neutrinos travel at a velocity 20 parts per million above the speed of light

[Sharky]

Re: neutrinos travel at a velocity 20 parts per million above the speed of light

Doesn't Special Relativity say that nothing with mass can travel faster than light?

Last I heard, neutrinos are massless. How is that a violation?

It is known whether neutrinos are affected by gravity, as light is?

Also, IIRC, photons don't move a single velocity; it varies over short distances, and the value we know as c is just an average. Perhaps neutrinos don't have the same type of variations? Or is it possible that photons are somehow interacting with neutrinos in a way that slows them down slightly, as when light passes through much heavier matter such as glass?

[ASH]

Re: neutrinos travel at a velocity 20 parts per million above the speed of light

Doesn't Special Relativity say that nothing with mass can travel faster than light?

No -- nothing at all, including particles without rest mass.

Last I heard, neutrinos are massless.

This used to be the understanding, but that changed in 1998 with the discovery of neutrino oscillations, which require that neutrinos have non-zero rest mass.

It is known whether neutrinos are affected by gravity, as light is?

Everything that travels through space-time is, by definition, affected by gravity.

Also, IIRC, photons don't move a single velocity; it varies over short distances, and the value we know as c is just an average.

Only virtual photons are treated as having any probability of traveling faster than c, and they aren't directly observable; all real photons and other particles are treated as obeying the speed limit. So, you wouldn't expect an observable particle like a neutrino to exceed c, even momentarily.

Perhaps neutrinos don't have the same type of variations? Or is it possible that photons are somehow interacting with neutrinos in a way that slows them down slightly, as when light passes through much heavier matter such as glass?

There are some interesting materials in which the group velocity or phase velocity of light can technically be made to exceed c, but these special cases aren't actually violations of the speed limit because the information carried by those signals still travels at c or slower.

As for interactions between neutrinos and photons, it is speculated that neutrinos might have a very small magnetic moment, in which case they would couple to electromagnetism. However, there is no known electromagnetic coupling, and the observed penetration of matter by neutrinos is such as to rule out any significant coupling.

It is best to think of the speed of light in vacuum as a unit conversion factor rather than a speed. The most intuitive way to think about special relativity is as looking at a map from different angles. The distance between two points on a map doesn't change, regardless of how you hold the map, or which angle you look at the map from. Special relativity says the same thing, only the "points" are "events", the "map" is "space-time", and the "angle" you are holding the map at is your "inertial frame". The whole thing about c being a unit conversion factor is really just the geometry we all learned in junior high, with a small twist. Consider the case of the map. The straight-line distance between two points can be calculated using the Pythagorean theorem: just find the up-down and left-right separation of the two points, and take the square root of the sum of the squares. If you hold the map at a different angle, you'll measure different up-down and left-right separations, but the straight-line distance you calculate with the Pythagorean theorem is still the same. Now, in special relativity, "up-down" is "space", "left-right" is "time", and instead of the Pythagorean theorem you calculate a space-time interval based on the difference of the squares of the space and time separations, instead of the sum. But the basic physical premise is pretty intuitive: there is some underlying reality that doesn't change according to your perspective. For a map, what you call "up-down" or "left-right" might change depending upon how you're holding the map, but the points are real, and the distance between the two points doesn't change; for space-time, the events are real, and although the separation in space and time between two events might change depending upon your state of motion, the space-time interval doesn't change. Only here's the thing: you can't mix space and time in a calculation like this without using the same units for both. What we're saying is that time is just another direction, so we need to be able to measure separation in time using meters, just like we measure separations in space. (After all, you can't make the Pythagorean theorem work if you measure up-down distances in feet and left-right distances in inches.) And that's all c is. It is just the unit conversion factor that allows you to do geometry -- nothing more magical than there being 12 inches in a foot.

