I Topic about physics axioms, theory, laws etc..

[user079622]

Does physics has axioms (like math), "fundamental blocks" from which we can build theory, laws and what are they?
1. How was it discovered that F=ma, do we know from mathematics that f=ma or only after we conducted an experiment?
2. How do we know that light is constant in all reference frames, was it first shown to us by mathematics or by experiment?
Which experiment?
3.If theory predict same results as experiment, even theory is not physical, is theory considered correct?
4. Why often say, physics is never 100% correct, for example why moment= force x lever arm is not 100% correct?

 

[kuruman]

The only axiom that I can think of is that mathematics can be used to describe the world around us.

For the remainder of your questions, I recommend that you do some web research first, then come back here and ask us to explain what you didn't understand.

 

[Dale]

1. How was it discovered that F=ma, do we know from mathematics that f=ma or only after we conducted an experiment?

That was from experiment. Now, we consider those experiments so reliable that we have incorporated it into our definition of force.

2. How do we know that light is constant in all reference frames, was it first shown to us by mathematics or by experiment?
Which experiment

Experiment. A good summary is section 3 in the Experimental Basis of Special Relativity page.

3.If theory predict same results as experiment, even theory is not physical, is theory considered correct?

How can a theory predict the results of experiments and not be physical?

4. Why often say, physics is never 100% correct, for example why moment= force x lever arm is not 100% correct?

Physics is a branch of science. Science is always open to new data that may falsify current theories.

 

[user079622]

That was from experiment. Now, we consider those experiments so reliable that we have incorporated it into our definition of force.

What experiment Newton did to find F=ma?

How can a theory predict the results of experiments and not be physical?
es.

For example circulation theory of lift, we know airflow dont flow around wing in circle, so it is not physical but give correct results.
https://www.onemetre.net/Design/Downwash/Circul/Circul.htm

Physics is a branch of science. Science is always open to new data that may falsify current theories.

You mean like string theory (where founder of theory state that theory is not correct), does students still learn string theory at universities as something that is correct?

 

[user079622]

Is this axioms?

• The laws of physics are the same in all inertial frames.
• The speed of light in vacuum is constant in all inertial frames.

 

[Dale]

What experiment Newton did to find F=ma?

I think that he rolled balls down an incline.

For example circulation theory of lift, we know airflow dont flow around wing in circle, so it is not physical but give correct results.
https://www.onemetre.net/Design/Downwash/Circul/Circul.htm

I don't know anything about this theory, but if it always gives correct results then what makes you think that it is not physical? On the other hand, if a theory says lift is produced by circulating air currents and experimentally you determine that lift is produced when the air is not circulating, then what makes you think that it gives correct predictions?

In other words, we judge the "physical"-ness of a theory by whether or not it correctly predicts the outcome of physical experiments.

You mean like string theory (where founder of theory state that theory is not correct), does students still learn string theory at universities as something that is correct?

String theory is not even 0% correct yet, let alone the 100% correct you were asking about. String theory has yet to make any testable predictions at all.

No, I am talking about actual experimentally validated theories. We always allow for the possibility of future experiments to provide new information.

 

[user079622]

I think that he rolled balls down an incline.

I thought it was derived theoretically, using logic and mathematics, like E=mc^2

I don't know anything about this theory, but if it always gives correct results then what makes you think that it is not physical? On the other hand, if a theory says lift is produced by circulating air currents and experimentally you determine that lift is produced when the air is not circulating, then what makes you think that it gives correct predictions?

In real world, air travel from leading edge toward trailing edge at both surface of wing.
Air do not travel from trailing edge toward leading edge at bottom side of wing(circulation)

 

[fresh_42]

Does physics has axioms (like math), "fundamental blocks" from which we can build theory, laws and what are they?
1. How was it discovered that F=ma, do we know from mathematics that f=ma or only after we conducted an experiment?
2. How do we know that light is constant in all reference frames, was it first shown to us by mathematics or by experiment?
Which experiment?
3.If theory predict same results as experiment, even theory is not physical, is theory considered correct?
4. Why often say, physics is never 100% correct, for example why moment= force x lever arm is not 100% correct?

