• Question: Why does shining light on a particle to determine its position change the velocity of the particle?

    Asked by nightangel94 to Chris, Dave, David, Fiona, Jack on 21 Jun 2013.
    • Photo: Jack Miller

      Jack Miller answered on 21 Jun 2013:


      Hi nightangel94,

      Great question! The main answer is that light has momentum (for light, p=E/c), and can therefore impart a force on a particle (as F=dp/dt) and change its velocity. This slightly odd fact comes out of Einstein’s special theory of relativity, which (amongst lots of other things) basically says that energy and momentum are kind of the same thing. Light has energy (proportional to its frequency — E=hbar omega) and, therefore, it has energy.

      A very brief overview of the argument goes like this: relativity is all about the fact that nature doesn’t care how you look at it. If you’re a bystander watching two cars crashing head-on into each other (say), you see two cars, moving in opposite directions, whack into each other. Yet, if you were unlucky enough to be in one of those cars, you’d think you were happily sitting down, admiring a nice dashboard perhaps, when, for some reason another car decided to drive into you at very high speed. The occupants of the other car would see exactly the same thing.

      Relativity is all about studying how different things look in different “cars”, or, to use the right term, frame of reference. When energies are low (the cars are moving slowly compared to the speed of light), things behave as you expect them to — if the bystander sees two cars colliding at velocities +10 m/s and -10/ms, then the occupants of each car will see another one whacking into them at ±20 m/s respectively. Likewise, if someone in a car moving at 10 m/s let off a firework going at 400 m/s in the direction of the car’s motion, someone on the street would measure that firework as going at 410 m/s. This can be expressed in the ‘Galilean transformations’ for moving between frames of reference — x’=x-vt and t’=t — i.e., position in one frame that moves relative to another (x’ relative to x) is just shifted by the distance between the frames at a given time t (i.e. vt). Time is unaffected (t’ =t).

      When you get to go _fast_, things are different. Very different. It turns out that there’s a “speed limit” built into the universe — the speed of light, c, and as you approach c, all manner of interesting things happen. A guy called Lorentz derived the correct ‘correction factor’, let’s call it gamma, and derived updated ‘Lorentz transformations’ that work as you approach this speed limit. It turns out that:

      gamma=1/(sqrt(1-v^2/c^2))

      and

      x’=gamma(x-vt)
      t’=gamma (t-vx/c^2).

      You should notice that gamma is one for v=0, and approaches infinity as v approaches c. When gamma is one, these become the same as for the normal, Galilean transformations (as v/c^2 is really, really small).

      This has some really, REALLY odd consequences that are very important for particle physicists and astrophysicists in particular (as high-energy particles are the only thing around that move close to the speed of light). In particular, they give rise to two phenomena: length contraction, and time dilation. If you consider a bar moving close to the speed of light relative to an observer, and apply the above transformations, it’s possible to derive the fact that the apparent length of the bar in the stationary frame is shorter than the length of the bar in the bar’s frame. Likewise, if you do the same thing but for a clock, you’ll come to the conclusion that moving clocks run slow. This is why we can detect certain types of particles produced in the upper atmosphere at sea level — if time dilation wasn’t true, they’d have decayed long before they get down here.

      So, if we now think of momentum, it’s a property that something has when it moves relative to something else. If I’m running into you, I have momentum in your reference frame, and you do in mine. If, however, I’m moving along through space at constant velocity, I don’t have any momentum at all in my frame — I just have mass.

      This leads to the relativistic expression for energy when something is moving, E^2=p^2 c^2 + (mc^2)^2. Light is massless, so, m=0, and we get the expression I stated way up the top — that E=pc for a photon.

      Hope that helps!

      — Jack

    • Photo: Chris Mansell

      Chris Mansell answered on 21 Jun 2013:


      Jack has explained that light has momentum.

      When two things hit each other – in this case, a light wave and a particle – their total momentum after the collision has to equal their total momentum before the collision. Changing one’s direction changes one’s momentum. So if the light wave is travelling in a different direction after the collision (because, say, it has been reflected), then we know that the particle must also be travelling in a different direction (i.e. with a different velocity). If the light wave doesn’t change direction, it means that it missed the particle!

      Additional bits of information:

      Light also has a momentum in in the theory of classical electromagnetism, which was formulated before the theory of relativity that Jack describes.

      Even earlier than this, Kepler observed that comet tails point away from the Sun and suggested that sunlight caused the effect.

      The sun’s light hits the satellites that we use for GPS. (Sat navs and smart phones make use of GPS.) This changes their velocities and for accurate GPS, this needs to be taken into account.

      There is an idea to use the sun’s light to push (i.e. transfer momentum to) a space rocket. This idea is known as a solar sail.

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