Why c is regarded as an upper limit on speed is a bit too complicated to describe well in text (and honestly, 17 years after taking special relativity, I didn't retain the details of the argument as well as the stuff about the interval), but it relates to the same basic geometry. The apparent order in which events occur depends upon their separation in time, and if v>c, it starts becoming possible "to hold the map" in a way such that effects precede their causes. As long as v<=c, effect always follows, or is simultaneous with, cause, no matter how you hold the map. So v>c for the transmission of information is regarded as nonsensical.

[Sharky]

Re: neutrinos travel at a velocity 20 parts per million above the speed of light

ASH, thanks for that info. Very interesting.

The way I've always looked at c as being an upper limit on speed is: from the perspective of an object traveling at the speed of light, the size of the universe in the direction of travel becomes infinitely thin. Since such an object could be anywhere in the direction of travel instantly from its perspective, it's meaningless to travel faster.

On a somewhat related note, do you happen to know where I might find a good explanation of the physics of the vacuum: vacuum energy, particles popping in-and-out of existence, and things like that?

[charliebrown]

Re: neutrinos travel at a velocity 20 parts per million above the speed of light

dang Ash that was a great read, thanks.

How is old Beaverton? I used to work for Sequent computer systems. I had a few junkets there.
If you're ever in chi town, look me up.

[sunskyfan]

Re: neutrinos travel at a velocity 20 parts per million above the speed of light

Over the years Super-luminal phenomena have been observed but they are geometric illusions: http://en.wikipedia.org/wiki/Superluminal_motion

Gravitation also affects the apparent speed of light. C being the idealized speed of light in a vacuum. Light travels at different speeds through different mediums such as glass and air. If this were not the case lenses would not do what they do and form images. When light passes through an objects gravitational field its speed relative to light that passes farther away is different and you get gravitational lensing effects.

Both of these are clearly observed phenomena concerning the different speeds of light in nature that are explained but don't violate the basic premise that information cannot be conveyed faster than C (defined above). My point is that anybody observing a phenomena that appears to be super luminal has a lot of difficult accounting to do before making an extraordinary claims. However, until there is a good reckoning between gravitation and quantum physics I certainly keep a open mind to extraordinary possibilities including transmitting and receiving information faster the C.

PS ... I didn't know the SN1987A observation. Very cool.

[Sharky]

Re: neutrinos travel at a velocity 20 parts per million above the speed of light

This used to be the understanding, but that changed in 1998 with the discovery of neutrino oscillations, which require that neutrinos have non-zero rest mass.

Doesn't Relativity say that an object with a non-zero rest mass can't travel at the speed of light? Infinite energy needed, mass becomes infinite, etc? How does modern physics explain that?

[Starving Steve]

Re: neutrinos travel at a velocity 20 parts per million above the speed of light

Doesn't Relativity say that an object with a non-zero rest mass can't travel at the speed of light? Infinite energy needed, mass becomes infinite, etc? How does modern physics explain that?

If you divide by zero, the universe of mathematics gets crazy too. Just divide anything by zero and then look at your calculator.

There are certain strange laws of the universe: I.) Thou shalt not divide by zero, ever. II.) Thou shalt not travel nor observe anything travel faster than c. III.) Nothing can happen before it has begun to happen. IV.) There is a square root of negative 1, and imaginary numbers exist in the universe. V.) Space-time is bent by mass. VI.) One can not travel backward in time. VII.) The universe and everything in it is running toward chaos and heat. VIII.) Nothing lasts forever.

For more information on God's laws, please consult with God. Nothing shall violate any of His laws. No exceptions nor complaints.

[seanm123]

Re: neutrinos travel at a velocity 20 parts per million above the speed of light

LHC Rap, I sure wish I could go back to 1985.....

http://www.youtube.com/watch?v=j50Zs...e_gdata_player

[Sharky]

Re: neutrinos travel at a velocity 20 parts per million above the speed of light

If you divide by zero, the universe of mathematics gets crazy too. Just divide anything by zero and then look at your calculator.

Sorry, I don't understand how this relates to my question.

