No Time?

 No Time

Time Dilation

Considering that light goes, well, the speed of light or more accurately, the speed of causality due to the Lorentz transform, then it must take no time to travel from the emitter of a laser to the target of an experiment after passing through a beam splitter. Relative to the photon the emission, the splitting of the beam, the diffraction grating and the collision of the photon onto the screen where we observe it happens instantly. Only to the observer does it appear to take time. Perhaps Bell was right; it already knows what the choice was (even using the delayed choice variation of this experiment).

As a quick review and for those that may not be totally familiar with the relativity equation of time and distance, time will speed up for a body as it approaches the speed of light. The following equation with the Lorentz transform in it demonstrates this feature.

T_o is the time called “proper time”, the time for the object in question, the time in the frame when the object is at rest. T(i) is the relative time for the object in motion. Now notice that when the velocity v(i) approaches c, the speed of light, then the value in the denominator approaches 0. This tells us that the object that is in relative motion will be moving faster and faster in time. Of course, to the traveller, they will see normality inside their vessel in which they are travelling and all things outside will appear to be going ever so much faster. There is a point where this relative time will reach infinity as will the mass of the object in motion and a lot of other things as well. But if we crossed that c barrier, if we could, then time would instantly be a negative number but with a complex conjugate, the square root of minus one. This means that time and space would have traded places just as after entering the black hole event horizon.

Also, the distance light travels will contract, space contracts in the direction of travel as shown by the relativistic formula of distance modified by Lorentz.

Do we have evidence which supports this? Yes! First we must explain a little bit about muons. A muon is almost identical to an electron, except that it is 207 times heavier. But it doesn’t hang around for long as it decays into other particles in 2.197µs. This has been demonstrated with the large hadron collider. Muons are produced in high energy collisions. A muon’s life is long enough so that when they are produced in our upper atmosphere, by collisions of high speed protons into the atoms, the particles reach the Earth’s surface.

With a lifespan of is 2.197µs one would think that the muon would decay before hitting the surface of the earth because even traveling near light speed they would decay in about 660 meters. What gives? Because of time dilation, time running much slower for them than for us, they reach the surface before they decay. The cosmic rays, protons, which produce the muons are traveling at near light speed and so the muons produced would also travel near that speed. When a high energy primary particle coming from space collides with a nucleus of the upper atmosphere, it generates a spray of particles which later interact in their turn. Among these secondary particles are short lived positive or negative pi mesons that decay into positive or negative muons.

...where L' is the contracted length, L_o is the rest length, v is the velocity of the frame of reference, and c is the speed of light.

This demonstrates that if you travel towards light or away from it that, relative to the observer, it will always be the same speed. But to the photon the target is just next door, at 0 distance.

There are two different experiments that bring us to see the nature of photons, or for that matter, all particles, as somewhat of a conundrum. They seem to be both wave and particle depending on how they are observed plus they can be entangled instantly ‘transmitting’ their information across vast distances. I will review the dual slit experiment here even though we are all familiar with it, just in case we have readers who may need an introduction to the situation.

The Dual Slit Experiment

If we assume that light is comprised of only particles, and these particles were fired through a slit and struck a screen on the other side, we would think that the result would be a pattern corresponding to the size and shape of the slit. However, when we actually do this experiment with a single-slit the pattern the screen shows is a diffraction pattern where the light is spread out. The smaller the slit, the greater the angle of spread.

If we now make two parallel slits the light going through both of these slits interfere, somewhat like what would happen if light was a wave as the produced pattern has a series of light and dark bands. The width of the bands is a property of the frequency of the illuminating light. But the discovery of the photoelectric effect demonstrated that light can behave as if it is composed of discrete particles.

When using electrons, a similar thing happens except with the single slit you simply get a single band where the electrons hit their target. With the dual slit using electrons you will get a diffraction pattern. The same thing actually happens with light if you were to control the release of the photons individually.

The Delayed Choice Experiment

According to the complementarity principle, a photon can be a particle or of a wave, but not both at the same time. Which one it appears to be depended on whether experimenters use a device intended to observe particles or to observe waves. It boils down to how you look at it. When this statement is applied very strictly, one could argue that by determining the detector type one could force the photon to become either a particle or a wave. When a photon is observed or when it interacts with something then it is destroyed. When a photon is detected it "appears" in the consequences of its demise, one can only observe its effects in sensor such as the cones in your eyes or a charged coupled device (the sensor of a digital camera). The photon is being absorbed by an electron in the receptor that accepts its energy which is then used to trigger the cascade of events that produces information from that device. A photon always appears at some highly localized point in space and time. In the apparatuses that detect photons, the locations on its detection screen that indicate reception of the photon give an indication of whether it was manifesting its wave nature during its flight from photon source to the detection device. Therefore, it is commonly said that in a double-slit experiment a photon exhibits its wave nature when it passes through both slits and appears as a dim wash of illumination across the detection screen, and acts like a particle when it passes through only one slit and appears on the screen as a highly localized line blur.

Given the interpretation of quantum physics that says a photon is either in its guise as a wave or in its guise as a particle, the question arises: When does the photon decide whether it is going to travel as a wave or as a particle? Suppose that a traditional double-slit experiment is prepared so that either of the slits can be blocked. If both slits are open and a series of photons are emitted by the laser then an interference pattern will quickly emerge on the detection screen. The interference pattern can only be explained as a consequence of wave phenomena, so experimenters can conclude that each photon "decides" to travel as a wave as soon as it is emitted. If only one slit is available then there will be no interference pattern, so experimenters may conclude that each photon "decides" to travel as a particle as soon as it is emitted.

One way to investigate the question of when a photon decides whether to act as a wave or a particle in an experiment is to use the interferometer method. Here is a simple schematic diagram of an interferometer in two configurations:

Open and Closed

If a single photon is emitted into the entry port of the apparatus at the lower-left corner, it immediately encounters a beam-splitter. Because of the equal probabilities for transmission or reflection the photon will either continue straight ahead, be reflected by the mirror at the lower-right corner, and be detected by the detector at the top of the apparatus, or it will be reflected by the beam-splitter, strike the mirror in the upper-left corner, and emerge into the detector at the right edge of the apparatus. Observing that photons show up in equal numbers at the two detectors, experimenters generally say that each photon has behaved as a particle from the time of its emission to the time of its detection, has traveled by either one path or the other, and further affirm that its wave nature has not been exhibited.

If the apparatus is changed so that a second beam splitter is placed in the upper-right corner, then the two detectors will exhibit interference effects. Experimenters must explain these phenomena as consequences of the wave nature of light. They may affirm that each photon must have traveled by both paths as a wave; if not so, that photon could not have interfered with itself.

Well it seems we have a conundrum here. Is it a wave or a particle and show can it ‘know’ how it is that our equipment is observing the poor little particle? Relative to the photon there is no distance between the detector and the emitter, also it travels between those two points instantly. The delayed choice experiment only appears to be a choice that is delayed relative to the people observing it and not to the photon. I propose that there is no choice.