What does $E=mc^2$ mean? And what does time dilation mean? I am still confused and skeptical about this formula. Can Somebody explain to me as non-academic people?

  • $\begingroup$ Why do you think the mass-energy equation and time dilation are related? $\endgroup$ – BLAZE May 28 '17 at 16:20

In highschool physics we learn that a mass $m$ with velocity $v$, has a kinetic energy equal to $\frac12 m v^2$.

This $m$ comes from the resistance to force which is defined as $F=ma$, Newton's second law. It is an "axiom", postulated but the three laws of Newton describe mechanics macroscopically with great accuracy.

$m$ is the inertial mass. The larger the $m$ the more force is necessary to move it. $m$ is invariant in Newtonian mechanics, and there exists a law of conservation of mass, so it is additive.

When velocities become very high, close to the velocity of light, special relativity is necessary to describe the mechanics. The relativistic mass , follows the rule $E=mc^2$, and the mass $m$ depends on the velocity as seen here:

relativistic mass

The effective inertial mass, i.e. the resistance to acceleration becomes even more complicated, depending on the direction of acceleration:

He defined mass as the ratio of force to acceleration, not as the ratio of momentum to velocity, so he needed to distinguish between the mass m_rel = γ^3xm parallel to the direction of motion and the transverse mass mass m_T = γX m , perpendicular to the direction of motion.

This implies that the higher the velocity nearing the speed of light limit, the "heavier" the particle is in resisting change, even though when at rest it has a fixed mass, in particle physics called the invariant mass. .

The complexity of the concept is the reason it is no longer used in particle physics, replaced by the fixed invariant mass concept, which is the "length" of the Lorenz energy momentum four vector.

Time dilation is the slowing of time due to the rules of special relativity.

The most evident case of time acting oddly in relativity, and one that has been experimentally verified, is the concept of time dilation under special relativity. Time dilation is the idea that as you move through space, time itself is measured differently for the moving object than the unmoving object. For motion that is near the speed of light, this effect is noticeable and allows a way to travel into the future faster than we normally do.

One experiment that confirms this strange behavior is based on unstable particles, pions and muons. Physicists know how quickly the particles would decay if they were sitting still, but when they bombard Earth in the form of cosmic rays, they’re moving very quickly. Their decay rates don’t match the predictions, but if you apply special relativity and consider the time from the particle’s point of view, the time comes out as expected.

In fact, time dilation is confirmed by a number of experiments. In the Hafele-Keating experiments of 1971, atomic clocks (which are very precise) were flown on airplanes traveling in opposite directions. The time differences shown on the clocks, as a result of their relative motion, precisely matched the predictions from relativity. Also, global positioning system (GPS) satellites have to compensate for this time dilation to function properly. So time dilation is on very solid scientific ground.

To really understand what is going on one needs to study a bit the current state of physics theories.

  • $\begingroup$ "and the inertial mass $m$ depends on the velocity as seen here [...]" Well, for forces transverse to the relative velocity. For forces (anti-)parallel to those forces it's $\gamma^3 m$. Which is my biggest reason for advocating against the use of relativistic mass even in cases like this where it looks like an easy way to do a problem. If haven't really told the OP what is going on until you've also explained about velocity composition and how that makes the 'effective mass' different in different directions. $\endgroup$ – dmckee --- ex-moderator kitten May 28 '17 at 17:59

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