I.) Thou shalt not divide by zero, ever.

That's what mathematical limits are for. You don't divide by zero; you calculate the result as the denominator tends to zero in the limit.

IV.) There is a square root of negative 1, and imaginary numbers exist in the universe.

Yes, but not as physical entities. Imaginary numbers, like their non-imaginary counterparts, exist as concepts.

VIII.) Nothing lasts forever.

I don't agree. The universe had no beginning, and will have no end; it just is -- it's the metaphysical given.

For more information on God's laws, please consult with God. Nothing shall violate any of His laws. No exceptions nor complaints.

If only it was so easy.

[ASH]

Re: neutrinos travel at a velocity 20 parts per million above the speed of light

The way I've always looked at c as being an upper limit on speed is: from the perspective of an object traveling at the speed of light, the size of the universe in the direction of travel becomes infinitely thin. Since such an object could be anywhere in the direction of travel instantly from its perspective, it's meaningless to travel faster.

That's a good point.

On a somewhat related note, do you happen to know where I might find a good explanation of the physics of the vacuum: vacuum energy, particles popping in-and-out of existence, and things like that?

Those phenomena are described by relativistic quantum field theory (QFT), and the Wikipedia write-up is actually the best short explanation I've come across. I should mention that relativistic QFT is beyond my mathematical abilities; I am aware of the results of the theory in a qualitative way, and in some cases I have applied those results in simpler calculations, but I don't have the chops to derive those results. I took a fair amount of non-relativistic quantum mechanics in school, which was (to me) challenging enough... but the math required to make all that stuff obey special relativity is what separates the men from the boys, and I definitely fell into the latter category. The same thing happened with general relativity; special relativity is relatively accessible, but general relativity requires significantly more mathematical sophistication. That said, some of the physics and math associated with vacuum energy and virtual particles, etc., actually shows up in non-relativistic quantum mechanics that I have studied, and sometimes results from relativistic QFT get spliced into non-relativistic quantum mechanical calculations where they apply (like when you study the interactions of light with matter for the purpose of designing a laser). I've had enough formal exposure to those topics to speak to them a little.

Virtual particles, vacuum energy, and zero point energy are all the same thing, and at a basic level, they are just a manifestation of the fact that momentum is associated with frequency, and in order to have a frequency, a pattern has to repeat and take up space. In special relativity, momentum and energy are respectively the space- and time-projections of a single 4-dimensional vector property, and what is true of momentum and a repeating pattern in space is also true of energy and a repeating pattern in time. What this means is that an exact location/time is fundamentally incompatible with an exact momentum/energy, because in order to have an exact frequency, it would have to repeat forever, and that would take up an infinite amount of space/time.

Even though you can't have something that simultaneously has an exact location/time and an exact momentum/energy, you can have something that is simultaneously at a mixture of locations or times with a mixture of momenta or energies. In particular, even though you can't simultaneously be exact about pairs of incompatible properties, you can have states in which the range of both are narrowed down. Zero-point energy is a consequence of the fact that a mixed state of spatial locations and momenta -- or equivalent incompatible properties -- happens to be the lowest-energy stable state (a.k.a. the "ground state") for a wide variety of systems, from atoms to vibrating crystals to the electromagnetic field. To give an example, the lowest-energy stable state of the hydrogen atom doesn't involve an electron sitting exactly on the nucleus, with an infinitely broad range of momenta, nor does it involve the electron moving at an exact momentum, but spread out over all of space. Instead, the electron is confined within the general vicinity of the nucleus, and its momentum falls within a certain range, but neither property has a single value. There is some kinetic energy associated with the momentum spectrum of the electron, and when the ground state of a system has some energy, we call that energy zero-point energy.

