Is the speed of light not constant at the quantum mechanical level?

[dkv]

Moderation note: This thread was created from posts originally appearing in the Space forum thread 15712, because they have drifted far from the original subject of the speed of light in vacuum as a “universal speed limit”.

 

There is a huge misunderstanding. What theory suggests is that the speed of light is measured constant when the frame of references are inertial.

At the quantum mechanical level speed of light is no longer considered constant.

Moreover c is not constant when we measure speed of light in plasma or glass...

Even the Vaccum is filled with virtual photons and electrons.. Speed of light is never constant.

The results of michelson morley experiment were not exactly null.

Despite the null interpretation of their experiment by Michelson and Morley,it is quantitatively shown that the outcomes of the original experiment, andall subsequent repetitions, never were null. Additionally, due to an incorrectinter-session averaging, the non-null results are even larger than reported.Contrary to the received view, Illingworth’s and other repetitions of the ex-periment were consistent with Miller’s positive results. On the theoreticalside, a new systematic error is uncovered: the angle between the projectionof earth’s velocity on the plane of the interferometer and the reference armof the apparatus has been practically ignored. This phase angle produces anoticeable change in the position of the peaks from one turn to the next ofthe interferometer. Hence, the data analysis cannot be based on the averageof fringe shifts during a session, but rather on the calculation of individualspeed for each turn. This procedure was applied to the only two sessions re-ported in detail in the literature: Miller’s September 23, 1925 at 03:02 inMount Wilson and Illingworth’s July 9, 1927 at 11:00 in Pasadena. Surpis-ingly, it was found that in both cases the measured speeds exactly corre-spond to the projection of earth’s orbital velocity only. As a result, the evi-dence against a preferred frame completely dissappears

http://enjoy.phy.ntnu.edu.tw/file.php?file=/120/Michelson%20Moley%20Experiment/Michelson%20Morley%20Experiment%20Revisit.pdf&shared=120

Even if we dont agree with the above interpretation... we must understand that speed of light is never constant due to quantum mechanical nature of the universe...

It is not possible to create absolute vaccum.

[Janus]

There is a huge misunderstanding. What theory suggests is that the speed of light is measured constant when the frame of references are inertial.

At the quantum mechanical level speed of light is no longer considered constant.

Moreover c is not constant when we measure speed of light in plasma or glass...

Even the Vaccum is filled with virtual photons and electrons.. Speed of light is never constant.

 

It is not possible to create absolute vaccum.

 

The huge misunderstanding is on your part. c refers to the speed of light in a vaccuum only. Light does travel at c in glass. The only reason its apparent speed is less is because it is absorbed and re-emitted by atoms along the way and there is a slight delay between the two. Between the atoms light travels at c. It also travels at c between the particles in space.

[dkv]

The huge misunderstanding is on your part. c refers to the speed of light in a vaccuum only. Light does travel at c in glass. The only reason its apparent speed is less is because it is absorbed and re-emitted by atoms along the way and there is a slight delay between the two. Between the atoms light travels at c. It also travels at c between the particles in space.

 

The space is filled with virtual energy, at distances close to few nanometers the space doesnt remain flat and fluid... it becomes highly turbulent. Higher the energy of photons greater the resistance comes from the space. At extremely high energies (GHz) the photon can suddenly loose its properties and get converted into electron and positron. (just as the bulb lights up if sufficient strength of current is passed) See Feynman diagrams.

The retarding force causing the apparent delay between two points in the speed of light is caused by space itself.

 

When the medium is not space then the light gets absorbed and re-emitted.

There is no doubt but the point is light jumps from one potential well to other.. There are substances which do not re-emitt the light immediately. They emit after a long time. The speed of light in such cases can not be defined.

However it is not possible to get the perfect vaccum therefore for all practical purposes we generally speak in terms of decrease or increase in the speed of light. But How do you propose to define speed if particles only jump from one state to another?

The point is the speed of light is not constant(apparently or for real).

[modest]

The space is filled with virtual energy, at distances close to few nanometers the space doesnt remain flat and fluid... it becomes highly turbulent.

