We know the maximum possible speed is that of light in a vacuum. But is there a maximum possible acceleration too?
Eric Kvaalen
Les Essarts-le-Roi, France
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In general relativity and in quantum mechanics there is no limit to acceleration. But if it turns out that there is a fundamentally shortest length of time, then there would be. In particle physics, decays are usually (if not always) considered to be instantaneous. In any case, if a nucleus emits a beta particle, it ends up going at almost the speed of light, and the decay takes very little time.
John Woodgate
Rayleigh, Essex, UK
Possibly, if Max Planck was right about fundamental minimum limits on measures of distance and time. In which case, the maximum acceleration might be to get to light speed in 1 Planck time, giving 5.559 脳 1051 m/s2.
Ron Dippold
San Diego, California, US
The fundamental limit is that force = mass 脳 acceleration. We can鈥檛 apply infinite force, so we can鈥檛 have infinite acceleration. Most chunks of matter, like us, can only accelerate at a certain rate before the force required gets so big it rips them apart. I calculate that a 1 cubic metre block of most types of concrete would collapse at a sustained acceleration of 15,000 m/s2, for instance.
There is also a quantum phenomenon called the Unruh effect in which acceleration through a vacuum leads to warming by virtual particles.Something accelerating at 1026m/s2 is expected to face Unruh effect temperatures of 400,000掳C! This, too, creates a practical acceleration limit for any molecular object, as it would disintegrate.
What about something like a proton then? The Heisenberg uncertainty principle sets a limit here. It says there is a fundamental restriction on how precisely we can know about pairs of properties of a particle due to quantum effects. Take position and momentum 鈥� if you know the position really well, you can鈥檛 know the momentum well, and vice versa. Energy versus time is the relevant pair here. In 1984, Eduardo R. Caianiello showed that since the energy of a particle at rest is very well known, there is a limit on how fast we can dump more energy into it by accelerating it. In particular, the maximum acceleration is the mass (in kilograms) multiplied by 5.1 脳 1059.
For a proton, which has a rest mass of 1.67 脳 10-27 kg, that means a maximum acceleration of 8.6 脳 1032 m/s2 from rest. The Large Hadron Collider takes 20 to 30 minutes to get protons near the speed of light, so is accelerating them at nowhere near this rate.
So yes, there is always an upper limit to the acceleration of anything that depends on the mass and strength of what is being accelerated. For particles, the latter isn鈥檛 really something we need to worry about, but for larger objects structural strength is an issue.
Mike Follows
Sutton Coldfield, West Midlands, UK
The short answer, at least for photons, is that they don鈥檛 accelerate. These particles of light are emitted (or launched) at light speed. Of course, this could be perceived as infinite acceleration, which could be explained away by the fact that photons have zero mass (though they do have relativistic mass as a result of movement). But how do we explain why photons appear to slow down or speed up as they move between media with different refractive indices?
Visible light is part of the electromagnetic spectrum. Like all such radiation, one component of light is an alternating electric field. This forces electrons in any atoms it encounters to oscillate up and down in the same way that boats bob up and down on a passing wave. These excited electrons can then reradiate electromagnetic radiation as light, exactly the same as what was absorbed 鈥� but there is a slight delay. In effect, photons of light appear to be absorbed in a medium and then re-emitted a little later, so light seems to slow.
The denser the medium, the more often light is delayed, which reduces its average speed and explains why various materials have different refractive indices. It would be like driving on a motorway at the speed limit, but instantaneously stopping for a break at every service station and then instantaneously starting again. Despite travelling at the national speed limit whenever you move, your average speed would be lower.
Materials absorb photons of light when the energy to raise one of the electrons in the constituent atoms to a higher energy state is just right. As a consequence of the Heisenberg uncertainty principle, the smaller the difference between photon energy and this transition energy, the longer energy is 鈥渂orrowed鈥� by the atom and the more the light is delayed. Blue light is slowed more than red light as it passes through glass because blue is closer to the absorption energy. To extend the motorway analogy, longer rest breaks would mean a lower average speed.
To answer this question 鈥� or ask a new one 鈥� email lastword@newscientist.com.
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