Location or Momentum

Bruster Rockit: Space Guy!                           by Tim Rickard

A key element of quantum mechanics is Heisenberg’s uncertainty principle, which forbids the simultaneous measurement of the position and momentum of a particle along the same direction, as so aptly illustrated by Tim Rickard above. 

  for a photon, where E is the energy, c is the speed of light and p is the momentum.    So the momentum of a photon is equivalent to the energy of the photon divided by the speed of light or p =  E/c  where E is also related to the frequency of the photon by Planck’s Constant E = hf.   h is Planck’s constant and f is the frequency assigned to the photon.   f is also related to the wavelength of the photon by f = c/λ.  

So E = hc/λ = cp       Therefore    p = h/λ

But we know the values for both h (6.26×10^-34 joules sec.) and for λ if we know the color of the photon.  Usually if we are dealing with coherent light (red laser for example) then we know the wavelength λ very accurately.   Thus we know the momentum very accurately.

There is another factor in this equation – spin angular momentum of the photon which is independent of its frequency.  Spin angular momentum is essentially circular polarization for a photon.  Angular momentum is ±h/2π.   It is the helical momentum of the photon along its flight path.   In order to pin down the momentum we also need to know its angular momentum, but it is a constant that is either spinning one way or the other, no half spins no quarter spins just +h/2π or -h/2π.   

The key for this discussion is that we know the momentum for any photon if we know its wavelength.   p = h/λ and the direction of its spin ±h/2π.   According to Heisenberg’s principle we cannot know the location of the photon if we know its momentum.  Since we do know its momentum we are at a loss to try to pin the location to a particular spot such as through a narrow slot or pinhole.  

Whenever we try to fit a photon through a slot, we are trying to pin down the location as it goes through the slot.  The narrower we make the slot the closer we are trying to pin it down.   Nature resists by causing havoc with our measurements – fuzzy behavior/weird effects.

Pair Production

Pair production is a possible way for nature to slip one by us – putting a photon through both slots simultaneously, thus confounding our measurements completely.   When a photon hits an obstacle such as the thin barrier between the two slots, it melds through the slots around the barrier as in my earlier posts or possibly down-converts to a lower frequency pair of photons (or up-converts to a higher frequency) through pair production (conserving energy by the frequency change).  These pairs recombine on the far side of the barrier through an up (or down) conversion process causing an effective interference due to jiggling in the conversion process. 

Our barrier strip knocks the photon silly, and it responds by splitting up, zipping through the two slits independently, then recombining in a way that looks like interference.

Virtual Photons 

Another type of pair production would be through creation of a virtual photon – a pair with one real and one virtual as also mentioned in an earlier post.   The scenario is the same – barrier knocks photon silly, virtual photon forms, passes through other side, then effectively recombines while interfering with the “real” one.   The original and virtual photons could actually be down converted or up converted photon pairs that recombine by up or down conversion causing interference-like behavior.

In either case, blocking one slit or the other would prevent melding and also prevent pair production as well as the formation of virtual photons.

Pair production through down/up conversion and/or virtual pairs would fit better with particles with mass acting like waves that cause interference when passed through slits.  Even bucky balls and cats could potentially form virtual pairs if moving close to the speed of light.   Well, again, maybe not cats.

 Oldtimer

Virtual Particles – A new look at double slit weirdness

I was looking at a web site by Hitachi Global concerning “Advanced Research – Electron phase microscopy” today.   They have a neat movie based on the diagram of an electron microscope which you can find here:

(link to diagram)     http://www.hitachi.com/rd/research/em/doubleslit-f1.html

 These pictures are theirs and are copyrighted by them so all that can be done is show you the link.

Here is a link to their video of the results of a 30 minute run (sped up to just a minute or two):

http://www.hqrd.hitachi.co.jp/rd/moviee/doubleslite-n.wmv

They send electrons one at a time from the source, about 10 per second.  Those that make it around the rod are detected and displayed on a monitor.  

 After about 20 minutes, clear interference patterns develop on the monitor as shown in their video.   

The electrons are accelerated through 50,000 volts, and achieve velocities about 40% of the speed of light.

 These electrons appear to be passing simultaneously around the barrier and interfering with themselves.  Either that or they have some sort of lingering effect due to ctime as I posted in a recent article.   I have a new thought:

Virtual Particles

I believe that there is one obvious answer to such a weird quantum effect – virtual particles.   Photons and any particle achieving significant relativistic effects, such as high speed electrons, atoms, molecules, bucky balls, cats, and anything that can be raised to near the speed of light can also produce companion virtual particles – virtual photons, electrons, etc. when their flight paths are significantly disturbed.  (Well maybe not cats, but who knows?)   

We are getting into new theory here with a new thought experiment!   If an electron such as those in an electron microscope is accelerated to a high enough speed is then jostled by close encounter with a small barrier, it will generate an identical virtual electron on the other side of the barrier.  This applies to any particle raised to relativistic speeds.  If the other side of the barrier is closed off by a detector, then the virtual particle disappears without effect on either the detector or the original electron, being absorbed by the barrier along with the original electron.  If the barrier is open, however, it recombines with the electron after passing around the barrier to produce an interference with itself during the recombination process.

It is similar in effect to the process described in my Quantum Weirdness – Part 2 Double Slit Weirdness post whereby the photon melds around a slit.  Perhaps it is not a meld but a virtual photon recombination – the effect would be the same.