 

The turbulent quality of spacetime usually referred to as quantum foam is theorized to manifest at the plank length of about 10^-35 meters. I don't know where you got the figure "few nanometers" or 10^-9 meters, but it appears off by many, many orders of magnitude.

 

Higher the energy of photons greater the resistance comes from the space.

 

The speed of light is not dependent on its wavelength.

 

At extremely high energies (GHz) the photon can suddenly loose its properties and get converted into electron and positron. (just as the bulb lights up if sufficient strength of current is passed) See Feynman diagrams.

 

Can you give a scientific source saying pair production changes the speed of light?

 

The retarding force causing the apparent delay between two points in the speed of light is caused by space itself.

 

Your misconception appears to be that the uncertainty principle applies to the speed of light, which I don't think it does. It will affect (or apply to) the momentum or energy of a photon, but the speed of a photon is independent of those attributes. Virtual photons are a different story, but we'd need someone more knowledgeable in qft to explain why.

 

Your next misconception is that the above has some bearing on relativity which postulates that the speed of light is invariant. It does not. Quantum field theory and special relativity work together very well as manifested in QED.

 

Your post history shows an agenda toward debunking relativity and in that effort you are making some pretty wild claims in this thread. As you well know, it is a site rule to back up claims with scientific sources.

 

~modest

[dkv]

I dont have any hidden agenda against the SR or GR but I definitely think that the theory is logically inconsistent. If you wish to discuss SR then discuss I am ready.

Anyways,

Your point that space changes its property only at plank scale is wrong. Virtual pair creation and annihilation and quatum tunneling takes place at atomic scales..and not planck scale.

Offcourse if we reduce the dimensions further the speed of light becomes less and less defined.. but this is not due to uncertanity principle but due to the nature of quantum mechanics (sum over histories... photon can take any path between points)

Speed of light depends on wavelength . Try to measure to refractive index of a medium at different wavelengths. Your main assumption is that Vaccum is empty and therefore it is impossible to think of anything like refractive index of vaccum... However at small scale the space is filled virtual photons and electrons which are waiting to be knocked out by photons... thus effectively creating a virtual medium with real refractive index..

QED doesnt work well with SR . Virtual interactions do not conserve mass and energy.

I am surprised that you dont know about pair creation ... High energy photons can create electrons and photons..(I cant give link for every concept I share do some work)

[modest]

I dont have any hidden agenda against the SR or GR but I definitely think that the theory is logically inconsistent.

 

I said nothing of a hidden agenda.

 

Your point that space changes its property only at plank scale is wrong.

 

I said nothing of space changing its properties. I said that quantum foam is theorized to manifest at the plank length which is much smaller than the figure of a few nanometers which you incorrectly gave.

 

It is also entirely speculative and theoretical - not to mention you've done nothing to relate it to the speed of an observable photon.

 

Offcourse if we reduce the dimensions further the speed of light becomes less and less defined..

 

Not unless the speed of light is defined as the unobservable speed of a virtual photon over very small distances. Which, it is not.

 

but this is not due to uncertanity principle but due to the nature of quantum mechanics (sum over histories... photon can take any path between points)

 

This displays a complete lack of understanding.

 

Speed of light depends on wavelength

 

Please provide a scientific source backing up this claim.

 

QED doesnt work well with SR .

 

QED is built from SR. Please provide a source.

[dkv]

There are several occasions in which the vaccum can get distorted by the presence of field.. Large Magnetic or Electric or Gravitational field. In the absolute vaccum such fields are not absent.These field create vaccum distortions.

Casimir effect is a result of such distortions.

Intense Laser pulse can also produce real electrons and positrons in presence of a change.

Black Holes produce virtual pairs which can sometimes get trapped by its surface.(It is said that Black Holes radiate)

What is interesting is that in an accelerating frame the vacuum can appear to be filled with real particles because acceleration is equivalent to gravitational field.

Therefore if the observer is in an accelerating frame the high energy photons can create electron and positrons...

However we need to understand it from another point of view.

Virtual pair production and annihilations can take place without any external field because in such cases there is no of violations energy and momentum.

By measuring the speed of light at large distances we can detect such interactions...

