# Teaching relativity to a skeptic

by metiman
Tags: relativity, skeptic, teaching
Mentor
P: 17,210
 Quote by metiman Nothing. That would be perfect.
OK, then special relativity fits that bill.

 Quote by metiman I think the scientific method does allow you to choose which theory you believe a particular set of experimental data supports.
No, there is no choice allowed. If the data is predicted by the theory then the experiment supports the theory, if the data is not predicted by the theory then the experiment falsifies the theory.

 Quote by metiman One may believe for instance that there are simpler or just more plausible hypothesis to explain a given set of data.
Certainly, that is an aesthetic or philosophical preference. It is not possible to prove or disprove such preferences either via math/logic or experiment.

However, if you are familiar with Bayesian inference it is possible to quantify the idea of a "simpler" hypothesis in such a way that an experiment which supports both a simple hypothesis and a complicated hypothesis is rationally interperted as evidence favoring the simple hypothesis over the complicated one.
 P: 72 I guess the biggest problem that I would have with teaching someone GR, or more to the point, the interpretation of it is that I have basically accepted the space-time distortion model/interpretation on blind faith. The rubber sheet, bowling ball, marble model has never made sense to me. I cannot imagine a 2D rubber sheet. Only a 3D one. The depression in the rubber sheet created by the bowling ball into which the marbles are supposed to 'fall' would only be present if there were a classical gravitational field behind the sheet. I don't see how you can rely on the very model you are attempting to replace in order to demonstrate your own. Also I think the fourth dimension is supposed to be temporal. Not spatial. The rubber sheet model seems to rely on a spatial fourth dimension. Otherwise why would you end up with a physical depression in the flat sheet representing 3 dimensional space? If the distortion in the rubber sheet were strictly temporal that might explain why time would seem to slow down or even stop in a sufficiently strong gravitational field, but it wouldn't seem to explain the acceleration created by the presence of a massive object. So why do I accept this interpretation/model of gravity as absolutely true despite the fact that it seems about as silly/nonsensical to me as a square circle? Basically because I consider men like Einstein or Feynman or Wheeler or Thorne or Dyson or anyone who might work at a place like the Institute for Advanced Study or anyone who could be accepted into the physics programs at MIT, Caltech, Princeton, Harvard, or Berkeley, to be more intelligent than I in the way that I am more intelligent than, say, a spider monkey. The idea that they could be wrong, and I could be right about something like that seems even more improbable to me than the rubber sheet idea. In fact I actually consider it to be impossible. But if I were teaching the idea to someone I couldn't possibly make that argument. Hence my interest in eventually being able to prove that interpretation or at least demonstrate in any way how it could possibly be true without relying on blind faith. If there are no experiments which directly demonstrate this interpretation of the equations then it seems like some degree of blind faith would be required of the student in order to accept it. Not every student is going to be willing to do that. Of course these are all philosophical concerns about some sort of 'truth'. I assume that the field equations could still be used as kind of a more accurate version of the classical model of gravity. That conceptually you could continue to treat gravity as a field as long as you use Einstein's equations to solve the actual problem. Or maybe that's wrong. Is it necessary to accept the rubber sheet idea in order to use the equations correctly?
Mentor
P: 11,743
 Quote by metiman The rubber sheet, bowling ball, marble model has never made sense to me.
You'll find that most or all of the experts here agree that it's a crummy analogy.
Mentor
P: 17,210
 Quote by metiman I guess the biggest problem that I would have with teaching someone GR, or more to the point, the interpretation of it is that I have basically accepted the space-time distortion model/interpretation on blind faith. ... If there are no experiments which directly demonstrate this interpretation of the equations then it seems like some degree of blind faith would be required of the student in order to accept it.
Quite the opposite. There is no reason to ask a student to accept or reject any specific interpretation. It is not a matter of faith, but a matter of personal preference.

If they like the interpretation then they should use it, if they dislike it then they shouldn't. They can even change their prefered interpretation on a whim.

