Chapter 4.5 Interpreting mass–energy

The interconvertibility of mass and energy is a shock. We are accustomed to thinking that the world consists of some sort of stable stuff. It can move back and forth in space, or clump together and fall apart, but somehow survives all such rearrangements. What does it mean to say that this stuff is composed of motion? More poetically, are our bodies just forms of trapped motion? Are our movements just streaks of evaporating matter? Einstein’s equation does not answer these questions. It simply reports the fact that matter and energy can be converted into each other.

Lorentz’s minority interpretation offers an interesting explanation of why mass increases with speed. The idea that someone jumping from a skyscraper reaches a maximum velocity may be familiar. As the body rushes earthwards more and more quickly, it tries to push the air out of its way. But the faster the push, the more the air resists it.

Eventually there is a balance. Gravity tries to pull the body down even faster, but the air pushes back and prevents any more acceleration.

The body plummets downwards at a constant velocity, which physicists call (no pun) its “terminal velocity”.

There is an alternative interpretation of this. Instead of saying that the resistance of the air increases with the body’s speed we could insist that the mass of the body increases with the body’s speed. Both of these would imply that gravity would find it more difficult to further accelerate the falling body. Both of these are in accordance with the observed facts.

In more detail, near the top of the skyscraper gravity initially succeeds in accelerating the body. But as the body falls more rapidly we could say it responds less and less to the force of gravity and continues moving downwards only because of inertia. Since it is more difficult to make heavy bodies speed up, we could say that the body effectively gets heavier and heavier as it speeds up. That is why its acceleration dwindles to zero even though the downward force on it stays the same. In fact, at the maximum, terminal velocity, we could say that the body is infinitely heavy, since it no longer responds to the force of gravity at all.

If we did not know about the resistance of the air, and had no other way of sensing air, we might have found it natural to say that mass rises with velocity. This second interpretation is well known to physicists who study the way ships and submarines move through water. They say that such bodies have an effective mass that rises with velocity through a fluid. Interestingly, the same is true of electrons and other charged particles travelling through electromagnetic fields.

The faster the electron moves, the heavier it seems. It becomes more and more difficult to accelerate through the field. Physicists sometimes say that its effective or electromagnetic mass rises with velocity.

Lorentz suggested that the relativistic increase of mass was just such an effect. Since he believed in the existence of the ether, he concluded that rising effective masses were caused by its resistance.

That is, the ether behaves like other fluids and resists being shoved aside as bodies pass through it. Since there is so little ether in any volume of space, we do not ordinarily observe this resistance; only as bodies move extremely fast, say at nearly the speed of light, would its effects become significant.

As before, the minority interpretation is appealing because it offers a neat and persuasive explanation, but it depends on an undetectable ether.

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