Mail 693 Sunday, September 25, 2011

Relativity, causality, and the CERN faster than light neutrinos.

Additional material added Monday, Septermber 26, 2011

First, here is, I think, the consensus position:

Faster than light?

Nothing can travel faster than the speed of light. The problem is one of viewpoint in more ways than one.

The sun, the reality of the sun, is not 8 light minutes away, which if the Earth is zero-point of time, the sun as witnessed from the Earth would be minus 8 minutes with regard to zero-point. The reality of the sun is that (-)8 minutes (+)8 minutes to the sun’s zero-point of time (0 = 0).

Now, nothing but a photon will travel from 0-point Earth to (-)8 minutes sun. Anything else will travel from 0-point Earth to 0-point sun and always arrive at the sun 8 minutes earlier than any observer or instrumentation on Earth will witness it to arrive. If it takes 2 minutes for something to travel from Earth to the sun, the observation per the speed of light will be 8 minutes plus 2 minutes for an Earth observed travel velocity of 10 minutes from 0-point to (-)8 minutes. An Earth observed velocity slower than the speed of light.

Of course from the point of view of the sun, the traveler arrives at 0-point (the sun) before it leaves the Earth (-)8 minutes, a trip from (-)8 minutes to 0 in two minutes, the math being (+)8 minutes to get from (-)8 minutes to 0. Rather, (+)8 minutes inside two minutes, 8 minutes worth of light-time photo events in transit between the sun and Earth traversed in two minutes. A fast forward of a historical movie (the sun (-)8 minutes at Earth to the reality of the sun in its own spatial 0-point of time equals a voyage [forward] in space and time of (+)8 minutes within two minutes of travel time).

This works for all travel from object reals (0-point) to object reals (0-point) whether the travel is for a trillion trillionth of a light second’s distance ((-)x to 0 via (+)x) or ten trillion light years of distance ((-)x to 0 via (+)x). (+)x is the direction and nothing is ever going to travel backward in time or leap forward in time.

Mr. Pournelle, there is no space tied to time in the expansions and contractions of time of physicists. In a unification of space-time, the space is as flexibly relative as the time, exactly as flexibly relative, and time cannot be contracted or expanded without a concomitant spatial contraction or expansion, preventing the kind of time travel where children come out of travel older than their parents or grandparents, or a parent comes out of it younger than his children and even his grandchildren. You notice that the observation from the Earthly point of view above exactly contradicts the observation from the sun’s point of view. The Earth observer says there was no travel faster than the speed of light, 10 minutes to travel 8 light minutes (observing a decelerative travel 0 to (-)8 minutes). The sun as an observer would say that there most definitely was travel faster than light (observing an accelerative travel (-)8 minutes to 0). The traveler (the third 0-point of time) in point of view forward up through space-time to 0-point (the on-rushing sun) says no there wasn’t, and in point of view rearward down through space-time to (-)8 minutes (the distancing Earth) says yes there was. In all, the two contradicting observations cancel each other out.

G.L. Bradford

There are two ways of calculating where the Sun “really is now” when you see it in the sky. After all, the Sun has moved since the light we now see left the surface of the Sun. Surely it can’t be in the direction that you’d get if you pointed to the bright yellow thing you see in the sky. Only there is aberration – that is, Earth is moving (or under the principle of relativity the sun is moving) so that the light doesn’t come from the direction we thought. The light arrives from an aberrant angle. The aberration is in the direction of the velocity of the Earth (or of the Sun, depending on which reference frame you like). Magically, at least to a very close approximation, the Sun really is “that way right now” when you point to it in the sky. Now Newton assumed that gravity propagates instantly. That assumption leads to some predictions regarding where the planets will be over time, as for example when the planet will be in perihelion to its primary; and the prediction is wrong. If you assume that gravity propagates at the speed of light, Newton’s calculations turn out to work, and to be a lot simpler than if you do the complex math required by general relativity.