A particularly important type of zero-point energy is associated with systems that vibrate, such as atoms vibrating together in a piece of solid matter. Harmonic oscillators have the interesting property that their energy states are evenly spaced, but their ground state has an energy equal to half the normal energy step between states. The ground state's half-step worth of energy is zero-point energy, and you can think of it as the atoms continuing to vibrate, even at absolute zero temperature (when all the mechanical energy which can be removed from the lump of matter, has been removed). This is the stepping-off point for virtual particles and quantum field theory. It turns out that the electromagnetic field can be written in terms of parameters which have the same relationships as the mechanical parameters describing the motion of a harmonic oscillator, and so have the same type of mathematical solution: evenly-spaced energy states, and a ground state with a half-unit of energy. In the mechanical system, the units of energy in the evenly-spaced energy states are called "phonons", and the half-phonon in the ground state can be thought of as some residual vibrational motion that continues even at absolute zero. In the electromagnetic system, the units of energy are called "photons", and the half-photon in the ground state of the electromagnetic field can be thought of as some residual light that exists in vacuum, even when all available energy has been removed.

The half-photon associated with the zero-point energy of the electromagnetic field is an example of a virtual particle, and is also an example of how "vacuum" can have energy. Even in a vacuum, the electromagnetic field still has some energy in its ground state, and there are still "half-photons" present. Virtual electrons, quarks, etc., associated with other quantized fields are also present in "vacuum". They are often described as resulting from the tradeoff between certainty about time and energy. Over an indefinite period of time, one can be certain that the energy in the vacuum is zero, and that there are no electrons present. But over a limited period of time, the energy in the field spans a range of values, since an exact amount of energy is fundamentally incompatible with an exact time. Thus, over short spans of time, virtual electrons associated with the range of energy in the field exist, even if there are no electrons there over an infinitely long span of time. In order to satisfy conservation of charge and momentum, virtual anti-electrons have to be created along with the virtual electrons, in equal quantities. This is usually described as creating short-lived virtual matter-antimatter pairs which annihilate and disappear a short time after creation, leaving the long-term average energy zero. Alternatively, since an electron moving backwards in time looks like a positron moving forward in time, this is sometimes described as a virtual electron popping into existence, flitting around a bit for as long as the range of time associated with the range of energy permits, and then looping back around in time to its starting point and disappearing.

The thing about virtual particles and the vacuum energy is that although they cannot be directly observed (because you can't take energy out of the field when it is already at its ground state), they can be observed indirectly through their influence on other particles. For instance, virtual charged particles like electron-positron pairs can orient themselves in an electric field, partially shielding the charge of a real charged particle. This effect is called "vacuum polarization". Another exceedingly important example is the spontaneous emission of light, which is actually stimulated by virtual photons.

Anyway, that's the top-level view of what's going on in the vacuum. There's a lot of ugly sausage under the hood, which I do not (and cannot) understand in rigorous detail, but to the best of my knowledge this summary is accurate.

[ASH]

Re: neutrinos travel at a velocity 20 parts per million above the speed of light

Doesn't Relativity say that an object with a non-zero rest mass can't travel at the speed of light? Infinite energy needed, mass becomes infinite, etc? How does modern physics explain that?

You are correct. The official line is that high-energy neutrinos are travelling just under the speed of light. In particular, we can't deduce the neutrino rest mass from the neutrino oscillation observation, only the difference of the squares of the masses of pairs of neutrinos of different types (there are three known types of neutrino). However, the neutrino oscillation observation does tell us that at least one type of neutrino has a mass of at least 0.04 eV. The neutrinos emitted by supernova 1987A were thought to be created by a process that gives them an energy of about 14 MeV. So we're talking about a mass increase factor of something like 350 million, meaning that they are travelling pretty dang close to the speed of light.

