So I shouldn’t be amazed that gravity waves have a decent chance of exceeding ‘c’? Has physics advanced so much since I got out of college?
Johnathon Chance, you appear to misunderstand the nature of statistical confidence intervals. If the result of this experiment was (say) a measurement that the speed of propogation for gravity is .95c +/- .25c, that statement has a very precise meaning.
If the speed of gravity is in fact in the interval (.7c, 1.2c) then the probability of an experiment identical to this one giving a result at least as close to the actual value as .95c is is less than or equal to degree of confidence of the interval. (the degree of confidence is probably 50% for a measurement this imprecise)
What this essentially means is that if the actual speed of gravity is not in the given interval, then it is unlikely that the experiment would have produced the reported result; whereas if the actual speed is in the given interval, then the reported result is in the range of likely outcomes for the measurement. It does not mean, taken on its own, that the real speed of gravity has any particular likelihood of being or not being in the given interval or any portion thereof.
General relativity predicts that changes in the curvature of spacetime propagate at precisely the speed of light. Special relativity predicts that no information-bearing influence whatsoever can propagate faster than c if causality is to be maintained. General relativity has been well-supported by experiment in the past, and special relativity far more so. I doubt any serious physicists believe there is a substantial chance that changes in gravitational influence travel faster than c, and this experiment does not give any significant support to the view that they do.
To be more succinct, though less mathematical than JasonFin, Johnathan, you shouldshould probably be surprised if the speed of gravity turns out to be greater than C, simply because Relativity works, and one of the assumptions is that gravity propagates at the speed of light.
But that’s not what’s being said here. What’s being said is that we’re reasonably certain that the true value is somewhere in the range specified. Which, lo and behold, it is, assuming it really is C (and we have no basis for doubting that at present).
Also just because we’re almost darn sure beforehand that it does propagate at the speed of light doesn’t mean our attempt to measure it is going to be bang on.
It’s still going to have error.
And that error is what you stated, plus or minus 20%.
We do not magically get to shrink the error in the measurement simply because we think we know where we should be. The error range is based on the mathematics of the analysis of the experiment and our confidence level in it, and nothing more.
If we pretend we know nothing of the speed of light, then we shouldn’t be surprised or concerned with any measurement – we simply have a 20% margin of error.
What would be astonishing is if the speed of light did not fall within the error bar.
So what’s astonishing about the value as given for the propagation of gravity? Where would you expect the center of the error bar to be? And the range of that error?
Its not as if the speed of light hops around a lot. Its a pretty fixed value. So, likely, is gravity. We can’t center the error bar around the speed of light because that would assume we already knew the true value. We can’t chop off all of the error above C, because that too would imply we already knew the result or at least something about it. We can’t assume anything about the speed of gravity in trying to detect the speed of gravity.
However, I may have to disagree with Jason here for a moment. I believe that the measurements performed would result in a value with a center (expected value? mean?) and standard deviation. Doesn’t this mean that if you can assume or work out some sort of curve to the distribution that you can integrate under that curve between two values of the domain to find the probability within a given interval? Isn’t that how the various sigma intervals are calculated?
That would suggest that we could calculate the probability that the speed of light is above the stated measurement in the OP. We just do an integration from the mean value to positive infinity to work out the probability.
Sorry, it’s been a LONG time since I’ve done stats, but I thought that was the whole point of distributions.
Since we don’t know the speed of gravity, we cannot assume it is exactly C. Maybe it is 1.2C. There’s probably a nonzero chance its between, say, 1.1 and 1.3C, based on the only measurement we have so far, ignoring the many years of relativity. It’s more likely its between 1.05 and 1.15C, assuming a gaussian distribution of error.
Of course, its equally likely to be below C at the same distances from the mean, yes? Given a gaussian distribution.
I’d hesitate to say that there’s a large chance that the speed of gravity is greater than C, but unless I’m totally whacked on my stats, the one experiment we’ve directly performed does not preclude it, and in fact can suggest how likely it is based solely on that experiment.
Please correct me if I’m wrong. Stats I need more practice in.
Oops… I should correct myself.
There’s probably a nonzero chance its between 1.15 C and 1.25C, but a greater chance it’s between 1.05 and 1.15. I wanted to use the same interval but goofed.
So pretty much anything without mass is going to travel at c, huh?
I am totally lost. How can gravity equal the speed of light if gravity is only 9.8 m/s and light is only a few thousand times greater?
Could I get a quick remedial lesson about what’s being discovered?
9.8m/s^2 (not m/s) is the acceleration due to gravity on the Earth’s surface, not speed.
Lets say half of the Sun ceased to exist. It takes 8 minutes for light to reach the Earth, so on the Earth we would only see the event 8 minutes after it happened. If gravity is instantaneous, we would “feel” the lesser gravity 8 minutes before the light reaches us. If gravity travels at the speed of light, the lesser gravity would be felt at the same time as the light reaches the Earth.
Muldoon, what’s being verified experimentally is basically that were the sun to suddenly disappear, we would feel the gravitational effects of its absence at the same time as we see it disappear.
That 9.8 number (m/s[sup]2[/sup], by the way) tells us essentially how strongly the Earth pulls something to it. It does NOT tell us anything about how long it takes the Earth to notice that there’s something to pull on. The thing that’s being discovered is basically that the speed at which the information that tells the earth that something is around to pull on is the same as the speed of light. Does that make any sense at all or am I just babbling?