In feynman's diagram one can imagine a photon creating virtual particles with some probability and then annihiliating after time del t without violating Uncertainity principle. The only loss is experienced is terms of velocity of light.

Therefore speed of light is never constant.

(speed is an emergent property because photons simply keep jumping from high potential to low potential.)

 

The analysis predicts that the speed measured in low field is always greater than speed measured in high fields.

In space the speed of light keeps increasing with respect to the origin because origin is almost always in a higher field(gravitaional or electromagnetic).

This is a universal truth.

 

 

The structure of the QED vacuum and electron - positron pair production in super-intense, pulsed laser fields

 

virtual particle - Virtual particles in Feynman diagrams, Virtual particles in the vacuum, History

[CraigD]

There are several occasions in which the vaccum can get distorted by the presence of field.. Large Magnetic or Electric or Gravitational field. In the absolute vaccum such fields are not absent.These field create vaccum distortions.

…

In feynman's diagram one can imagine a photon creating virtual particles with some probability and then annihiliating after time del t without violating Uncertainity principle.

…

Virtual pair production and annihilations can take place without any external field because in such cases there is no of violations energy and momentum.

Dkv is on an interesting track, IMHO by considering and comparing pair production of real electrons and positrons to virtual electron/positron pairs. However, I can see a couple of troubling errors in the reasoning thus far.

Intense Laser pulse can also produce real electrons and positrons in presence of a change.

Black Holes produce virtual pairs which can sometimes get trapped by its surface.(It is said that Black Holes radiate)

Experimentally confirmed the first, and strongly theoretically predicted the second (Hawking radiation).

 

The photon doesn’t even have to be from a laser – any photon more energetic than the mass of two electrons - about 2.022 MeV, which equates to [math]\frac{2.022 \,\mbox{MeV}}{h} \dot= 4.8892 \times 10^{20} \,\mbox{Hz}[/math], high in the Gamma rays range, but not so high as to be uncommon, which is why a lot of radioisotopes are practical positron sources. In these cases, where the strong magnetic field can be imagined, in a classical metaphor, as due to the positively charged nuclei of the material. Cosmic ray photons, though rare compared to radioactive decay photons, can also have energy/frequencies high enough for pair production.

 

The key to pair production is for some force (AKA interaction) to deflect (change the momentum of) a virtual particle/antiparticle fermion pair (the electron and positron in the previous example) sufficiently that the electromagnetic attraction of their opposite charges don’t draw them together to annihilate back into the original boson (the photon in the previous example).

 

This is easy in the case of a charge interaction, such as with an atomic nucleus, because the direction of the force of the interaction for the particle and antiparticle are opposite.

 

With a gravitational force, it’s more difficult, as particles and antiparticles experience the same gravitational interaction with mass at the same position. Since the particle/antiparticle pair are not in the exact same position relative to the interacting massed, pair production is possible, but much more rare than that due to charge interaction, so to the best of my knowledge, pair production due to gravity – Hawking radiation and similar direct effects – haven’t been directly experimentally observed, though the theoretical argument for that it occurs is strong. The reason Hawking radiation is believed to occur near a black hole or other very dense body is because the difference in gravitational force and acceleration of two particles separated by even a small distance can be greater than the charge attraction of the particle and its antiparticle.

 

AFAIK, an accelerated lab, such as on a powerful rocket ship, would not cause pair production at all, because there is no difference in any forces experienced by the particle and antiparticle, other than their interaction with one another, with other charged particles, and very small gravitational forces.

 

At first glance, this appears to disagree with the General Relativity’s equivalence principle – typically stated something like

In any

local

inertial frame, acceleration due to an external, non-gravitational force is indistinguishable from the same acceleration due to gravitational force

However, on close inspection, one should realize that local in this context is very restrictive, referring to a single geometric point. Because the particle and its antiparticle aren’t located at exactly the same point, they aren’t local to one another in this sense. Thus, either with antiparticle pairs, other real particles, or idealized test bodies, once can distinguish acceleration due to non-gravitational force from that due to gravity, because the magnitude and direction of the latter varies with position, but for the former, does not.