Don't try to cram an interpretation down a student's throat, particularly one that you don't much care for yourself.
P: 72
 Quote by DaleSpam You cannot prove an interperation through experimental data, only the math. Often there are multiple interpretations for the same theory, and experiment can never, even in principle, distinguish between the two interpretations.
In that case consider the following syllogism:

1. You cannot prove an interpretation through experiment.
2. Experiment is a fundamental aspect of the scientific method. It is not optional.
3. Interpretation of a theory is not science.

 Quote by jtbell You'll find that most or all of the experts here agree that it's a crummy analogy.
Oh. Never mind then.
Mentor
P: 17,210
 Quote by metiman In that case consider the following syllogism: 1. You cannot prove an interpretation through experiment. 2. Experiment is a fundamental aspect of the scientific method. It is not optional. 3. Interpretation of a theory is not science.
That works for me.
PF Gold
P: 1,376
 Quote by metiman In that case consider the following syllogism: 1. You cannot prove an interpretation through experiment. 2. Experiment is a fundamental aspect of the scientific method. It is not optional. 3. Interpretation of a theory is not science.
Scientific method requires that hypothesis is falsifiable by experiment. It does not requires that hypothesis is provable by experiment.

And this is crucial point to understand if you want to teach something to a skeptic i.e. you can not prove to a skeptic that you are right using scientific method.
But you can prove that he is wrong if he sticks to falsifiable (scientific) ideas.
 P: 82 Why try to prove something as true to someone with a truly scientific (natural philosophers) mind? Show him/her why the ideas are considered as the most scientifically and theoretically accurate of all the ideas and theories... if the person does not accept these, but understands the arguments well enough, I can't think of a reason to try and convince him of "Truth". The students skeptic nature is what births new perspectives, ideas and theories which progress science. The students who prescribe blindly and with little critical and independent thought to the ideas should be more of a concern. We don't make progress without these skeptical students who choose to question beyond the current day 'experts'. It's counter productive growth wise to try and shut down the potential new 'paragons' of independent perspectives and get them to aspire to older schools of thought which were founded by individuals who sound like this theoretical student. Someone who refuses to accept popular opinion without full comprehension and knowledge of the ideas which have shaped the predominant thinking of today. The student who questions further with full knowledge of the popular perspective is invaluable... even if his/her questions aren't very good. In my mind they out rank the student who has no questions outside what has been taught. Basically, if the student is just absurdly stubborn and doesn't care to listen to any of the works of the founders of current scientific thought, they wouldn't be worth the effort. A proper student would be curious as to why our science is structured as it is, willing to learn about how it got to where it is now, but if new ideas and theories exist in their mind.... Hell, nurture them. If they can teach general and special relativity to a child, but they don't think it is right, they should have everything at their disposal to prove it wrong if they can. So don't teach them in the traditional sense... inform them, let them understand where we stand (scientifically and theoretically), and if they have the right stuff they will be your best students and best contributors to our future.
P: 127
 Quote by metiman In that case consider the following syllogism: 1. You cannot prove an interpretation through experiment. 2. Experiment is a fundamental aspect of the scientific method. It is not optional. 3. Interpretation of a theory is not science.
How does (3) follow from (1) and (2)? It sounds like it should but I don't see the logic. Perhaps a bit more expansion on (1) and (2) will convince me...

Actually, are you basically saying, "you can't know what is really going on in this experiment. You cannot prove what is causing the results... since you cannot prove what is going on, then interpretation is not a science, because science is all about proving stuff."

If this is what you are saying then how is it that we are able to advance technologically? Dumb luck? If technological advance is strictly speaking not in your definition of "science" then fair enough. But now this has ultimately come to your nit-picking... it is not a very useful argument.
P: 72
 Quote by zonde Scientific method requires that hypothesis is falsifiable by experiment. It does not requires that hypothesis is provable by experiment. And this is crucial point to understand if you want to teach something to a skeptic i.e. you can not prove to a skeptic that you are right using scientific method. But you can prove that he is wrong if he sticks to falsifiable (scientific) ideas.
Is it possible to design an experiment that could prove a hypothesis without that experiment also having the capacity to disprove it? It may just be the limitations of my imagination, but I cannot imagine one. If it were possible I think it would really be stretching the definition of "experiment". An experiment which can't fail to prove your hypothesis seems pretty useless to me.