The reason the neutrinos from SN1987A arrived about 3 hours before the light did has to do with how hard it is to get energy out of something as dense as the core of a collapsing star. The scattering cross section of a neutrino varies with its energy, and is something on the order of 10^-43 / cm². Neutrinos mainly interact with nuclear matter (protons or neutrons), so if you multiply this cross-section by the density of protons and neutrons in a medium, you get the number of interactions per centimeter of travel through that medium. A cubic centimeter of lead weighs 11.34 grams, and a proton or neutron weighs about 1.67*10^-24 grams, so there are 6.79*10²⁴ protons or neutrons per cubic centimeter of lead. Multiply this with the neutrino scattering cross section, and you get 6.79*10^-19 interactions per centimeter of travel, or one interaction on average after traveling 1.47*10¹⁸ centimeters. A light-year is about 9.46*10¹⁷ centimeters, so the average neutrino can penetrate about a light-year of lead without hitting anything. Nothing else can do this. When the core of a star is collapsing in a supernova, the material density is on its way toward 10¹³ - 10¹⁵ grams per cubic centimeter (at least). Neutrinos can make it out through such dense matter a lot faster than mechanical energy (like a shock wave), heat, light, or other particles. So that's why the neutrinos showed up 3 hours early -- not because they were traveling faster than light, but because they got clear of the stellar core sooner.

[ASH]

Re: neutrinos travel at a velocity 20 parts per million above the speed of light

dang Ash that was a great read, thanks.

How is old Beaverton? I used to work for Sequent computer systems. I had a few junkets there.
If you're ever in chi town, look me up.

Hi charliebrown. It's always a pleasure. Beaverton seems pretty healthy; Intel is building another big fab here, and I take that as a sign that they're committed to keeping their R&D here. As long as we've got Intel, Nike, and the myriad tech companies spawned by the great Tektronix diaspora (Triquint, Maxim, etc.), things will probably stay relatively prosperous. That said, we just put our kids in daycare (the wife just started at Intel), and didn't have to wait for an opening. That's probably a sign that not everything is booming.

I'd love to drop by someday; I sometimes have business at Argonne National Lab. Is that close enough to you for a visit? Please let me know if you're ever in the Portland area.

[Sharky]

Re: neutrinos travel at a velocity 20 parts per million above the speed of light

ASH, thanks for the very interesting and detailed answers, although it will take me some time to digest them.

My undergraduate studies were focused on math (real analysis), chemistry (organic and p-chem) and biology (30+ yrs ago now). I wasn't exposed to much quantum or relativistic physics or cosmology until long after that, and it was only then that I started to wish I had made it my area of study and work. Instead, I ended up taking a detour into doing rocket science and spacecraft design. Plenty of interesting physics there, too, but on a different scale.

[Starving Steve]

Re: neutrinos travel at a velocity 20 parts per million above the speed of light

Imaginary numbers exist as real entities in a five-dimensional world. Imaginary numbers would then mark a position on the fifth dimension axis. Thus, we might have: length, width, depth, time, and the 5th dimension.

Am I correct? I only read some stuff on the internet, and that seems to be what they were saying about imaginary numbers. But I am not a physicist. Maybe the 5th dimension is gravity?

Also, on the "nothing lasts forever" law, I thought our universe of 4 or 5 dimensions began with the Big Bang, and the Big Bang began with a black hole that collapsed in another universe. Again, I am venturing into physics, and I am not a physicist. The Big Bang was 15 billion years ago, and the Earth was formed 5 billion years ago. Moon in Earth orbit approx. 4.5 billion yrs. ago. Again, am I correct? The last Ice Age ended 10,000 years ago. The Little Ice Age ends in late 19th C. The liberation from Hitlerism was in 1945. Starving Steve born 1948. Last silver dollars in circulation in America 1962. Gold window closed 1971. Climax of the Great Inflation 1980. Greenspan appointed to the Fed in 1983. Twin towers fall in 2001. Real estate peak was in 2007. Great Recession began in 2008. Interest rates on 30-day U.S.Treasury bonds reach 0.0000% in 2011.

[sgominator]

Re: neutrinos travel at a velocity 20 parts per million above the speed of light

Doesn't Relativity say that an object with a non-zero rest mass can't travel at the speed of light?

Maybe You forgot the fact that Relativity is a THEORY