Assume that the light leaves the Sun and at that instant a well insulated observer teleports to the Sun. Why would he get there before the light left the Sun? I fear I am not following you. From the point of view of someone in Washington, the Battle of New Orleans took place after the Treaty of Ghent ended the war: a sailing ship got the news across the Atlantic before anyone was able to get a message from New Orleans to Washington, Somewhere along the path from the District to NO, say about Memphis, the new arrived simultaneously. All very well, but Packenham was still dead, and Andrew Jackson was still the hero who would become President, even though the news got to people in a different order. And if someone in Ghent – someone credible – had been able to teleport to Packingham’s camp the night before the assault, the result would simply have been that the battle didn’t happen, so far as I can tell. Which would greatly affect American history – possibly no President Andy Jackson, a renewal of the Bank of the United States, possibly the survival of the Whig Party … all interesting speculations, but I don’t see any paradox here.

Neutrinos/causality/headache

Dr. Pournelle,

Your speculation on FTL comments brought to mind two questions:

1. If some particle is observed to travel faster than c, why not recognize that particle as the basis for a space-time speed limit? The concept of causality violation, and all of its Wikipedia examples, seems to be based on light being the fastest means by which information (e.g. seeing your comet impact from Earth) can travel. From the lay perspective, that’s a circular argument in itself – if you accept that light is fastest, of course you’d run into paradoxes. If you re-draw the "light cone" as a "neutrino cone," with the edge between light speed and the speed recently measured at CERN expressed as a probability function, the paradoxes disappear again, at least so far into the math…I’m a pilot, not a physicist.

We could follow (and expand) your analogy of sailing ships delivering messages, and recognize that if the presence of a neutrino sixty nanoseconds earlier than it was supposed to arrive conveys a bit of information (vs. that neutrino arriving at light speed, to the proper observer), then causal relationships are not turned upside down, any more than with Andrew Jackson’s lack of a satellite phone, merely because we aren’t currently able to receive information that way. Perhaps some entity is so equipped.

Which brings up the second question:

2. Wouldn’t the most appropriate theory then be that neutrinos are what the stars use to communicate with each other, to avoid the apparent simultaneity of cause and effect? "Eta Carinae just Twittered: ‘Going supernova, guys, here’s your 60 ns heads-up…’"

Ian Rummel

But of course we are both naive…

Tachyonic Neutrinos and Causality

Tachyonic neutrinos suggest the existence of a preferred (true privileged) inertial frame. Baez discusses them in http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#19 . Now that we have them, what do we do with them? They destablise the vacuum; we exist; something has to give. They also cannot be used to transmit information at FTL speeds; we’ve measured their velocity in a beam that is turned on and off; oops…

Harry Erwin

Which is the heart of the matter. If there is a preferred reference frame everything changes. Of course that makes for some oddities, too.

A paradox of the Special Theory

This question has been buggin’ me for years – decades, really. I put it to Petr Beckman once, but he understandably begged off, as he didn’t believe in relativity.

The classic description of the dilation of time part of the special theory says that you have a spaceship, two clocks and a magic telescope. The clocks are synchronized, one of them is put on the ship and the ship takes off. Before long it is traveling at a significant portion of the speed of light, relative to us (on Earth, presumably). When we look at the clock on the ship with our telescope and compare it with our clock, we see that it is running slower, since it is traveling so fast.

But what if there are two telescopes, and one of them is on the ship? According to the special theory, won’t the astronaut, when he looks at the clock on Earth, observe that it is running slower than his, because the Earth is moving away from him so fast? Remember that the Earth is not fixed and that all velocities are relative.

If that confuses you, imagine that there are two space ships, each with a clock and a telescope. They start at the same point in space and accelerate in opposite directions until their velocity, relative to each other, is nearly the speed of light. According to the special theory, each would observe the other’s clock to run slower than his own. Which one is right? What will the clocks show when the drivers apply the brakes (this is a thought experiment, remember) and bring their ships to a stop (relative to each other)?

This seems to me to be a paradox of the special theory, but I don’t have an advanced degree in theoretical physics.

Richard White

Austin, Texas

Well, the math on that is fairly straightforward and not all that difficult as a thought experiment.

