Slashdot Mirror
Double-Slit Experiment in Time, Not Space
TheMatt writes "Thomas Young's double-slit experiment is a classic experiment that helped establish the wave-like nature of light. Since then, it has been done with atoms, buckyballs, and biomolecules. It has even been seen in a single molecule, and the single electron version was voted the most beautiful experiment by Physics World readers (covered previously on Slashdot). Now, PhysicsWeb is reporting that Gerhard Paulus and coworkers have conducted the double-slit experiment using a double-slit in time, not space. The "slit" was a crafted femtosecond pulse consisting of one-and-a-half cycles--say, two maxima and one minima--passed through an argon gas. Each maxima has a probability of ionizing an argon atom and producing an electron. The electrons were accelerated to a detector which observed an interference pattern since the detector had no idea which maximum produced the electron."
For those of you who are unfamiliar with the double-slit experiment, there is a very clear, non-technical explanation here.
This space for rent.
In this experiment we have an atom which has a 50% chance of being ionized at time t0 and a 50% chance of being ionized at time t1 (OK, the probablities cannot literally be those values but this is an example) so we have a superposition of two states - one corresponding to an atom ionized at one time and one ionized at another time. As the wavefunction for the atoms is essentially oscillatory it means that as the wavefunctions for these two separate states evolve they are out of phase with each other (or are sums of terms that are out of phase with each other). This means we can expect constructive or destructive interference depending on the exact value of t1-t0. This is what was observed.
Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
I thought the meaning of the double slit test was to prove that the single electron actually passed through both slits, and in essence interfered with itself.
But in this case we're dealing with two different electrons fired at different times, so it's not quite the same.
Even so, if the electrons create the interference pattern, that means they must have collided... in time? So the second electron reached the point of collision before it was actually fired.
Does that mean that every electron travels every possible path in space AND in time? So whenever it is possible for an electron to be fired, it does, and interferes with all other electrons fired at all other times?
My head hurts. Damn you, Science.
"Reactionaries must be deprived of the right to voice their opinions; only the people have that right." - Mao
What the double slit experiment did was allow us to show that light is both. In the experiment, one shines a pinpoint of light onto two very thin slits. The physics of waves dictate that waves will interfere in a characteristic pattern. This was later used with any matter of particles to show that the wave/particle duality, that is, all suitable small things act like waves or particles depending on the circumstances.
The experiment depends on the fact that we have no idea which slit any particular particle passes through. This uncertainty, in a certain sense, allows particles to go through both slits, which is why a single electron will interfere with itself. If we do know which slit an particle goes through, then then interference disappears. In this way we can show that particles are a wave until, in Schrödinger terms, we collapse it into a wave. So the experiment can show the duality.
So, to summarize, when the state of any particular particle is left uncertain, and certain other conditions are met, it will interfere as a wave. What they are doing here is introducing the uncertainty through a ultra-short pulse of light. There are two ways that the pulse could interact with the surrounding particles, but the universe does not know exactly which interaction occurred. There, the strange and headache producing phenomenon of the sub atomic world are allowed to manifest. I am not sure how this is time instead of space, but it is neat.
"She's a scientist and a lesbian. She's not going to let it slide." Orphan Black
Basically, you can look at light, or electrons, or whatever, as either a particle or a wave. Sometimes one interpretation will work better (light as a particle explains the photoelectric effect, light as a wave explains interference patterns, diffraction, etc). Current state of play is that the wave interpretation is always the best way to look at things, except when you observe the system everything collapses to particles, and when something mathematically inconvenient happens (you can explain the photoelectric effect in terms of waves, but the maths is horrible).
Classic two slit experiment with light consists of shining laser light on a barrier with two slits; each slit produces a diffraction pattern (http://en.wikipedia.org/wiki/Diffraction), the diffraction patterns interfere to produce the classic two slit pattern, see same link. This basically works because the laser light is coherent, you can (sort of) treat all the photons coming from the laser like one photon.
If you do this with electrons, because electrons are waves, you get the same patterns. Ditto any other particle.
Even if you do this experiment firing only one electron at a time you will get the same two-slit interference pattern, although 'common sense' tells you the electron can only pass through one of the two slits what actually happens is it passes through both at once. If on the other hand you fit a detector over one slit to register the passage of electrons, so you can tell which slit the electron passes through, you lose the interference pattern, you get two overlapping single slit diffraction patterns, which is not the same thing.