A photon, or any relativistic electron, or other particle jostled by the fields around atoms in a close encounter with the edges of a slit or other barrier would generate a virtual photon, electron or particle that would appear on the other side of the offending barrier and then recombine at a point downstream to cause an interference.   Barriers that block the other side would kill the virtual particle.   A particle that did not exist long enough to recombine with its generating particle would die without causing any effect on the offending detector or barrier.    Only particles that come close enough to be jostled by the fields of the barrier atoms would generate virtual particles on the other side.  Others not close enough to the barrier to be jostled by it would not create the virtual particles.

It is my thought that where there is such jostling, both the particle and its virtual particle might die in the edge of  the barrier if one or the other side were not open, and only those electrons that are far enough from the barrier to not create a virtual pair would continue through the open port to the screen, and thus not show any interference pattern.   

Only if both sides are open would a virtual pair survive a close encounter with a barrier and then be attracted together to recombine on a path toward a pattern maximum.   Scattering around the maximum would be a result of random spacing of near misses and pure chance.

It is another thought that if an electron is buffeted by a barrier and survives the trip but its virtual electron is lost in the material of the barrier, the electron that survives will still be affected by the virtual particle at the point of its destruction, perhaps its phase or displacement or both.   It just won’t show an interference pattern, but it would show some effect of the structure of the barrier material at the point the virtual particle is destroyed, making it possible to “see” the structure of the material within the barrier itself.  Maybe that is just a description of how an electron phase microscope actually works.  The phase is changed by the destruction of the virtual electron and that change depends on the structure at the point the virtual electron lands. 

Copyright 2007,

James A. Tabb

Marietta, Georgia

Quantum Weirdness – A Matter of Relativity? Part 5

Quantum Weirdness

A Matter of Relativity? 

Copyright 2006/2007 James A. Tabb

Part 5: Entangled Particles 

Selecting which atom we use with careful attention to its excitation states can create entangled particles. Some atoms emit two photons at a time or very closely together, one in one direction, the other in the opposite direction. These photons also have a property that one spins or is polarized in one direction and the other always spins or is polarized at right angles to the first. They come in pairs such that if we conduct an experiment on one to determine its orientation, the other’s orientation becomes known at once. They are “entangled”.

Figure 10 – Entangled Particles  

All of this was involved in a famous dispute between Einstein and Bohr where Einstein devised a series of thought experiments to prove quantum measurement theory defective and Bohr devised answers. The weirdness, if you want to call it that, is the premise that the act of measurement of one actually defines both of them and so one might be thousands of miles away when you measure the first and the other instantly is converted, regardless of the distance between them, to the complement of the first.  

Action-at-a-distance that occurs faster than the speed of light?  Some would argue (me for instance) that this is more of a hat trick, not unlike where a machine randomly puts a quarter under one hat or the other, and always a nickel under a second one.  You don’t know in advance which contains which.  Does the discovery that one hat has a quarter actually change the other into a nickel or was it always that way?  Some would say that since it is impossible to know what is under each hat, the discovery of the quarter was determined by the act of measuring (lifting the hat) and the other coin only became a nickel at that instant.   Suppose one hat is in Chicago and the other in Paris.  Is this action at a distance? It is easy to say that the measurement of the first particle only uncovers the true nature of the first particle and the deduction of the nature of the second particle is not a case of weirdness at all.   They were that way at the start. However, this is a hotly debated subject and many consider this a real effect and a real problem.  That is, they consider the particles (which are called Einstein‑‑ Podolsky‑Rosen (EPR) pairs) to have a happy-go-lucky existence in which the properties are undetermined until measured.   Measure the polarization of one – and the second instantly takes the other polarization.A useful feature of entangled particles is the notion that you could encrypt data using these particles such that if anyone attempted to intercept and read them somewhere in their path, the act of reading would destroy the message.

So there you have it – Weird behavior at a distance, maybe across the universe.   Or is it a matter of relativity?

I wish to suggest this: entangled particles are entangled at the time of emission and, from the relativistic perspective, they are still attached together at the point of emission until the time that one or the other is disturbed or destroyed, however far that is. Both ends of their flights are stapled together from the moment of their creation by relativistic space distortion. They both live in a go-splat world where time stands still and everything in their path is zero distance away and zero time lapse away due to the relativistic foreshortening of paths and time distortions to zero. In their time and distance collapsed world, if you can wiggle one, the other knows about it because they are both still stuck against their common emission point at one end until destroyed at the other.   There can be “real world” time elapsed during flight (from our perspective) but the photon is running on null time – relativistic zero time and both are still attached to a common point with both ends separated by zero distance and zero time, even if we measure it at tens of meters and dozens of nanoseconds. 

In Summary – Not So Weird After All

Photons and other particles that travel at c have paths that are effectively zero length and time spans that are of zero duration.   This applies to the path length and lifetime of the particle due to relativistic space time warping at c.   No matter how we measure the time and distance a particle travels in a real-world time frame, the particle has a simultaneous, instantaneous path and duration due to the warping of the space and time at c.

We measure the particle in flight at about a nanosecond a foot.   No matter.  The photon gets there instantaneously – no time elapses for the photon – no ageing takes place.  That means no matter how many mirrors or detectors we flip into or out of a path during our calculated flight time, the photon, traveling at c, transverses the entire path in zero time over zero distance.  Our perspectives are that different.   Mirrors or detectors that are in the path at the time it reaches a certain point by our measurement, were experienced by the particle at the instant it was emitted.   So it knows about it “in advance” due to the space time warp factor.   It does transverse the experiment, but cannot be fooled as it knows the entire path the instant it is created. 