As you state, the most that can be said with special relativity is that, to an observer traveling faster than light, there are some reference frames in which a sequence of events, say A precedes B for a sublight observer, appear to be reversed for the relatively faster than light observer — WHEN viewed by visualization of the light emitted at A and B. Casualty should be correct for such events when viewed by an appropriate FTL viewing scheme, and time reversal is not automatic. However, the FTL technique must admit of infinite velocity to completely avoid the problem — otherwise it would always be possible to find a restricted subset of the space where the casualty remains reversed. (That’s going on memory; I haven’t actually worked with the relevant equations since grad school.)

This does not discount the closed timelike loops of general relativity, which are a different but related phenomena.

I’ve occasionally considered buying Professor Beckman’s book but haven’t had the opportunity; conversely, his is hardly the first time I’ve heard the same suggestion. (Frankly, that might be The Skylark of Space.) I note that second-hand copies presently list for $120+ on Amazon.

I have the book, but I do not know who Beckmann’s literary executive is. It is certainly still in copyright.

Subj: Re: FTL neutrinos at CERN?

The paper has been posted:

http://static.arxiv.org/pdf/1109.4897.pdf

First impressions:

1. The quoted mu neutrino velocity is (v-c)/c = (2.48 ± 0.28 (stat.) ± 0.30 (sys.)) ×10-5 for average energies <E> = 17 GeV.

2. The FERMILAB MINOS experiment ALSO reported a FTL neutrino with statistics

(v-c)/c = 5.1 ± 2.9×10-5, which is within 1 sigma of the more precise CERN result, for an energy distribution E = 3 – > 100 GeV but much lower mean energy (not specified in the CERN paper).

3. The nominal SN 1987A neutrino velocity result for 10 MeV electron antineutrinos was |v-c|/c < 2×10-9.

4. At the end of the paper they present a first, crude attempt to assess an energy dependence. While the results are not of adequate statistics to draw any firm conclusions, their preliminary result is that neutrinos of > 20 GeV energy averaged 20% greater velocity (TOF) deviation than neutrinos < 20 GeV, which is less than 1 standard deviation of the difference statistics. However, such a result is contrary to the naive Feinberg tachyon.

Bottom line:

(a) We now have two consistent experiments with faster than light, very high energy neutrinos, one with two sigma statistics, one with six sigma statistics.

(b) We have a preliminary hint that the results, if they stand with greater statistics, are not consistent with classical special relativity tachyon theory.

Physicist

Which sums it up about as well as anyone can. Obviously the way to bet it is that this is experimental error. SF writers hope for something else, of course. Space opera writers need that FTL…

ADDITIONAL MATERIAL ADDED MONDAY 26 September 2011

"There are two ways of calculating where the Sun “really is now” "

Actually there are none. I have not commented on this before because I thought for sure you must understand this but I increasingly have the impression you really don’t.

In a relativistic universe, there is no such thing as "at the same time" across interstellar distances. The only occasion when you can have things "at the same time" is when they are also "at the same place".

What specifically causes the time travel effect is the relativistic slowing of clocks as observed from different inertial frames of reference. When the two frames of reference are separated, each one sees the other as having accelerated and thus having its clock slowed slightly. Trying to reconcile two mutually exclusive cases – that each clock is slower than the other guy’s – is what produces the paradox and the time travel. Lightspeed in this case isn’t an arbitrary limit, it’s fundamental to the math, because it’s fundamental to the time distortion – which has been experimentally verified. It’s not clear to me that the starting point and the end point in this particular experiment are actually different inertial frames of reference – which would seem to me to prevent the time travel effect, at least in this case – but properly exploring the implications of that would have to be left for a better physicist than I.

In general though it makes absolutely no sense to talk about where the sun "really is now". It isn’t. You can’t know. I don’t mean you don’t have the tools for it, I mean the knowledge is not physically possible within the structure of reality. The reason you think like that, and think it should be possible to know it, is because your human animal brain has evolved and is equipped to handle the everyday world of Newtonian mechanics, where "at the same time" generally makes sense. All your hypotheticals and counterfactuals about going a little bit or a lot faster than light to go check something are fundamentally Newtonian thinking. In this universe, things don’t work that way.

Unless of course the neutrino experiment turns out to be correct, in which case there is a lot more to the story. But every experiment up until now that was intended to verify various aspects of relativity has produced exactly the results the theory predicts.

