Experimental Results vs Predictions

[humanino]

That doesn't change what I say by one iota. If you require 3 standard deviations before falsification, so be it. If 4, fine with me, I'm good with 5, 6, 7, and 8. Just not infinite that's all. Once you go past the limit, whatever that limit is, there's no going back.

My comment was in the 1.5 +/- 0.2 vs 1.1 example. I am sorry I was just re-iterating the obvious.

Just out of curiosity though, how many standard deviations are required for publication?

5 sigma counts as a discovery (that's pretty well the paradigm in physics). It is more or less well accepted that above 2.5 sigma is the threshold of "anomaly" for publication.

 

[Jimmy Snyder]

That's why you should approach science by the means of null hypotheses.

Theory A predicts 2 and theory B predicts 1. I wish to run an experiment that will help to decide which is the better theory. What should my null hypothesis be? If the measured value was 1.1 then how many standard deviations will it take to decide on theory B? How many standard deviations will it take to be 100% certain that theory A is wrong? Suppose I use humanino's criterion and find that 2 is more than 5 sigma away from 1.1. Can I publish?

 

[DoggerDan]

Theory A predicts 2 and theory B predicts 1. I wish to run an experiment that will help to decide which is the better theory. What should my null hypothesis be? If the measured value was 1.1 then how many standard deviations will it take to decide on theory B? How many standard deviations will it take to be 100% certain that theory A is wrong? Suppose I use humanino's criterion and find that 2 is more than 5 sigma away from 1.1. Can I publish?

ISBN: 0-8120-1869-9. I somehow aced it in college, then ram-dumped it. This handbook kept me out of trouble over the last decade.

Well, it's a simplistic guide. Sometimes I actually had to dig back into my college texts.

 

[cmb]

Theory A predicts 2 and theory B predicts 1. I wish to run an experiment that will help to decide which is the better theory.

(Sorry, I didn't pick up on this first time.)

'Which theory is better...'? My opinion of that question; therein lies a fundamental misunderstanding of what a 'theory' is. Both theories are equally as good if not disproven by the confirmation of a null hypothesis. However, there may be a much bigger confidence in one than the other.
What did you mean by 'better'?

 

[Jimmy Snyder]

(Sorry, I didn't pick up on this first time.)

'Which theory is better...'? My opinion of that question; therein lies a fundamental misunderstanding of what a 'theory' is. Both theories are equally as good if not disproven by the confirmation of a null hypothesis. However, there may be a much bigger confidence in one than the other.
What did you mean by 'better'?

Is Newtonian mechanics equally as good as relativistic mechanics, or was Newtonian disproven by confirmation of a null hypothesis? If the latter, what was the null hypothesis?

 

[cmb]

Is Newtonian mechanics equally as good as relativistic mechanics, or was Newtonian disproven by confirmation of a null hypothesis? If the latter, what was the null hypothesis?

These are models, not theories so there is nothing to disprove. Models are what you choose them to be, and they are only as useful as they are useful.

For a discussion on models, see the recent thread; https://www.physicsforums.com/showthread.php?t=543684

Both have arisen through theories of how the universe works, this is true. The theory underlying Newtonian mechanics is now disproven. The null hypothesis was that time is not the same for all things in motion. That has been shown, therefore the null hypothesis is now proven.

However, Newtonian mechanics remains a very useful model for the world we generally experience and there is no need to include the theory of relativity in our everyday world.

The theory of relativity, that underlies the relativistic mechanical model, is still a theory because we have not yet found an exception to it.

Do you see how this works, yet? Theories are never proven, they are simply replaced once disproven. (In fact, I would caveat that to say that theories are sometimes replaced when a single theory unifies them with other theories.) In the case of relativistic mechanics, this will always remain a useful model for given circumstances, just like Newtonian mechanics still does. But it doesn't mean the theory that spawned that model is 'proved' just because people use the model.

Determining a null hypothesis for the theory of relativity is a little beyond my knowledge, and I would defer to someone well-read in that subject, but I'd guess finding something traveling faster than light speed would be a biggie, hence the interest in this recent muon-speed paper from CERN. So in that example, we have data whose overall accuracy is still being poured over, but clearly it is significant to publish it because potentially it may be evidence of a null hypothesis of relativity. That one experiment won't overthrow relativity, but as it is repeated and as the confidence in the result goes up, so the veracity of the theory will be reconsidered.

 

[Jimmy Snyder]

The theory underlying Newtonian mechanics is now disproven. The null hypothesis was that time is not the same for all things in motion.

Disproven by means of an experiment with error bars? What experiment? How many sigma?

 

[cmb]

Disproven by means of an experiment with error bars? What experiment? How many sigma?

see Einstein, Albert (1916). "The Foundation of the General Theory of Relativity". Annalen der Physik 49 (7): 769–822.

http://www.Alberteinstein.info/gallery/pdf/CP6Doc30_English_pp146-200.pdf

Quoting from wikipedia [http://en.wikipedia.org/wiki/Tests_of_General_Relativity];

Einstein proposed three tests of general relativity, subsequently called the classical tests of general relativity, in 1916:

1.the perihelion precession of Mercury's orbit
2.the deflection of light by the Sun

3.the gravitational redshift of light

These are not 'proofs' of relativity, they are null hypotheses of Newton's 'lineam rectam' Universe and are 'tests' in that they do not prove relativity, but serve to demonstrate that it is possible and not disproved.

(Actually, I am not sure Newton really came up with 'a theory', rather he stated a set of laws straight off. I suppose it is not unreasonable to argue that his 3 laws were, in themselves, a 'theory' of inertial mechanics. I'm writing, assuming that basis.)

 

[Jimmy Snyder]

1.the perihelion precession of Mercury's orbit
2.the deflection of light by the Sun
3.the gravitational redshift of light

1. Error bars.
2. Error bars.
3. Error bars.

 

[cmb]

You'll have to go do some studying for yourself if you are interested in this data, it is not really the subject of my post. Sorry, but have you looked for it yourself?

 

[Jimmy Snyder]

You'll have to go do some studying for yourself if you are interested in this data, it is not really the subject of my post. Sorry, but have you looked for it yourself?

I just did. Actually, what I found is a review of a movie so most of it is irrelevant. However near the bottom of the page you will find a graph taken from the paper by Dyson, Eddington and Davidson, published in 1920, that is considered the experimental confirmation of GR and thus the falsification of Newtonian gravitation. It is this graph, and no other part of the article to which I refer.

http://garethrees.org/2008/11/25/eddington/"

I make no claims for the accuracy of the data. If you read up on the history of the experiment and its interpretation, you will see that the measurements were difficult and subject to criticism, justified or otherwise. I take them at face value and assume that they are correct and provide no justification for doing so. I make a very rough estimate of sigma and get that the angle of the best fit line is approximately 1 sigma from the GR prediction, and 5 sigma from the Newtonian prediction. This 5 sigma gap means that by humanino's criterion, they were right to publish. Nowhere in any of this do I see 100% guarantee though.

Of course, this was not the only experiment done to date. However, in 1920 it was and it was because of this paper that GR came to be accepted over Newtonian gravitation. This is science as it is, not perhaps as it should be according to some philosophy.