Suppose a distant exploding star emits a photon that arrives at our telescope 4 billion years later (by our normal world calculation).  The photon may pass around lensing galaxies on both sides at once because the entire path, including the incredible width of the galaxies, is of virtually zero width and zero depth to the photon which is traveling at c.   The detector’s position, forward of a focal point or behind it, is also experienced by the photon during that same zero path, zero lifetime defining moment of creation, life, and death.  All due to the incredible time and distance warp at c.  So we think it is weird that the change in our detector, at or behind the focal point seems to affect the chosen path of the photon around the distant lensing galaxy.   Not to the photon.  It knew all along, since “all along” was an instantaneous null time and null distance, warped together.

Photons moving through a double slit experiment have all the elements in its path effectively (although not actually) plastered to its nose and all the elements have zero width and zero depth to the photon during its lifetime.   From our perspective, we consider it moving through the experiment, encountering edges, slits, possibly mirrors or detectors.   Whatever we throw in its path, the photon experiences it as if it were there from the moment of its creation because that is the only moment it has.   All because it lives in a relativistic go-splat world.

Photons moving through crystals and reversed crystals see all the paths simultaneously and its entire flight path as one event – all happening simultaneously.   All open paths are valid because they are essentially congruent, allowing the photons to retain their polarity if there are paths that maintain its ability recombine at the far end.  If any path is broken by a detector when it would pass by in our real world measurement system, then it is encountered in its relativistic world during its null time existence.

Quantum Weirdness Is a Matter of Relativity! 

James A. Tabb

Marietta, Georgia

Originally published among friends February 6, 2006

Quantum Weirdness – A Matter of Relativity? Part 4

Quantum Weirdness

A Matter of Relativity?

Copyright 2006/2007 James A. Tabb  

Part 4: Photons that hit tilted glass

Individual photons directed at tilted glass have an option of being reflected or going through. They can’t do both because they can’t be divided, or so we are told. Yet some experiments seem to imply that they sometimes take both paths unless a detector is in place. It is my thought that the foreshortened world of the photon explains this phenomenon too  

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Figure 9:  Photons on tilted glass

 

Relativity at Work 

Because the photon is moving at the speed of light, the entire path from emission to destruction has zero length and zero time passage.   Time and space are both warped while it is in flight.   It does not matter what we measure or calculate.   The entire experimental assembly is to the photon like a flat surface with all the options congruent to the front surface, that surface being stuck to the point of its emission, and shrunk to zero thickness, glass, air paths, mirrors and all. All the open paths are the same length (zero) to the photon, regardless of how we measure them.   

   

If a detector is in place, it is in the way immediately, independently of distances and times as we measure them. The photon is instantaneously (from a relativistic perspective) connected to the screen by all optional paths that lead to the same points, and the photon separates without breaking until it begins to meld together somewhere. Otherwise it takes one path or another and still gets where it is going.   

There is an argument that the photon must go through the glass whole since the photons transmitted through the glass are actually retransmissions within the glass, not the same photon that impacts it. That argument then says that the other path has to either have had no photon or a whole one also (creation of energy not allowed). It also says that the photon must retain a whole packet of energy.   

My argument is that the entire path, including the glass and the remaining path through the experiment all the way to a recombination point is impossibly thin to the photon at the time it hits it.   There is no separation because the paths are zero distance apart.  This argument also avoids the messy retransmissions within the glass argument, as they are not necessary.  

It can then “feel’ itself through this very thin apparatus. It is thus capable of separating into two paths that recombine at the proper point before the photon separates at the surface of the glass. This keeps the photon whole and yet allows it to take multiple paths.  

Our perspective seems to be that the flight path is of finite duration and the paths seem to be of vastly different lengths. Thus we don’t always understand what is happening. The photon could care less about our perspective – it is working within a highly warped time and space and we are not.  If it finds a way to recombine without violating its energy conservation directive, it will do so even if a portion of it separates at the glass, wraps around the various mirrors and recombines with a portion that is passing through the glass. That is ok since the total distance of its flat world is still zero and the physical recombination takes place before the physical separation takes place.  United they move!   

The experimental apparatus grows as the photon passes through it.  Those parts in front of the photon are still stuck to its nose and of zero remaining depth.  Those parts to each side of the photon have normal depth and structure.  Those it has passed are invisible and forever behind it, vanished.   When it hits a glass surface, all the paths in front of and also along its reflected paths are plastered as if congruent.  Thus all open paths are available at that instant.  If any are closed, then those paths are not available for passage.     

Even where a detector is switched in (from our perspective) after it passes through the glass, it is a closed path to the photon at the glass surface because the entire path has zero depth the instant it is emitted due to the photon being at c throughout its entire path.   Indeed the path with the detector is closed when it is emitted, as all the paths are of zero depth the instant emitted, even if the photon is switched in at some later time (from our perspective).   Relativistic foreshortening is instantaneous to an object running at c.  This is all taking place in a space-time warp where length is zero, time is zero for the photon’s flight but not for us, the stationary observers!  