Roughly, if you have two slits and whenever an electron is fired at the slits you do not know which slit it went through, but the classical probability (what you'd expect if you didn't know quantum mechanics) of either slit is 0.5, then you will get a two-slit pattern.
This is basically the same experiment, except instead of two slits in space a little distance apart there are two possible source times for the electron, separated by a small time gap. There is no way to know whether a detected electron was produced at the first or second time, so the maths works out (roughly) the same as for the two slits in space case and you would expect to see the classic two-slits pattern. But it is kind of neat that someone's actually found a way to test that idea.
**Skip the first part if you know the basics.
If you pass a water wave through a wall with two slits in it, you will get interference. If you put another solid wall (no slits) beyond and parallel to the first wall, you will see that the water line on the 2nd wall looks like a sinewave with magnitude tapering off as you get further from the slits.
If you pass particles (electrons, photons, etc) at a wall with two slits, and place a "detecting wall" beyond the first wall, then the distribution of electrons hitting the detecting wall would be similar to the wave observed against the 2nd wall in the water example.
--New Experiment--
In the new example, two pulses of light can trigger an electron to be released. Think of these two pulses as pulling a trigger on a gun while playing russian roulette. The electron is the bullet and the detector is your head. If you pulled the trigger at 0 secs and 2 secs, you'd expect to see a person die at 0.01 seconds and/or/neither 2.01 seconds, assuming it took 0.01 seconds for the bullet to reach the person and kill him.
The detector, however sees an interference pattern. This is like seeing deaths at 1 second or 1.5 seconds. The interference pattern is measured as a function of time, and instead of seeing two blips in time, they saw a range.
Cagle has been peddling this theory for quite awhile. Do a quick search on cagle in any of the sci.physics groups and you will see his posts along with extremely patient people who try to point out the flaws in his logic (cough!).
We defeated the Nazis, the next evil: Libertarians
Who is this "We" you refer to?
And since when do people who work hard to support civil liberties get lumped in with people who work even harder to take then away?
I think you need to spend a bit more time at Cato's website and learn what Libertarianism really represents. (Hint: diminished state control of our lives)
"Rocky Rococo, at your cervix!"
Wait, rotating in one dimension? I assume that in layman's terms, one dimension would best described as a line, with a single point being dimensionless. So in order to rotate in one dimension... what? You can move up and down a line with respect to some point, but that's linear movement!
Yeah, I think you're right. No idea of your credentials, but the physicist often is right in such discussions.
The double-slit experiment classically involved sending light through two small slits closely separated, onto a dark screen. If light was particulate, you'd expect to see only two bright spots on the screen. But you see a whole interference pattern, with the brightest spot located between the two slits.
This is because of diffraction, and that light acts like a wave, so you get constructive and destructive interference on the screen.
What we didn't know until the 20th century is that light consists of photons, which are individual quanta of electromagnetic radiation. These photons interfere with each other in space as they go through the slits, to give the characteristic interference pattern on the far screen. Or, that the photons don't go through a single slit, but the photons actually go through both slits, and you don't know where the photon is until you measure it (ie, let it hit the screen).
The current experiment effectively used a laser to create two 'slits' in time. They made two quick laser pulses (really two maxima and one minimum). The pulses have some probability of creating an electron, and by making two discrete pulses in time, there is a similar 'interference pattern' associated with observing the electron at various points in time. This means that the electron wasn't created from one laser pulse or the other, but was effectively created through both slits, the time separation of which created an interference effect.
There's no new quantum mechanics here, but here's an attempt at a layman's explanation of what's called the propagator. In classical mechanics you have a well-defined trajectory from a set of well-defined initial conditions (ie, a ball on a spring has a well-defined position and momentum at some time, and you can exactly predict where the ball will be at future times). See this article for example.
Quantum mechanics extends this because there is a classical path the ball would take, but also infinitely many other 'quantum' paths that can also bring the ball from position X at time 0 to position Y at time T. Many of these are classically impossible. But Quantum Mechanics deals with a wavefunction (which describes the state of the system) which is complex. So you need to consider all these other paths too, but each path has an associated phase with it. When you maintain this phase coherence between all paths, you are basically building a similar interference pattern. So when you take the modulus squared of the wavefunction to find the probability of finding the electron, you have interference from the wavefunction going through either of the two slits in time.
The difficulty is that you have to repeat the experiment many times to see when you measure the electron, just like w/ the classical double-slit experiment you need enough photons to give a relative intensity that can be measured.