There are no axioms in physics. Axioms are unquestioned preliminaries, and all descriptive sciences, including physics, rely on observations, experiments, and measurements, not on God-given truths. You could introduce any statement in physics by "to our current/best knowledge/measurements/observations". This is a defining property of an inductive science such as physics. Mathematics is a deductive science built on a set of assumptions. It only requires being free of contradictions. Physics has contradictions resulting from simplifications due to its area of validity. Newton is contradicting Einstein, but you will not use general relativity to analyze a car accident. And it currently looks as if even Einstein isn't the final word.

 

[user079622]

There are no axioms in physics. Axioms are unquestioned preliminaries, and all descriptive sciences, including physics, rely on observations, experiments, and measurements, not on God-given truths

Isnt this axioms/postulates in my post #5?

 

[fresh_42]

Is this axioms?

• The laws of physics are the same in all inertial frames.
• The speed of light in vacuum is constant in all inertial frames.

No. They are observations. Many physical theories have arrived at the same result in a laboratory as well as in the observable universe. That's why we assume this, not because it couldn't be wrong in a different context. You would be surprised what all can be confirmed by astronomical observations.

 

[user079622]

No. They are observations. Many physical theories have arrived at the same result in a laboratory as well as in the observable universe. That's why we assume this, not because it couldn't be wrong in a different context.

Postulates is same as axioms?

 

[TensorCalculus]

Postulates is same as axioms?

The word postulate is similar to that of axiom, but from my understanding they aren't the same:

An axiom is always True no matter the circumstances (e.g. A statement that is True is not False) whereas a postulate may always be true only in a specific field or a specific context, and false in another.
The other thing is that axioms are self-evident/self-proving, but postulates are something we sort of just take for granted.

There was a good discussion on the Mathematics stack exchange about this, I think. I'll link the thread here if I can find it.

 

[fresh_42]

Postulates is same as axioms?

No, they are different, and it also depends on where you use these terms. In mathematics, I would call the axiom of choice or the continuum hypothesis a postulate, whereas the Peano axioms are clearly axioms. This already shows that language is often a matter of history and common agreements rather than a linguistic or philosophical correct definition. Those distinctions should be made outside of the sciences they are using them.

The constancy of the speed of light may be called a postulate, a desirable truth that can be accepted until something tells us it is not. An axiom is an unconditional truth which do not exist in descriptive sciences.

 

[user079622]

No, they are different, and it also depends on where you use these terms. In mathematics, I would call the axiom of choice or the continuum hypothesis a postulate, whereas the Peano axioms are clearly axioms. This already shows that language is often a matter of history and common agreements rather than a linguistic or philosophical correct definition. Those distinctions should be made outside of the sciences they are using them.

The constancy of the speed of light may be called a postulate, a desirable truth that can be accepted until something tells us it is not. An axiom is an unconditional truth which do not exist in descriptive sciences.

I always thought that everything we learned in school of physics is 100% correct. Now I see that math and physics is very different in that aspect..
Can I say math is absolute truth, physics is just best current approximation for reality?

 

[TensorCalculus]

Physics being the best current approximation for reality sounds somewhat on the right path

Maths being the absolute truth... not really. It sort of depends on the context, but even then... can be a bit iffy sometimes is the best I can put it I guess. Sure one of the experts here (Fresh_42, Dale, Kuruman, I summon thee forth) will be able to say that in a much better way :)

 

[Ibix]

Can I say math is absolute truth, physics is just best current approximation for reality?

No. The point is that maths isn't generally about truth, it's about self-consistency. Physics needs self-consistent models, but they also need to have some testable connection to the real world.