The difficult thing to wrap our minds around is the fact that the instant the photon is emitted, whether on a distant star, or on a filiment within our laboratory, the entire path that it takes occurs at the same instant of time throughout its path, birth, flight, death – all instantaneous to the photon (no matter what happens within that path in our “normal world” time-frame) .   If a detector is absent at the instant the photon is emitted and then switched in later before it arrives (from our normal world perspective), the photon is fully affected at the instant of emission (from a relativistic world perspective) as if it had been there the whole time, and thus the outcome is determined at that instant, not when we think it has passed.   It cannot be fooled.  

It is all a matter of relativity 

Next:  Entangled particle weirdness explained.

 

Quantum Weirdness – A Matter of Relativity? Part 3

Quantum Weirdness

A Matter of Relativity?

Copyright 2006/2007 James A. Tabb

Part 3: Polarized Light Weirdness

Figure 7 shows calcite crystals in which the light is split into two parts, a horizontal (H) and a vertical (V) channel. If we send individual photons through, they go through only one channel or the other, never through both, and those that come out of the H channel are always horizontally polarized, those that come out of the V channel are always vertically polarized as we might expect.

Figure 7. Photon in Calcite 

It is possible to orient photons to other angles at the input. One such arrangement is to adjust them polarized so that they are tilted 45degrees right or left. If we orient the input to 45 degrees, tilted right (+45), we get half of the photons coming out the H channel and half out of the V channel, one at a time, but these are always horizontal or vertical polarized, no longer polarized at +45. 

 

Figure 8. Reversed Crystals

Now comes the weird part as shown in Figure 8. If we put a second calcite crystal in line with the first one, but reversed so that the H channel output of the first goes into the H channel of the second and the V channel output of the first goes into the V channel of the second, we expect the output to consist of one photon at a time (and it is), but since the first crystal only outputs H or V polarized photons we expect only H or V polarized photons out of the second crystal.

However, if we test the polarization of the output, we find that the photons coming out are oriented to +45. Individual photons go in at +45 at the input, become individual H or V oriented photons in the middle, but come out oriented +45 again at the output! Somehow the two channels combine as if the individual photons go through both channels at the same time, despite rigorous testing that detects only one at a time.  Quantum weirdness at work.

The polarization problem, like the double slit problem, is often called a quantum measurement problem. An often-quoted theory is that the photon does go both ways, but any attempt to detect/measure one of the paths disturbs the photon such that the measurement results in a change in the path of the photon.

Relativistic Effects Again

When you apply relativistic effects to this scenario the effect is exactly the same. The calcite crystals and all the paths are initially zero length as the photon approaches them.

The crystals and the paths expand as the photon enters them until the photon spans them end-to-end of the entire experiment. The two paths are separated by zero distance and have zero length and can be treated as if they are only one path. The experiment has no depth.

Much like the case of the double slits, if the paths are complete such that the edges of the photon can “feel” itself through the crystals when it hits them, it partially separates and then melds together at the front to recombine without ever becoming two parts while maintaining its integrity, in this case +45.  If the paths are not complete, it is forced to choose one path or the other. When it is able to meld around a path, the recombination restores the wave polar orientation.  When it can’t, the recombination does not occur and the polar orientation is destroyed.

Once again, the effect is due to the relativistic effects of time dilation and length distortion/contraction for the photon.

Next:  Photons that hit tilted glass weirdness explained. 

Does Time Exist?

There is no question that we experience what we call time.   There is a precision with which we can measure the progression of events over time that is phenomenally accurate.   Things age and particles decay over “time” and it is consistent.    However, physical laws that use time as a reference work equally well for time reversal – going backward – a particle hitting another particle, generating other particles and emitting photons will work just as well running backward according to physics.   We just have never experienced time reversal and this disconnect with the laws of physics seems to be a mystery.  This disconnect is used by many to express the opinion that time exists.   However the fact remains that equations of space and time break down at certain points and time falls out of some of them as an unnecessary factor.

Think of this: photons live in “null” time.  They live and die in the same instant because they travel at the speed of light and therefore if time exists for them, they do not experience it.   They experience zero flight time over zero distance no matter how far apart the start and finish line are.  They live in a go-splat world.    A photon leaving a star a billion light years away destroys itself in our eye the instant it is emitted, having not aged even a fraction of a nanosecond in its long trip.   Space and time are that warped!

The space and the time have been warped because of the speed of the photon.  It travels at the speed of light.   Our very definition of speed involves time so when we say the speed of light we assume that time exists, but for the photon time does not exist.  

A photon experiences zero distance and zero time due to its incredible speed.   Every photon that lights our office or illuminates our book arrives the instant it is emitted.  It has not aged even though we can calculate that it moved from the bulb to our book and then to our eye at about one nanosecond per foot of travel.  The photon did not experience the “time” that we measure or calculate.  It aged not at all.  Time does not exist for any particle moving at c.  It only exists for us as calculated or measured in a laboratory.  But does it exist as a real dimension?  Does it have a physical basis?  

A photon in flight between point a and point b is invisible to any and all observers.  It does not exist in flight and can only be detected at b when it actually arrives.   The photon in flight experiences null time – time zero – no time – non-existent time, and travels a null path – or no path at all, regardless of the length of its travel.   Time for the photon does not exist, nor does distance.  Those measurements of time and distance for the photon are for our domain only – the human one.