 

For example, one can in principle determine if one is in a box resting on the surface of a planet or in a spaceship accelerating at exactly the planet’s surface acceleration of gravity, because in the surface-resting box, the measured acceleration is slightly greater near the floor of the box than near the ceiling, while in the spacecraft-born box, they are the same.

 

Thus, dkv’s reasonable conclusion

What is interesting is that in an accelerating frame the vacuum can appear to be filled with real particles because acceleration is equivalent to gravitational field.

Therefore if the observer is in an accelerating frame the high energy photons can create electron and positrons...

is, I think, wrong.

[modest]

In feynman's diagram one can imagine a photon creating virtual particles with some probability and then annihiliating after time del t without violating Uncertainity principle. The only loss is experienced is terms of velocity of light.

Therefore speed of light is never constant.

 

In qft, an observable photon must satisfy [math]E^2-p^2c^2=m^2c^4[/math] while a virtual photon need not. A virtual photon can then have mass or variations in the speed of light while observable photons can not.

 

On shell and off shell - Wikipedia, the free encyclopedia

 

As far as virtual pair production / annihilation, can you explain how you came to the conclusion that "The only loss is experienced is terms of velocity of light" or give a source agreeing with that claim. I would really like to know if that is the case.

 

~modest

[dkv]

The equivalence principle relates to a point but due to the acceleration of frame the points appear to attract each other. The attraction at low speeds approximates to the newtonian gravity(F=Gmm/r^2) due to the curved nature of space time.

Which gives us the required gradient to see the virtual particles as real.

Hence the argument is correct. It is also mentioned in one of the links I posted.

 

The real photon conserves energy and momentum but the same real photon at sufficient energy ,can change into electron and positron under the influence of an external field.

The question is what happens when the energy of the real photon is less than the threshold energy ? Can it create real electron and positron ? No.

Can it create virtual electron and positron ? Yes because violation of conservation of energy is allowed for a time dt!!

In such a case the time over which this violation is allowed creates a ficticious dragging force.. because the virtual pair creation and annihiliation takes some amount of finite time(no matter how fast the process is because light can not travel instantaneously from one point to the other by creating virtual electrons and positrons in empty space)...

When the light crosses the threshold limit of energy it travels no more but condenses into real particles.. The idea is very and continuous.

[modest]

The equivalence principle relates to a point but due to the acceleration of frame the points appear to attract each other.

 

In fact, they are stressed apart both in freefall in a gravitational field and in an accelerated frame. When two points of some distance separation along X are given the same acceleration along X, they will eventually drift apart. The distance between them, X1 - X2, will grow as a relativistic effect. It can also be said that the two points must have different acceleration to maintain equal distance.

 

Obviously I disagree with Craig on this point.

 

in the surface-resting box, the measured acceleration is slightly greater near the floor of the box than near the ceiling, while in the spacecraft-born box, they are the same.

 

Thought experiments along these lines go by Born rigidity or “Bell's spaceship paradox” and it is more completely reveled using Rindler observers in Rindler coordinates.

 

Accelerating a rod evenly in SR requires more force applied to the trailing edge than the leading edge. It’s explained in the link to accelerated coordinates above.

 

This makes sense to me in terms of Hawking radiation. A particle and antiparticle will have two different distances from the source of the gravity well. For the two particles to maintain at least constant distance the closer will require more energy so their natural tendency would be to scatter (or at least attempt to). The force of constant acceleration required to accomplish this outside extreme gravity situations would approach infinity considering the acceleration of gravity approaches infinity at the event horizon.

 

The attraction at low speeds approximates to the newtonian gravity(F=Gmm/r^2) due to the curved nature of space time.

 

I can’t make sense of this sentence.

 

Which gives us the required gradient to see the virtual particles as real. Hence the argument is correct.

 

“seeing the particles as real” as you’re saying seems entirely different than making them real such as Hawking was talking about.

 

It is also mentioned in one of the links I posted.

 

Your source says this:

 

In some cases, however, it is possible to boost the pair apart using external energy so that they avoid annihilation and become real particles.

 

In an accelerating frame of reference, the virtual particles may appear to be real to the accelerating observer; In short, the vacuum of a stationary frame appears, to the accelerated observer, to be a warm gas of real particles in thermodynamic equilibrium.