Here's a little math for anyone curious. The time progression of a wavefunction looks like
|Psi(t)>=exp(-i*H*t/hbar)|Psi(0)>
where |Psi(t)> is the wavefunction at time t, i is the square root of negative one, H is the Hamiltonian Operator, hbar is the Planck constant. See here for more information on the Hamiltonian for classical and quantum mechanics. In many cases it's the energy operator (expressed in terms of position and momentum), and acts on discrete energy eigenstates.
But you can see that time translation evolves the 'phase' of the wavefunction. And if the wavefunction isn't in a single energy eigenstate but a combination of them, each individual component will have have the phase evolve at a different
Comment removed based on user account deletion
No, time isn't a wave. As another poster mentioned, time is another dimension.
But it's much more tricky than that, time is very different from space. If you rotate a vector in 3-D space, it's length (x^2+y^2+z^2) will remain the same, even though the x,y, and z components are different and kind of mixed together. What Einstein showed is that in 4-dimension space-time, the quantity (-t^2+x^2+y^2+z^2) is what is conserved if you 'rotate' in 4-D spacetime (in other words, if you change reference frames, like going from standing on the ground to standing on a freigh train). So spatial dimensions look spherical while the time dimension looks hyperbolic.
There are obvious parallels between Space and Time in non-relativistic quantum mechanics, namely a time translation evolves the wavefunction by a factor exp(-i*H*t/hbar) and a spatial translation evolves the wavefunction by a factor exp(-i*p*x/hbar). What this means is that momentum is the 'generator' of space translations, and the 'Hamiltonian' is the generator of time translations.
But making relativity works in quantum mechanics isn't as straightforward as physicists hoped, and involved alot of extra work, which finally culminated as quantum field theory. You can read more detail here . But here's a quick summary :
In quantum mechanics, position and momentum aren't just parameters but are operators. They don't commute, which is why you cannot simultaneously know a position and momentum. But time is NOT an operator, it is a parameter, it's the corresponding Hamiltonian that is the operator. So you have 4-dimensional space, 3 dimensions act like operators, 1 dimension acts as a parameter.
So anyway, back to this experiment, what the physicists did was to show that an electron, with a probability of being created during two discrete times (each of the laser pulses) turns out to have an interference pattern just like photons traveling through two slits in space.
The resulting electrons weren't produced from laser pulse 1 or laser pulse 2, but were produced from a superposition of both pulses, and the complex phase that I showed previously with time evolution causes an interference pattern between the two pulses.
We already knew that particles are also waves... What does this experiment show us that's new? Does it show that two particles are a wave, or something?
It tells us nothing new about waves and particles, but it does confirm that there is no difference between a pair of slits separated by space and a pair of slits separated in time.
IOW it confirms that time is just another dimension.
You make the mistake of thinking you can educate the fundamental stupidity out of people. You can't.
You do sound like a Physicist :)
Actually, Mathematicians don't say that. Mathematicians say that a closed curve is homeomorphic to S^1, and a line to R^1, ie, there exists a bijective, bicontinuous mapping between the sets.
The "topology" of a space is actually the set of all open sets in that space. (Which trivially could not be a set like S^1.) In essense, the thesis of general topology is that all continuity related problems can be redefined in terms of open sets. If you'll recall, in classic analysis an open set is defined as an open ball with respect to the metric of the space in question. This produced spaces that while perhaps not equivalent to R^n were very similar in many ways, in particular because there existed a way to meaningfully define the distance between any two points.
In topology, we do away with the metric definition of an open set entirely, and leave the concept of an open set essentially undefined (well, subject to a few sanity restrictions involving unions and intersections of open sets). This allows mathematicans to study spaces that really are nothing like the ones we experience regularly, and the vast majority of them are really, really unfriendly, which is one of the reasons that topology is the course that scares many math majors away.
However, it gives way to Algebraic Topology, which is without a doubt one of the most beautiful branches of pure math.
Physics is cool and all, if you're not quite bright enough to make it in Math. Ha ha. *jab*
A fine summary, but I'm going to nit-pick on the order in which the experiments were done.
What the double slit experiment did was allow us to show that light is both.
The double slit experiment showed us that light was a wave. This understanding allowed a Grand Unified Theory of Optics (not that they called it that) which explained reflection, refraction and diffraction in terms of waves.
We didn't know light was both until Einstein's 1905 paper on the photoelectric effect (for which he won his Nobel.)
For electrons, it was the other way around. First we knew they were particles, then the electron double split experiment proved that they also behaved as waves.
Quattuor res in hoc mundo sanctae sunt: libri, liberi, libertas et liberalitas.