Now consider an extension of that thought – most of the particles that make up our world vibrate and exchange energy with each other.  That occurs even at temperatures close to zero.   There is also a froth of virtual particles that pop into and out of existence continually at all times even in a so-called perfect vacuum.     All the energy exchanged through photons is timeless because all photons are moving at c.   Even gravity moves at c.  Gravity is also timeless within its self.   The exception is for atoms that bump into each other and exchange energy through vibration and bumping.   Or do they?   Do they actually touch or isn’t there an exchange of particles  moving at c that keep them apart?

If the energy transfer by photons is timeless, the photons are timeless, gravity is timeless all due to the speed of light as experienced by the particles that carry them, then does time exist or are we merely measuring external events by counting uniform progressions that we experience and can see?

I know and acknowledge that we can measure the speed of a photon to a very high precision.  I know that we can measure the speed of gravity as other planets tug on ours and on each other.    The measurement is based on the progression of the components of our clocks.   We do live in a dimension that experiences progression of events in one direction which we call time.  

However, we can measure but we cannot see.  We can observe the effects but not the event.   The truth is that whenever something is traveling at c, simultaneous observations are impossible.  Every observer of the same event sees something different.    Have you ever seen time?  Maybe the change in a clock, which is actually only a measure of repetitive events, whether a wind up (measuring escapement events) or a NBS clock counting cycles of an atomic nature, but not time.  We can’t see time, only experience it.  We can’t measure time, only define it.

Time for us may be just a projection of ourselves on a line defined by a progression of events that occur in a uniform manner, but it may not really exist.    We are bundles of energy made up of atoms and particles in extraordinarily rapid motion.  Take us down to the quantum world and we are made up of many quadrillions of particles exchanging energy among themselves in mostly empty space.    In such huge numbers there is an average motion and an average progression of events that may make up our concept of time.  Certainly our most accurate “clocks” are merely counting cycles of an atomic nature.   Even the National Bureau of Standards admit they are “not measuring time, but only defining it“.

Does time exist just for us because we experience this progression in a uniform manner? Perhaps it is not actually an extra dimension as we have been so often told.

Do you think time exists as a dimension in the same manner as x, y, z?  Is time real?  If you have been following my last two posts, you will understand it is the lack of time, at least on the photon level, that explains quantum weirdness.   And explains it well.

What do you think? 

Oldtimer

PS:  here are some other articles by Oldtimer on the subject of time

Enjoy!

Quantum Weirdness – A Matter of Relativity? Part 2

Quantum Weirdness

A Matter of Relativity? 

 

Copyright 2006/2007 James A. Tabb 

Part 2 – Double Slit Weirdness

When a proper light source (coherent – light from a single source all at the same frequency) is placed in front of a screen with a narrow slit, the light is diffracted (spread out) as it goes through the slit and appears as a shaded band centered on a screen or photographic film. The light is scattered and/or bent by the edges of the slit as shown in Figure 3.

Figure 3. Single Slit Diffraction

 If we add two more slits located side by side between the first slit and the screen, the light passing through each of the new slits is diffracted again such that the photons from each slit are bent across each path and combine to reinforce or cancel each other where they strike the screen.

 

Figure 4. Double Slit Interference

The result is an interference pattern (light and dark bands) on the screen as shown in Figure 4. If you block either of the two middle slits, the interference pattern disappears. If a photographic film replaces the screen and the intensity is reduced so that only a few hundred photons are sent through the double slits before the film is developed, the interference pattern will be made up of individual dots organized in a pattern that duplicates the interference pattern. Keep the film in place long enough and the patterns become more complete. Put a cover over one of the slits and the film still shows dots, but no interference pattern, only a diffraction band. Put a detector in one of the slits and the interference pattern also disappears.

Now if the light source is reduced in intensity enough to send only one photon at a time, a weird result can be seen if the photographic film is left long enough (days or even months in a very dark box) where both slits are left open. The interference pattern continues to develop on the film, even though there is no possibility of interference (or even photon bumping) unless the individual photons go through both slits somehow.

Part of the current explanation is that the photon goes both ways, but any measurement (putting a detector in the path) always disturbs the measurement. In fact a whole class of quantum theory has developed around the inability to make precise measurements due to the measurement disturbance problem. How do we explain this quantum weirdness?

A Matter of Relativity

There are two processes going here. One process is the real time that our experimenter sees, about 1 nanosecond per foot of photon travel. The photon is traveling through the experiment with real and measurable delays from the emitter to the first slit and from there to the double slits and from there to the film. The other process is that the photon’s relativistic path is zero so it is in contact with the film and the emitter at once and all of its paths in between are of zero length and require zero time. All paths that can lead to the same path are conjoined. Time of flight and distances for the photon expand only as it passes through the setup. The photon and the observer see simultaneous events differently. All the events are simultaneous to the photon, but none are to the experimenter.

All the elements of our experiment have no depth and seem to be congruent as if they were paper cutouts that have been bonded together with the emitting source. As observers, we can’t see it. As the photon leaves one element of our experiment, such as the first screen with one slit, the double slits are squeezed down to a point and plastered across its nose. The photon easily fits across both slits of the second screen as the distances to them are zero and thus the distance between them is also zero. Indeed it fits across the entire second screen, but the edges are less distorted. Since the photon is also plastered across the slits, everything behind the slits is also plastered there – the entire path is available at one instant as in Figure 5 a. The photon is able to take all paths (even simultaneously) that lead to a common point because they are all in front of it as it enters our experiment, and zero distance separates all the paths. No amount of fiddling with flipping mirrors or detectors will fool the photon into disclosing its path because the mirrors and detectors are also plastered to the photon’s nose throughout its (instantaneous) flight. The mirrors and detectors are in place when the photon makes its decision or they are not. The result is path shut or open.