R

I am aware that if one accepts the theory of relativity then one accepts the premises, and the premises say “no privileged reference frame”, and thus it is meaningless to ask “where is the Sun really truly.” One of the reasons why some rather respectable people rejected Einstein: not from pique, but because they found it needlessly complex as an explanation of the observed data. The observation is that there’s a bright yellow disk in the sky. We see it can can point to it. And we have done experiments that tell us reliably that it takes 8 minutes for the light from that bright yellow disk to get to us.

Beckmann asks the question this way: “Is the bright disk in the sky a souvenir left by the sun where it was 8 minutes ago, or is that the direction to the real sun where it is now?”

To most of the people in the world including – as Beckmann observes – the janitor in the lecture hall, that is a meaningful question; yet as you point out, Einstein’s relativity (as opposed to the Principle of Relativity which has been around far longer than Einstein’s) makes the question, if not meaningless, then vary complicated. I point at the disk and say “If I go in that direction for 8 light minutes, where will I be relative to the Sun?” It is precisely the complexity of asking question which spurs some to seek alternatives. And as Beckmann observes: “It is a sobering thought that when the professors are through arguing, they find the position of the sun exactly where the janitors never doubted it to be; and if we apply this janitors’ principle to [a] fictitious body S’ which travels at the same angular velocity as the earth but lies beyond it, so that its light – like the sun’s gravitational force – has the same direction as sunlight, but the opposite sense, then clearly everything that has been said about the propagation of light must equally well apply to the propagation of force.”

Newton’s classical physics assumed that the propagation velocity of gravity was infinitely fast; using his equations but assuming that gravity propagates t a finite speed yields the same results as Einstein’s equations, and assuming that that velocity is c gives results that fit quite well to the observed data. And it’s a whack of a lot simpler. Beckmann continues “the present theory assumes that forces propagate with velocity c from their sources, that Newton’s Laws and the Maxwell equations are valid when all velocities are referred to the local force field rather than to an observer, and that the relativity principle is valid in Euclidean space and unreformed time, This leads formally to the same expressions for mass, momentum and energy, and to the same relations among these thee as in the Einstein theory, but the corresponding effects are rooted in the phenomena themselves, independently of any observer’s location of perceptions.” (Einstein Plus Two page 72)

The FTL neutrino doesn’t change any of this for Beckmann and the other “revised classical” theories. Thus Einstein can’t ask where the Sun really is, but if the FTL neutrinos prove out, then the rest of us can sensibly ask “where’s the Sun just now?”

Faster Than the Speed of Light?

Jerry,

First some questions.

Is there a difference in the speed of light in a vacuum versus the atmosphere?

Is Time consistent throughout the Universe?

How many dimensions beyond the four that we can currently sense and measure exist?

Why do we let Schroedinger tell us that we may change the state of the cat in the box when we know that there is no rational reason that opening a normal box will affect the state of the cat?

(However, the currently available methods for observing the spin of an entangled photon clearly will change the state of the entangled pair. The difference would seem to be between destructive and non-destructive means of observation.)

When is a transfer of information that appears to be FTL, in fact not FTL?

(To answer my own question, when the actual transmission distance is less than the distance measured by the observer. This is a possible answer to the entanglement quandary.)

To sum up, our problem is that our view of the Universe is limited by what we can sense and our measurement techniques. Perhaps the Universe is actually much smaller in volume than what we currently observe. Perhaps, using dimensions that we currently cannot observe, things are much closer together than the appear to us.

Maybe God isn’t playing dice with the Universe.

Bob Holmes

I am certain that some variant of string theory will come to the rescue.

My question is, suppose an alien space ship headed toward the Earth at a high fraction of the speed of light. That means that the ship has gained weight. But since there are no privileged reference frames, it’s equally valid to say that Earth and all on it have gained weight, Given that, can Jenny Craig get that pesky alien to slow down so that we’re not so fat?

Of course if we don’t know that the aliens are coming at 0.98 c, then will their ship have any effect on us? But when we learn…

You may have already seen this …

"We don’t allow faster than light neutrinos in here" said the bartender. A neutrino walks into a bar.

—

Brian Dunbar

Geidus

"Display some adaptability"