 

This is all it says. I’m not sure what they mean by saying it “appears” real; but, it is different from using forces to make them real.

 

For example, a gamma ray without pair production will leave no path through a bubble chamber. With pair production you’ll see the particle and antiparticle. Whoever observes the bubble chamber - no matter their speed or acceleration relative to the chamber will agree with the scientist standing next to the chamber in its frame. Either it made a pair or it did not.

 

The real photon conserves energy and momentum but the same real photon at sufficient energy ,can change into electron and positron under the influence of an external field.

The question is what happens when the energy of the real photon is less than the threshold energy ? Can it create real electron and positron ? No.

Can it create virtual electron and positron ? Yes because violation of conservation of energy is allowed for a time dt!!

In such a case the time over which this violation is allowed creates a ficticious dragging force.. because the virtual pair creation and annihiliation takes some amount of finite time(no matter how fast the process is because light can not travel instantaneously from one point to the other by creating virtual electrons and positrons in empty space)...

 

I don’t think so.

 

In relativistic QFT the speed of a photon comes from the position space propigator. Where the photon is real or observable, it is on shell. From the link:

 

In relativistic quantum mechanics and quantum field theory the propagators are Lorentz invariant. They give the amplitude for a particle to travel between two spacetime points...

 

which does not apply (as I keep saying) to a virtual photon,

 

Internal lines [on a Feynman diagram] correspond to virtual particles. Since the propagator does not vanish for combinations of energy and momentum disallowed by the classical equations of motion, we say that the virtual particles are allowed to be off shell. In fact, since the propagator is obtained by inverting the wave equation, in general it will have singularities on shell...

 

~modest

[CraigD]

The equivalence principle relates to a point but due to the acceleration of frame the points appear to attract each other. The attraction at low speeds approximates to the newtonian gravity(F=Gmm/r^2) due to the curved nature of space time.

Which gives us the required gradient to see the virtual particles as real.

Hence the argument is correct. It is also mentioned in one of the links I posted.

Although nowhere in it or in similar sources can I find any support for these claims, the

encyclopedia.stateuniversity.com page dkv references does indeed state

Thus, virtual particles are often popularly described as coming in pairs, a particle and antiparticle, which can be of any kind. In some cases, however, it is possible to boost the pair apart using external energy so that they avoid annihilation and become real particles. In an accelerating frame of reference, the virtual particles may appear to be real to the accelerating observer; In short, the vacuum of a stationary frame appears, to the accelerated observer, to be a warm gas of real particles in thermodynamic equilibrium.

Although, this encyclopedia article doesn’t provide any references, it appears to be referring to the Unruh effect. Though not directly experimentally verified, this prediction of quantum mechanics appears sound, on about the same footing as Hawking radiaton - it’s commonly described as “a toy model of to explain Hawking radiation” (eg: in the wikipedia article “virtual particle”).

 

It’s important to understand, however, that the Unruh effect is not the same effect as pair production due to a photon with energy greater than 2.022 MeV passing through the strong electromagnetic field near an atomic nucleus or the strong gravitation field near a black hole or other very dense body. The Unruh effect predicts that, viewed by an accelerating observer, the vacuum will radiate real particles at a greater rate than when observed by an observer accelerating at a lesser rate. Unlike pair production, where the energy of the real initial photon and of the produced real particle/antiparticle pair are the same, the energy of the Unruh effect’s observed real particles don’t correspond to any initial real particles – they “appear out of the vacuum” of virtual particles.

 

It’s also important to understand that Hawking radiation is not the same as pair production due to particle/antiparticle pairs being differently acclerated by a strong gravitational field (I’m guilty, I fear, or confusing these two in my previous post). Like the Unruh effect, Hawking radiation doesn’t require any initial real particles, while pair production, again, does.

 

I fear that dkv confuses pair production with other effects even more grievously. In

The real photon conserves energy and momentum but the same real photon at sufficient energy ,can change into electron and positron under the influence of an external field.

The question is what happens when the energy of the real photon is less than the threshold energy ? Can it create real electron and positron ? No.