As the photon moves from the first screen to the second, the second screen moves with it (attached to its nose) until it reaches its normal (real world as we see it) dimension and then expands as the photon moves into the slits as in Figure 5 b. Portions perpendicular to the path of the photon become normal size and atoms from the edges again buffet the photon.  Everything behind the photon is of no consequence, gone – vanished.

Figure 5. – Relativistic Double Slit

 From the relativistic point of view, the photon has a number of crisis points such as within the first slit. As it passes through the first slit, the atoms at the edge of the slit buffet it and the photon’s path is randomly diffracted from the original path.   The slit has grown to normal size (perpendicular to the photon’s travel) but now the photon is virtually attached to the entire screen containing the double slits in the background that represent the next crisis point or wakeup call. If neither slit is blocked, it has an opportunity to go through both.

Figure 6. Photon Recombining

I see the photon as being a packet of energy that obeys the laws of conservation of energy. It flows around the barrier between the two slits only if it can recombine on the other side without ever completely breaking into two separate pieces. It behaves almost like a perfect fluid and leaks through where it can, but unlike a perfect fluid, it cannot separate into multiple “drops”.

If the packet can meld behind the slit spacer as in figure 6, it does so before it separates in front of the spacer. The melding process takes place an integral number of wavelengths from the slits and results in a change in path that leads to an impact in the interference pattern, a pattern that can be calculated using the methods of QED.  As soon as the melding takes place, the photon separates in front of the slit spacer and begins joining the rest of the body already melded together, so that the photon is always a full packet of energy

If melding does not take place because of a blocking detector or some other shield, then the photon pulls itself into whichever slit passed the bigger portion of its packet and slips through that slit whole.  If it is the blocked slit, it is destroyed there.  If it is the unblocked slit, it comes though whole but does not interfere with itself because it did not meld around the slit due to the blockage in the other slit.  It may also be destroyed by the slit itself.   The photon is destroyed in the blocked slit or on the film behind the open one, never both. It makes no choice. In the case of a blocked slit, there is no recombination. The side with the larger energy pulls the photon through an opening if there is one and if that opening has a detector or blockage, it dies there.

The answer to the weirdness of photons seeming to interefere with itself is that it is due to the forshortening of the experiment due to the effects of relativity.

Next:  Polarized Light Weirdness Explained

Quantum Weirdness – A Matter of Relativity? Part 1

Quantum Weirdness

A Matter of Relativity?

Copyright 2006/2007 James A. Tabb

Part 1: Introduction and Photons In Glass

Quantum Electrodynamics (QED) theory has developed to be the theory that defines almost all of the understanding of our physical universe. It is the most successful theory of our time to describe the way microscopic, and at least to some extent, macroscopic things work.

Yet there is experimental evidence that all is not right. Some weird things happen at the photon and atomic level that have yet to be explained. QED gives the right answers, but does not clear up the strange behavior – some things are simply left hanging on the marvelous words “Quantum Weirdness”. A few examples of quantum weirdness include the reflection of light from the surface of thick glass by single photons, dependent on the thickness of the glass; the apparent interference of single photons with themselves through two paths in double slit experiments; the reconstruction of a polarized photon in inverted calcite crystals, among others.

This paper introduces some ideas that may explain some of the weirdness.

Photons and Relativistic Effects:

I suggest that most of the difficulties we have in addressing the various weirdness phenomena at the particle level can be traced to relativistic effects. It all comes down to the two different simultaneous viewpoints: The one we can see and measure, and the one the photon experiences. Relativistic effects rule the photon world and our life experiences rule ours.

Consider that photons travel at the speed of light and thus experience relativistic effects. What are these effects? Einstein gave us some tools to work with to describe the various space-time relativistic changes as shown in Figure 1. There is a mass equation also, but the mass increase is not a factor here, since we know that the photon has no rest mass.

Figure 1.   Relativistic Effects at c

The photon’s clock stops because the time between clock ticks becomes infinitely long at c. Similarly, the distance traveled becomes zero because the photon’s unit inch becomes infinitely long and stretches to the end of its journey in one bound. In other words, the entire path is foreshortened to zero length, and everything in its path is compressed to a dot.

We, on the other hand, see the photon from our experimental perspective. Photons move at speed c, take a nanosecond to go about a foot, take centuries to go from a nearby galaxy to earth, all of which we can measure or calculate with confidence and confirm with experiments.

The Photon’s Go-Splat World

The photon lives in a “go-splat” world. The clock of a photon completely stops the instant it is emitted and stays stopped throughout its journey. The distance traveled by a photon becomes zero as compared to the distance measured by the stationary observer. It may take a photon a billion years to cross from a distant galaxy to our telescope from our perspective, but for the photon, as soon as it is emitted, it arrives – splat; there is no time elapse in the photon world. In effect, the space and time between the photon’s emission and its destination are severely warped.

Therefore, the photon’s world is flat and stapled together, front-to-back, between its start point and its end point. In effect, the photon is touching its emitter on one end and our eye on the other with zero depth of field. Whatever phase it has at the time of emission, it has when it hits our telescope because it is all frozen in time. Physicists call the time experienced by the photon null time and the path the null time path.