Nevertheless I could change premise #1 to something like: You can neither prove nor disprove (falsify) an interpretation of a theory through experiment. IOW an interpretation of a theory is inherently non-falsifiable. Presumably because an interpretation is qualitative and non-mathematical and experiments are inherently quantitative in nature. Unless I could think of a scientifically valid non-quantitative experiment. My first thought might be the Michelson-Morley experiment, but no. That was quantitative too.

Note that I'm not actually sure that premise #1 is true in every conceivable case. It may depend on the particular interpretation. It does seem to be true for at least some interpretations, and I find the idea interesting. I just wanted to bring DaleSpam's idea to its logical conclusion in order to try to decide if I agreed with it.
P: 72
 Quote by jewbinson How does (3) follow from (1) and (2)? It sounds like it should but I don't see the logic. Perhaps a bit more expansion on (1) and (2) will convince me...
You are assuming the truth of the first two statements (premises) right? Perhaps there is some additional logic I could throw in.

1. The qualitative interpretation of a theory can neither be proved nor disproved through experiment.
2. The scientific method requires experiment of some kind to check your (quantitative) hypothesis against reality.
3. Something can be called science if and only if it uses the scientific method.
4. Interpretation of a theory is not science.

In unstructured natural language you could say something like: An interpretation of a theory is not science because it can neither be proved nor disproved through experiment. Checking experimental data against theory is what science is all about. Or perhaps more tersely: Qualitative interpretations of theory are non-falsifiable and therefore cannot be called science.

 Quote by jewbinson Actually, are you basically saying, "you can't know what is really going on in this experiment. You cannot prove what is causing the results... since you cannot prove what is going on, then interpretation is not a science, because science is all about proving stuff."
I am saying that if you believe premise #1 as DaleSpam does (and maybe I do as well) and you also believe premise #2 as I do and as I can only assume most people on this forum would, then statement #3 logically follows. If you cannot falsify an interpretation through experiment then that interpretation has more in common with religion or philosophy than it does with science. It may still be considered useful by some people, but technically it cannot be called science. I could even go further with the following syllogism:

1. Science or the scientific method is the only method for gaining knowledge that actually works. At least for our species, but probably for any species.
2. Interpretations are not science.
3. Interpretations can not (directly) contribute anything toward gaining knowledge.

If you combine the two syllogisms you would have to conclude something like: The only way to learn anything about the world is quantitatively through mathematics. If something cannot be described mathematically then it is not knowledge. At best it would be an unproven, unprovable belief that must be accepted on faith. Or because your feelings tell you that it's true. Non-mathematical or qualitative knowledge would be a contradiction in terms.

Since we don't have a 'reality-o-meter' it is difficult to know when our ideas about what is really going on are correct. Those ideas about what is really going on would have to be testable through experiment. Probably through a different experiment. Does that introduce a recursion problem? In order to test an idea you would require a qualitative experiment or at least a quantitative experiment with an unequivocal and inescapable qualitative conclusion derived directly through deduction.

 Quote by jewbinson If this is what you are saying then how is it that we are able to advance technologically? Dumb luck? If technological advance is strictly speaking not in your definition of "science" then fair enough. But now this has ultimately come to your nit-picking... it is not a very useful argument.
Since I assume most people believe premise 2, the syllogism really stands or falls on premise 1, and it sounds like you do not believe it. If that's the case then the syllogism falls apart. DaleSpam is basically saying that the mathematics are really the only scientifically important part of any theory. He might well argue that all scientific progress has been a direct result of the quantitative relationships expressed through the mathematics. It certainly does seem difficult to dispute this. At least from a historical perspective. I'm still thinking about the idea. I had always thought of scientific theory as being a combination of quantitative and qualitative statements, but now I am not so sure. Perhaps the qualitative statements are not scientifically important.