And yes, anything without mass is going to travel at c.
Maybe an analogy would help. I’m going to assume you’re at least a little familiar with the rubber sheet picture? Where the earth might be a bowling ball and a sattelite might be a marble, and the bowling ball deforms the sheet and attracts the marble towards it?
Then 9.8 m/s[sup]2[/sup] would tell you about how much the bowling ball deforms the sheet, well c tells you how fast that deformation of the sheet spreads.
I suppose my real issue (earlier) stemmed from the (to me) blythe assumption that gravity COULD be assumed to possibly propagate faster than light. I sort of assumed that any error bar would bang into that at the top end and stop.
I guess I am being dense, but I do not see how this measurement of the bending of light (that is the effect of gravity on photons) has anything to do with the speed of propagation of gravitons (assuming they exist), which is what is normally meant by the speed at which gravity propagates.
To change the subject slightly, it was always assumed that neutrinos travel at the speed of light. Certainly, the neutrinos from the 1987 supernova seemed to arrive simultaneously with the light. But if neutrinos have rest mass, which it now seems they do, then they must travel slower than that and their speed should depend on their energy, right? But how do you measure the velocity of a neutrino anyway?
Thanks Noone Really (welcome to the boards too) and g8rguy. Good explanation. And I did know that gravity is 9.8m/s, just didn’t occur to me add ^2 to the units, sorry buds. But now I have a much better understanding of the issue.
Thanks g8rguy for mentioning the rubber-sheet analogy.
I was very confused with this whole thread because I was always under the impression that gravity was an inherent attribute of space-time (ala the rubber sheet analogy) rather than something that propagates through space.
I can see from your post (that the speed of gravity is describing how fast the rubber sheet deforms) that the two concepts are not incompatible.
So… does this mean that gravitons (or some such thing similar) are now generally accepted to exist?
This is a very neat observavtion, but we were already pretty sure that gravity propagates at a finite speed. There is indirect observation of gravitational waves, and you can’t have a wave if propagation speed was infinite. (The indirect observation involves binary pulsars which were observed to be losing energy at exactly the rate predicted by relativity. The energy is lost to gravitational waves.)
I’m not certain you could say that gravitons are assumed to exist. Quantum Mechanics has as part of its fundamental workings the notion that there is an exchange of…something. Photons, neutrinos, gravitons, etc. Hence the name Quantum Mechanics (a quanta of…something…is being exchanged and those somethings come in discrete, well defined amounts [i.e. no 1.5 photons, it’s all or nothing]).
So, when looking at gravity QM likes to think of gravity acting via the exchange of gravitons.
Do gravitons exist?
No one has ever seen one but they might.
Does QM imply they exist?
I don’t know but I think so (do virtual particles count as real things?).
Are gravitons merely a convenient way for people working in QM to think about what is happening?
Almost certainly.
I would say that gravitons have been pretty widely accepted for a good bit of time, actually, but I don’t think they’ve never been observed experimentally and I’m not sure that they will be within my lifetime.
It’s been a while since I’ve taken a course on particle experiments, but remember that you should be able to detect not only total energy but also total momentum, that latter by knowing that energy and momentum are conserved and being able to detect the momentum of the other particles in a collision. If you had both E and p, you’d of course be able to calculate m and v.
So, if gravity propagates at the speed of light, how is it able to escape a black hole?
Could we take the result of the experiment plus the existence of black holes and infer that the the speed is actually faster than light?
Curious question, atarian.
I suspect gravitational waves inside a black hole still propagate through space and escape the hole. Otherwise you wouldn’t have a black hole.
How about a proof by contradiction style argument – maybe the only way to resolve this without ugly math.
Let’s assume black holes exist (that is, a mass, compressed into a tight enough area, will have an escape velocity).
Let’s assume gravity propagates at a finite velocity (even if its not that of light).
Let’s assume the propagation of gravity is subject, itself, to limits of C on escape velocity from a source. Meaning gravity waves are subject to spacetime curvature by gravity.
Let’s assume the gravity emanates from the center of the hole.
For any mass, at any given radius from the center, the escape velocity increases continuously as you approach the center (assuming you don’t reach a solid surface), and this escape velocity grows towards infinity as the radius approaches zero. At the radius where the escape velocity is C, that’s the event horizon which occurs in black holes.
However, anywhere inside the hole, the escape velocity is higher, until it is effectively infinite at the center.
This means that for any escape velocity, there is a radius inside of which gravity can’t escape.
Which means nobody would ever feel the force of the hole, unless gravity were instantaneous.
But our measurements suggest gravity isn’t instantaneous.
One of our assumptions must be false.
I’m willing to believe holes exist. I’m willing to believe gravity propagates at a finite rate.
So it seems to me either the gravity emanates from somewhere other than the center, or that gravitational waves are not affected by gravitational waves (wells).
This doesn’t preclude gravity from being faster than light, but I think it shows there are other reasons why gravity might not be affected by the hole.
I’m sure my logic’s flawed somewhere, but I haven’t had my morning coffee yet.
I think it’s an interesting question too. If there is a flaw, perhaps the flaw in the assumptions by William_Ashbless is here…
My brain hurts with this statement. It sounds too self-referential. How can gravity affect itself? Maybe gravity waves are not subject to spacetime curvature… they are spacetime curvature.
If the speed of gravity was not constant, what would be the ramifications to Relativity?