It is this stapled together, zero time world that I believe explains much of the quantum weirdness we experience. Our life and experimental experiences are so strong that we can’t easily get our minds around the relativistic phenomena.

What the photon would know of the experimental setup, whatever it is, consists of wake-up calls at various edges or medium changes and eventually wherever it is absorbed in our screen or detector, all zero distance apart. This is vastly different from our perspective where everything is so carefully laid out, separated, calibrated with finite distances and photon flight times.

From our perspective, if it is going across a table, it moves about a foot every nanosecond. If it is going across the universe it takes years, even millions or billions of years to get from there to here. However we see it or calculate it, the time it takes for the photon’s lifetime is always zero. Go-Splat! As soon as it leaves on its journey, it arrives.

Quantum Weirdness in Glass

One of the weird aspects of photons involves reflection from glass of varying thickness. Send a laser pointer beam perpendicular to a pane of glass and about 4% of it will reflect back, on average, but, by carefully selecting glass of various thicknesses, the reflections vary from 0% to 16%. Glass a foot thick can be slightly adjusted in thickness to not reflect at all! All the light goes into the glass – perfect transmission. QED easily shows how this works for light beams. Rays from the back of the glass interfere with the rays coming in the front so as to cancel the reflection if the wavelength is a multiple of ½ wavelength.

However, the cancellation at ½ wavelength also works for individual photons for thick glass, and there seems to be no answer other than “quantum weirdness”. How does an individual photon know how thick the glass is the instant it hits the front surface when the back surface is thousands of wavelengths away? The reflected photon would be six feet away before a copy could make a round trip through a foot thick piece of glass. (Two feet round trip at 1/3 speed of light in air)

Quantum Weirdness and Relativity

Lets look closer at our foot thick piece of glass. The photon is moving at c and from a relativistic perspective our piece of glass has zero thickness (our entire experiment has zero thickness) as shown in Figure 2a.

Figure 2. Photon in Glass

Immediately after impact, a full  half wave of the photon fits completely into the glass (2c), no matter how thick. The photon’s wavelength in glass is only 1/3 of its air wavelength. If the thickness of the glass is a multiple of a half-wave of the (shortened) photon, the photon will go right on through without reflection. Otherwise, depending on the thickness, some percentage (0 to 16%) of them will reflect.  In effect, the glass collapses to zero thickness if it is an exact multiple of the half wavelength, and if not, there is an overhang on one of the collapsed thicknesses that determines the probability of reflection.  Thus the photon does not have to “wiggle” its way to the far side and back to make its decision. If it is going to reflect, the decision is immediate due to the glass being foreshortened to fit the photon. It is, in fact, relativistic foreshortening of the glass.

Note, although the surfaces in the drawing above and those that follow are drawn with straight lines and flat, they are shown that way only for illustrative purposes. At c, all the points in the direction of travel are pulled to one point at the nose of the photon because they are zero distance apart to the photon, and surfaces near the path are severely bent.

It should also be noted that, once within the lattice of the atoms of glass, the atoms to each side of the photon resume their normal spacing and are no longer foreshortened. This is because they are perpendicular to the direction of travel. Those atoms in front continue to be shortened to meet the photon. Thus the photon length and the glass thickness exactly match, regardless of thickness, if the glass is an exact multiple of a half wavelength.  In that case, the photon completely enters without reflection. If the thickness does not fit the wavelength of the photon exactly, there is a crisis due to a mismatch in which the glass is not quite zero thickness to the photon. The probability of reflection depends on the degree of mismatch, but the reflection decision is made while the photon is still at the front surface and just inside.

There are two effects going on simultaneously: The relativistic effects for the photon and the realistic effects for the observer. The photon fits within the entire experiment (zero thickness, no wiggle time due to no time elapse) while we, as the stationary observers, see the entire experiment where the photon is traveling at c and has to wiggle 130,000 times to get through the glass in a measurable time (about 3 nanoseconds for a foot of glass). One case of quantum weirdness explained by relativistic effects.

Next: Explaining Double Slit Weirdness

Random Thoughts About Relativity

Facts About Relativity  

In order to introduce some of my ideas, it will be good for the reader to become familiar with some of the weird behavior of particles traveling at very high speed, high enough to invoke relativistic effects.

As seen by a stationary observer:

1) The closer a moving object gets to the speed of light, the slower its moving clock gets.

At the speed of light, it is zero – to the moving object, everything is simultaneous.  Start, Splat. The moving object sees the outside world as distorted, getting shorter in length, and at c, the length from here to there is zero, no matter how far the stationary observer measures it.  Photons live in a go-splat world.

2) The closer a moving object gets to the speed of light, the shorter its length gets.

At the speed of light, it has zero length to the stationary observer, but normal length to the moving object.  Everything seems normal to the moving object  until it gets to c – the problem for the moving object at c is that there is no time to seem normal – everything is instantaneous.

3) The closer a moving object gets to the speed of light, the larger its mass gets due to kinetic energy increase (for objects that have mass).

At the speed of light, an object with mass would have infinite mass.   This rules out object with mass ever getting up to c.  Photons do not have mass so they can move at the speed of light.   Nothing with mass can go that fast.

4) The closer a moving object gets to the speed of light, the more energy you have to use to get it there.

You have to give more and more energy to the object to get it  closer and closer to the speed of light. Energy equals mass times speed of light squared.  At the speed of light, the energy required is infinite.  You can never push an object with mass that hard.