Can it create virtual electron and positron ? Yes because violation of conservation of energy is allowed for a time dt!!

he appears to state that the energy of the virtual electron and positron pair associated with a photon have a different total energy than the photon, violating conservation of mass-energy, which is not predicted by theory. The requirement that mass-energy be conserved is the reason why photons under the energy of the combined mass of the particle/antiparticle pair do not produce virtual or real particle pairs.

 

I have an intuition – possibly correct, possibly not – of what dkv is attempting to say: that the speed of light is determined by the speed of the possible virtual particles equivalent to a photon. I don’t think this is a theoretical prediction of quantum mechanics, however, nor am I aware of any experimental data suggesting that – as he suggests – very high energy photons are slower than lower energy ones. As present day gamma-ray astronomy routinely detects such very high energy photons, but no measurable difference in their arrival times vs. lower energy ones, if such an effect were present, I believe it would be well observed and confirmed.

[dkv]

There is decrease in the volume of the "particles" as the time moves forward due to the equivalence principle. How this decrease actually takes place is depends on the problem... For example due to Earth's rotation and Monn's Gravity the equatorial region bulges out...

The attraction between Ocean Waves and Moon can also be understood in terms of acceleration.

Anyways the point is that due to acceleration vacuum can get distorted and that is what the article is saying.

[dkv]

You are confusing real and virtual particles. To produce real particles criteria of energy conservation must be met. But for virtual particles this need not be the case.

I am not confusing.

[CraigD]

To produce real particles criteria of energy conservation must be met. But for virtual particles this need not be the case.

As I understand the terms and theory, this is not correct.

 

According to the wikipedia article “virtual particle”

Virtual particles exhibit some of the phenomena that real particles do, such as obedience to the conservation laws.

Real or virtual, the mass-energy of a particle, such a photon, which changes into one or more other particles, must be the same as that of what it changes into.

 

Dvk, what’s the source of your understanding that virtual particles need not obey conservation laws?

[modest]

A source for confusion may be sources such as thefreedictionary.com which simplistically defines virtual particle as: "A subatomic particle whose existence violates the principle of conservation of energy but is allowed to exist for a short time by Heisenberg's uncertainty principle."

 

more accurately (I think) is:

Virtual particles conserve energy and momentum. However, since they can be off shell, wherever the diagram contains a closed loop, the energies and momenta of the virtual particles participating in the loop will be partly unconstrained, since a change in a quantity for one particle in the loop can be balanced by an equal and opposite change in another. Therefore, every loop in a Feynman diagram requires an integral over a continuum of possible energies and momenta. In general, these integrals of products of propagators can diverge, a situation that must be handled by the process of renormalization.

 

-Propagators in Feynman diagrams

[dkv]

Virtual particles are not real particles. They are virtual because they hide behind the uncetainity principle. However the line between the Real and Virtual particle is very thin. Both arise due Mathematical equations...

Virtual particles can violate the conservation of energy for a time dt as defined Heisenberg Uncertainity principle. The momentum must remain conserved.

They can also carry charge.

The Feyman diagrams based on virtual particles have produced very accurate results. I dont think there is any flaw in my understanding of virtual particles.

W boson can be both real and virtual... When an interaction takes place thru the virtual mode then the Energy need not be conserved for a short duration.

example neutron decay .

Frame 1: The neutron (charge = 0) made up of up, down, down quarks.

Frame 2: One of the the down quarks is transformed into an up quark. Since the down quark has a charge of -1/3 and and the up quark has a charge of 2/3, it follows that this process is mediated by a virtual W- particle, which carries away a (-1) charge (thus charge is conserved!)

Frame 3: The new u quark rebounds away from the emitted W-. The neutron now has become a proton.

Frame 4: An electron and antineutrino emerge from the virtual W- boson.

Frame 5: The proton, electron, and the antineutrino move away from one another.

Neutron Beta Decay

The conservation of energy seems to be violated by the apparent existence of these very energetic particles for a very short time. However, according to the above principle, if the time of a process is exceedingly short, then the uncertainty in energy can be very large. Thus, due to the Heisenberg Uncertainty principle, these high-energy force-carrier particles may exist if they are short lived. In a sense, they escape reality's notice.