speed of light

[prokofiev]

... but forgot to account for the fact that from the perspective of the satellite the source and destination are moving, so the actual place (in the satellite's frame) of the destination moves (very slightly) closer or further from the source's original place (in the satellite's frame) during the travel time of the neutrinos. ...

Er, I must be not understanding something because I thought that that (the relative motion) was what you needed to put into Lorentz transformation? Are you saying they didn't use the right data when they did the math? This isn't related to my field in any way so you're probably right, but now I'm confused...

For anyone else that needs to look up Lorentz (I didn't remember the name): http://en.wikipedia.org/wiki/Length_contraction

There are two effects:

1) The distance between CERN and Gran Sasso is smaller (due to relativity; there's length contraction) in the satellite's frame. CERN and Gran Sasso are continually moving in the satellite's frame, but stay a constant distance apart, which is slightly smaller than the distance in our frame. This is not in dispute.

2) In the satellite's frame, CERN and Gran Sasso are moving. The original place CERN was is where the neutrinos left from. The final place of Gran Sasso is where they arrived. The distance between the original place CERN was and the final place Gran Sasso was in the satellite's frame isn't quite the same as the fixed distance between CERN and Gran Sasso at the same time in the satellite's frame.

To summarize (2): If you're standing on the ground watching a train go by, and two people on opposite ends of the train are blinking lights at each other, to you the light travels farther when blinked in the direction you see them moving and a shorter distance when blinked in the opposite direction (to the people on the train, they're equal). Since light always goes at the same speed in your frame (or any frame), it takes more time in one direction than the other, according to you.

(If they were throwing balls at each other, the distance would look longer in one direction and shorter in the other, but when the ball goes in the longer direction it would look faster, and take [almost!] the same amount of time as the ball in the other direction, since there's almost no correction for relativity since the balls go much slower than the speed of light.)

The paper we're discussing says the opera team considered (1) but missed (2). I haven't read the opera team's paper so I don't know if that's correct.

[SpongeBob]

...and the plausible explanations begin: http://www.technologyreview.com/blog/arxiv/27260/

This is just beautiful. It should be included as a problem in future physics textbooks: 'They measured the neutrinos to have arrived around 60 ns earlier than expected. How can that be explained by taking into account the movement of the reference system of the satellites and the system of the emission and observation labs.'

[daniel_the_smith]

There are two effects:

Thanks, I still don't understand it but my ignorance is more clearly defined now.

[prokofiev]

There are two effects:

Thanks, I still don't understand it but my ignorance is more clearly defined now.

Sorry I didn't explain more clearly

One more quick attempt:

1) is just length contraction

2) doesn't have much to do with relativity. Suppose you're standing still and see two people playing catch who are moving at the same speed in the same direction (maybe they're on a conveyor belt, or running at the same speed, or on a train). When the leading guy throws the ball to the trailing guy, the ball travels less than the distance between them, because the trailing guy catches up while the ball is in the air. When the trailing guy throws the ball to the leading guy, the ball travels more than the distance between them, because the leading guy keeps going while the ball is in the air.

Really fast things like light and really slow things like balls interact differently with the change in distance in (2), which, together with really poor wording, is probably why my post was confusing.

[daniel_the_smith]

Sorry I didn't explain more clearly

Oh, I don't think it's your fault

I had thought that #1 and #2 were the same effect, but that can't be correct because #2 is explainable via Newtonian mechanics, and #1 is an effect of relativity, so there is clearly a hole in my understanding. Off to read the relevant wikipedia pages when I have time...

If this explanation is correct, it is pretty funny that the team got relativity correct but not the simpler effect. Or maybe they made the same mistake that I did in thinking it was the same, and that they had thus accounted for it.

[mitsun]

I had thought that #1 and #2 were the same effect, but that can't be correct because #2 is explainable via Newtonian mechanics, and #1 is an effect of relativity ...

Maybe this will help:

#1 is Lorentz contraction, making the distance between source and detector appear shorter to the satellite than to a ground observer. This contraction does not care which direction neutrinos travel.