If there is one human activity that really doesn't care much about qualitative aspects of scientific theory surely it must be engineering (technology). For example I am planning to build an electrical device which uses electrons traveling at relativistic speeds. I will certainly require Einstein's special theory in order to predict the mechanics and behavior of those electrons. I don't need to be able to answer why the equations give accurate predictions. I just have to know that they do and then use them as they were intended. Plug and chug.
PF Gold
P: 1,376
 Quote by metiman Is it possible to design an experiment that could prove a hypothesis without that experiment also having the capacity to disprove it?
It is not possible to design an experiment that could prove a hypothesis. Point. "With" or "without" does not matter.

Look in wikipedia Scientific method
"Note that this method can never absolutely verify (prove the truth of) [conjecture]. It can only falsify [conjecture].[17] (This is what Einstein meant when he said, "No amount of experimentation can ever prove me right; a single experiment can prove me wrong."[18])"

or under Empiricism
"According to Peirce's doctrine of fallibilism, the conclusions of science are always tentative. The rationality of the scientific method does not depend on the certainty of its conclusions, but on its self-corrective character: by continued application of the method science can detect and correct its own mistakes, and thus eventually lead to the discovery of truth".[30]"

"Fallibilism (from medieval Latin fallibilis, "liable to err") is the philosophical principle that human beings could be wrong about their beliefs, expectations, or their understanding of the world. In the most commonly used sense of the term, this consists in being open to new evidence that would disprove some previously held position or belief, and in the recognition that "any claim justiﬁed today may need to be revised or withdrawn in light of new evidence, new arguments, and new experiences."[1] This position is taken for granted in the natural sciences.[2]"

 Quote by metiman Nevertheless I could change premise #1 to something like: You can neither prove nor disprove (falsify) an interpretation of a theory through experiment. IOW an interpretation of a theory is inherently non-falsifiable. Presumably because an interpretation is qualitative and non-mathematical and experiments are inherently quantitative in nature. Unless I could think of a scientifically valid non-quantitative experiment. My first thought might be the Michelson-Morley experiment, but no. That was quantitative too.
You should state #1 as "interpretation of a theory is not falsifiable".

And my comment is that interpretation is part of the theory. Mathematical part alone is not falsifiable as well. So we need both parts to make it falsifiable. This is along the same lines that Fredrik said in post #11.
P: 72
 Quote by zonde You should state #1 as "interpretation of a theory is not falsifiable".
Fair enough. The word proof is unfortunate. 'Demonstrate a close correlation between experimental predictions and experimental data' would be better I think. Too bad we don't have a single word for that in English.

 Quote by zonde And my comment is that interpretation is part of the theory. Mathematical part alone is not falsifiable as well. So we need both parts to make it falsifiable. This is along the same lines that Fredrik said in post #11.
Well you could define a theory as anything that makes a prediction about the results of an experiment, whether that prediction is quantitative or qualitative. When I think of an "interpretation" of a theory I think of something that tries to explain the why about the results of an experiment. Maybe even some kind of cause and effect relationship. As long as that explanation of why is falsifiable through experiment then it is valid science even if it has no associated equation. But many interpretations do seem non-falsifiable. Consider the Many Worlds interpretation of the double slit experiment for instance. The question that I have is whether all interpretations, all attempts to answer the why of experimental results like the double slit experiment are inherently non-falsifiable.

Fredrik stated that mathematics alone are not falsifiable, but it really depends on what you mean by mathematics alone. You do have to define the variables. Otherwise the sequence of letters and numbers has no meaning in the real world. If you include the meaning of the variables as part of the equation then equations seem perfectly falsifiable to me. They are just statements expressing a purely quantitative relationship. Like F = mA. If just saying "The force F exerted on on object with mass m results in an acceleration A." is an interpretation then I would have to agree that an interpretation is necessary to a theory and that a meaningless sequence of undefined letters and numbers does not make a theory.
PF Gold
P: 1,376
 Quote by metiman Fair enough. The word proof is unfortunate. 'Demonstrate a close correlation between experimental predictions and experimental data' would be better I think. Too bad we don't have a single word for that in English.
You can use words "confirmed" and "verified". That would mean 'theory was tested and it passed the test'.

