose we accelerate a proton to a speed $v$ then crash it into some large mass $M$ so that the proton comes to rest inside the large mass. Then we measure the speed $u$ that the large mass + proton ...
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1 vote

Magnetic Monopole mass-energy effect into Einstein-Field equations

Assuming Maxwell Electrodynamics, the effect is identical to an electric charge. For example, the solution of a charged black hole can also be considered for a black hole containing magnetic charge (...
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2 votes
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How can positive energy fields negatively contribute to the mass?

Suppose you have a positive and a negative charge infinitely far apart. Each charge has a field around it and that field stores energy. The mass of the charged objects will include the energy of the ...
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1 vote

Relationship between mass and the radius of curvature of space and time

What is the relationship between mass and the radius of curvature of space and time created due to the presence of the mass? It is not that simple. The curvature of space-time does not only depend on ...
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-1 votes

Relationship between mass and the radius of curvature of space and time

The relationship between mass and the radius of curvature is encoded in the following equation:\begin{align}R_\mu=\frac{2G}{c^3}P_\mu\end{align} where $R_\mu$ is the component of the radius of ...
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Paradox approaching the speed of light/Planck temperature?

In the context of special relativity, what does it mean to accelerate a proton near the speed of light? In the proton's frame light moves away at $c$ in all directions, so it's not moving. If you want ...
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Have information bits a mass-energy equivalence?

Glancing at the paper https://www.researchgate.net/publication/333751969_The_information_content_of_the_Universe_and_the_implications_for_the_missing_Dark_Matter from a holistic standpoint, and ...
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3 votes
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Is mass defect of atoms considered when the mass of electron is measured within atoms?

It's correct that the mass of a hydrogen atom is different from the mass of a proton plus the mass of an electron, but this doesn't matter since this is not how the current value for the electron mass ...
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