#2 is velocity addition, making the distance traveled by the neutrino, as observed by the satellite, less than the distance between source and detector, as observed by the satellite. (The detector moves toward the neutrino while it is in flight). This velocity addition does depend on the direction of the neutrino. The same effect exists in Newtonian physics, but a relativistic generalization of the formula must be used.

[SpongeBob]

I thought that special relativity says that 1) moving objects are contracted and 2) moving clocks run slower.

If 1) has been taken into account, can the error be explained by the team not taking into acount 2) or is there something else that needs to be factored in?

I thought that special relativity could be completely derived from the assumption that the speed of light is always measured as c, regardless of the frame of reference.

[prokofiev]

If 1) has been taken into account, can the error be explained by the team not taking into acount 2) or is there something else that needs to be factored in?

The opera team accounts for both (even the van Elburg paper says this).

To follow up on all this, here's a recent interesting article http://www.livescience.com/16621-faster-light-neutrino-relativity-gps-clocks.html

Strangely, the opera team's response seems confused about the effect we're discussing?:

OPERA responded to van Elburg's accusation. "The author [van Elburg] is not really taking into account special relativity (SR), but he is trying to compose the speed of the satellite with the speed of the radio waves, which makes no sense in SR," spokesman Pasquale Migliozzi told Life's Little Mysteries. "Composing speeds" is a special way of adding them together in special relativity.

Van Elburg countered that Migliozzi has not correctly understood his argument. "I am not composing velocities but adding two distances in a single reference frame," Van Elburg said. A reference frame can be thought of as the point of view of a moving object — in this case, the GPS satellite.

But anyway they claim the GPS system accounts for such effects:

Migliozzi also asserted, "The author does not know that relativistic effects are accounted for in the GPS system." To this, van Elburg said he is checking his facts and will follow up with additional details soon.

[jts]

Round Two, fight! ding ding

http://www.nytimes.com/2011/11/19/science/space/neutrino-finding-is-confirmed-in-second-experiment-opera-scientists-say.html?_r=1&hp

[Joaz Banbeck]

I still want to see it done with two groups of neutrinos going in opposite directions at the same time, and average the results.

Until that point, they're playing a nearly insoluble guessing game: "You didn't think of this complication!"..."Oh, yes we did!"...and there is seemingly no end to the possible quibbles over correct measurement. The objections must be eliminated one-by-one by math. But if there are two groups going in opposite directions, many of the objections are eliminated by logic - because they cancel themselves.

[flOvermind]

Shouldn't be that hard... We just need to build another LHC underneath Gran Sasso

[Joaz Banbeck]

Shouldn't be that hard... We just need to build another LHC underneath Gran Sasso

Shouldn't be too difficult - Italian real estate is going to be real cheap soon. And once you've gotten the bugs out while building one LHC, the second one should be relatively easy.

[jts]

Shouldn't be that hard... We just need to build another LHC underneath Gran Sasso

Shouldn't be too difficult - Italian real estate is going to be real cheap soon. And once you've gotten the bugs out while building one LHC, the second one should be relatively easy.

I just thought of an excellent source of fiscal stimulus... now if we could only convince the ECB to underwrite it...

[Redbeard]

Shouldn't be that hard... We just need to build another LHC underneath Gran Sasso

Shouldn't be too difficult - Italian real estate is going to be real cheap soon. And once you've gotten the bugs out while building one LHC, the second one should be relatively easy.

Brilliant!! Besides. we already have the blueprints! There won't be any design costs! We could franchise this!!!

[Joaz Banbeck]

Shouldn't be that hard... We just need to build another LHC underneath Gran Sasso

Shouldn't be too difficult - Italian real estate is going to be real cheap soon. And once you've gotten the bugs out while building one LHC, the second one should be relatively easy.

I just thought of an excellent source of fiscal stimulus... now if we could only convince the ECB to underwrite it...

Again, it is simple: just repossess Greece and sell it to the Germans. It should be more than enough cash.