 Quote by metiman Well you could define a theory as anything that makes a prediction about the results of an experiment,
This is very popular position but I am not sure I fully agree with that. Traditionally the core of the theory is explanation and then you use predictions (preferably quantitative) to test how good is that explanation.

Say we can have some empirical data and do some curve fitting using that data. Now we can make predictions using untested parts of that curve (we interpolate or extrapolate empirical data). This is not a theory as it lacks explanatory part, right?

 Quote by metiman whether that prediction is quantitative or qualitative. When I think of an "interpretation" of a theory I think of something that tries to explain the why about the results of an experiment. Maybe even some kind of cause and effect relationship. As long as that explanation of why is falsifiable through experiment then it is valid science even if it has no associated equation.
For me explanation is the theory. If we have equations with very direct connection to physical observations I would probably call it something like "empirical theory".

 Quote by metiman But many interpretations do seem non-falsifiable. Consider the Many Worlds interpretation of the double slit experiment for instance. The question that I have is whether all interpretations, all attempts to answer the why of experimental results like the double slit experiment are inherently non-falsifiable.
Local realistic explanations are falsifiable.

 Quote by metiman Fredrik stated that mathematics alone are not falsifiable, but it really depends on what you mean by mathematics alone. You do have to define the variables. Otherwise the sequence of letters and numbers has no meaning in the real world. If you include the meaning of the variables as part of the equation then equations seem perfectly falsifiable to me. They are just statements expressing a purely quantitative relationship. Like F = mA. If just saying "The force F exerted on on object with mass m results in an acceleration A." is an interpretation then I would have to agree that an interpretation is necessary to a theory and that a meaningless sequence of undefined letters and numbers does not make a theory.
If theory is introducing new physical quantity called force than important part of the theory is to say what we consider a force. Along with practical examples in a form of experiments.
Otherwise we can state that force is "whatever causes acceleration A of an object with mass m according to law F = mA". Not sure it this is a theory. And it does not seem falsifiable.
P: 4,017
 Quote by metiman The rubber sheet, bowling ball, marble model has never made sense to me.
It has little to do with General Relativity. Use the search function to find several threads explaining this.
P: 4,017
 Quote by metiman I'm more concerned about experimental evidence for the existence of space-time or Minkowski 4-space as a physical reality as opposed to a useful mathematical model or construct which may or may not exist in the actual world.
It is just a useful mathematical model.
P: 3,187
 Quote by metiman Thanks for the links. I figured proving special relativity itself would be relatively trivial. I'm more concerned about experimental evidence for the existence of space-time or Minkowski 4-space as a physical reality as opposed to a useful mathematical model or construct which may or may not exist in the actual world. [..]
That's faulty; sorry but you are trying to convince someone of wrong ideas. Technically, a theory can hardly be "proven", it can only be supported by increasing evidence; and special relativity as it was originally formulated has, strictly speaking, been disproved by general relativity (it is only valid at constant gravitational potential, contrary to its original formulation). And a number of well-known promoters of special relativity considered Minkowski 4-space as a useful mathematical model or construct; the belief that Minkowski 4-space is "a physical reality" as opposed to a mathematical construct is not part of relativity theory.
P: 3,187
 Quote by metiman [..] If there is one human activity that really doesn't care much about qualitative aspects of scientific theory surely it must be engineering (technology). For example I am planning to build an electrical device which uses electrons traveling at relativistic speeds. I will certainly require Einstein's special theory in order to predict the mechanics and behavior of those electrons. I don't need to be able to answer why the equations give accurate predictions. I just have to know that they do and then use them as they were intended. Plug and chug.
And that is exactly how that theory was intended.
Its postulates were inferred from observation and are about phenomena; they do not require a physical model of hidden reality (which he called "superfluous"). Thus the theory lacks that kind of "why" on purpose. See: http://www.fourmilab.ch/etexts/einstein/specrel/www/
 These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies.

 Related Discussions Educators & Teaching 9 Special & General Relativity 8 Special & General Relativity 12 Special & General Relativity 29 General Discussion 9