What is the equation that describes the way in which time slows down as you approach the speed of light?

The equation is known as the time dilation equation and is:

Δ t = Δ T/ √[ 1 – (v/c)²]    Time dilation

Where  Δ t is the moving object time ticks and Δ T is the stationary object time ticks, v is the velocity and c is the speed of light.

When the velocity approaches c, the term v/c becomes very close to 1 and then the term Δ t becomes very large because the right side is divided by a very small number approaching zero.  This means that the distance between clock ticks gets very long for the moving object.   Time begins to stand still as it reaches the speed of light because the distance between tics becomes infinite.

What happens to space (in direction of motion)?

Δ x = Δ X/√[ 1 – (v/c)²]      Space distortion

Where  Δ x is the ruler mark as measured by the moving object and Δ X is the ruler mark as measured by the stationary object.

When the velocity approaches c, the right hand term approaches infinity.  essentially, a unit measure, such as an inch for the moving object would stretch millions of miles as measured by the stationary object at speeds near c.  

conversely, a foot long ruler moving near c would be invisibly short as seen by the stationary object – a term called foreshortening. 

Conversely again, the stationary object would seem impossibly close and impossibly short to the moving object near c.  At c, neither could see the other even with the best of instruments until they collide, which would be instantaneous for the moving object.  (To do so would imply that the image was moving faster than c.)

 So someone (very small and massless) sitting on a photon would think they see time normally, but the time of flight would seem to pass instantly from time started to time finished because no time would elapse (Δt very large).   Of course there would be no time to measure time (or even think about it) because the photon would instantly hit the other end of its path, no matter how far away that is.

Someone sitting and watching nearby would see time normally (from their perspective), but in their case, ΔT would be very short (time interval ticks near 0) and they would seem to age quickly compared to the someone riding on a photon.

The total time of flight might seem 100 years to an observer, but seem instantaneous for one traveling at the speed of a photon. The observer would age instantly according to the one moving fast, and the observer would think the one moving quickly didn’t age at all.   Weird isn’t it?  Weird but true.

Similarly, distance gets shorter as an object approaches c as seen by the observer and longer for the observer as seen by the object that is moving fast.

In other words, the time that passes in one time frame (Δ t) is the time that passes in another (Δ T) divided by the square root of 1 minus the velocity squared divided by the speed of light squared.

Enough of this – keep in mind that photons don’t have time to age, and photons arrive the instant they are emitted.  A photon emitted in the furthest star that we can see by telescope arrives the instant it is emitted.   (From the photon’s point of view).   They live an instantaneous “go-splat” life.

From our point of view it may have taken billions of years to get here.  Both viewpoints are valid.  That is the weird nature of relativistic speeds.  Time and space are distorted. 

One last thing:  Effect of speed on atoms:

Atoms are flattened in the direction of their motion.  Normally about 10 -8 cm in diameter they change from a sphere to a flattened disk as they approach the speed of light (from our stationary perspective only).

Particle accelerators have to be designed to account for both time dilation and space contraction in order to work. 

Atoms have mass so they can never reach the speed of light, but particle accelerators push particles, including atoms, to very high speeds that require design changes to keep them on track around their path – changes that involve the equations above.

Next – some of the quantum weirdness explained, example by example from the earlier posts.

Quantum Weirdness in Entangled Particles

Entangled Particles

Selecting which atom we use with careful attention to its excitation states can create entangled particles.  Some atoms emit two photons at a time or very closely together, one in one direction, the other in the opposite direction.  These photons also have a property that one spins or is polarized in one direction and the other always spins or is polarized at right angles to the first.  They come in pairs such that if we conduct an experiment on one to determine its orientation, the other’s orientation becomes known at once.   They are “entangled”.

 

Figure 10 – Entangled Particles   

All of this was involved in a famous dispute between Einstein and Bohr where Einstein devised a series of thought experiments to prove quantum measurement theory defective and Bohr devised answers. 

The weirdness, if you want to call it that, is the premise that the act of measurement of one actually defines both of them and so one might be thousands of miles away when you measure the first and the other instantly is converted, regardless of the distance between them, to the complement of the first.   Action-at-a-distance that occurs faster than the speed of light?

Some would argue (me for instance) that this is more of a hat trick, not unlike where a machine randomly puts a quarter under one hat or the other, and always a nickel under a second one.  You don’t know in advance which contains which.  Does the discovery that one hat has a quarter actually change the other into a nickel or was it always that way?  Some would say that since it is impossible to know what is under each hat, the discovery of the quarter was determined by the act of measuring (lifting the hat) and the other coin only became a nickel at that instant.   Is this action at a distance? 

It is easy to say that the measurement of the first particle only uncovers the true nature of the first particle and the deduction of the nature of the second particle is not a case of weirdness at all.   They were that way at the start.

However, this is a hotly debated subject and many consider this a real effect and a real problem.  That is, they consider the particles (which are called Einstein‑‑ Podolsky‑Rosen (EPR) pairs) to have a happy-go-lucky existence in which the properties are undetermined until measured.   Measure the polarization of one – and the second instantly takes the other polarization.

A useful feature of entangled particles is the notion that you could encrypt data using these particles such that if anyone attempted to intercept and read them somewhere in their path, the act of reading would destroy the message.

So there you have it – Weird behavior at a distance, maybe across the universe.

Next:  Some Random Thoughts About Relativity