So you could read Einstein's postulates as axioms of an arbitrary 4d geometry we call Minkowski geometry (you need homogeneity and isotropy of space too, which Einstein explicitly assumed but didn't call postulates). They become postulates when we associate particular numbers in the mathematical model with numbers on the readout of some sensor. Then we are postulating some physical fact and the theory could be falsified. Falsifying special relativity wouldn't falsify Minkowski geometry (that makes no sense) but it would mean that Minkowski geometry was not a good model for the behaviour of real physical systems.

 

[fresh_42]

Can I say math is absolute truth, physics is just best current approximation for reality?

I wouldn't go that far. From Wikipedia:

Kurt Gödel showed in 1938 that the axiom of choice does not lead to a contradiction in the context of Zermelo-Fraenkel set theory if one assumes that all other axioms are consistent. Furthermore, Paul Cohen showed in 1963 (and subsequently in 1964 and 1966) that the negation of the axiom of choice does not lead to a contradiction. Both assumptions are therefore acceptable from a formalistic point of view.

This doesn't sound like an absolute truth, only that you may build consistent theories on either assumption. There have been similar discussions on other aspects of mathematics, like Russel's paradox, constructivism, or a three-valued logic. The only important point in mathematics is that whatever you use as axioms, they should not lead to contradictions.

Physics is a bit more complicated on this. Nobody would seriously expect the famous apple to fall upwards from the tree. But, technically, this doesn't make it an unconditional truth. We just never observed such a case. Hence, the distinction is a matter of philosophy, not physics. We heavily rely on the fact that physical theories are true in the realm of their validity, and they are, just not a philosophical truth.

 

[hutchphd]

I think that he rolled balls down an incline.

's
I think Galileo gets the credit for this technique. Newton was born with a year of Galileo's death so he knew of the work I would guess.
I think we do better to remember that Physics is not an edifice of facts but rather an agreed-upon technique that supplies a fortress where we separate useful ideas from the easy, arcane, and foolish ones. In that context it has proven a great boon to human beings. We ignore it at our peril.

 

[Dale]

In real world, air travel from leading edge toward trailing edge at both surface of wing.
Air do not travel from trailing edge toward leading edge at bottom side of wing(circulation)

Then why would you claim that the circulation theory gives correct results? I don't know the theory, but if it says the air needs to go backwards to generate lift and the air in fact does not, then in what way is it correct?

Since I am relying on you to describe this theory it could be that the theory is correct and doesn't say what you think it says (i.e. you misunderstand circulation), or it could be that the theory is not correct (i.e. it does not give correct predictions), or it could be that the theory is correct but not useful (i.e. it gives correct predictions for scenarios that don't arise in practice). But in all cases, we judge a physical theory by how accurately it predicts physical results, not whether people misunderstand the theory and not whether the scenarios are common.

I thought it was derived theoretically, using logic and mathematics, like E=mc^2

I thought I already told you that it was experimental (at first) and now is a definition.

I always thought that everything we learned in school of physics is 100% correct.

Does that sound like something that any science can achieve? Recall that the foundation of all science is the scientific method. What possible application of the scientific method could produce "100% correct"?

 

[user079622]

Then why would you claim that the circulation theory gives correct results? I don't know the theory, but if it says the air needs to go backwards to generate lift and the air in fact does not, then in what way is it correct?

Result is correct but assumption of air movement in theory is not what happen in real life. I dont know why..

I thought I already told you that it was experimental (at first) and now is a definition.

Yes you told that for F=ma.

What possible application of the scientific method could produce "100% correct"?

I think this is 100% correct. Isn't it?

 

[A.T.]

I think this is 100% correct. Isn't it?
View attachment 363462

The definition of torque? It doesn't make sense to ask whether a definition is correct or not. You could say that a definition is always correct, per definition. But that is an empty statement.

 

[hutchphd]

A definition is exactly that. Is an apple correct ? Is an apple an orange? No it is not
Is a definition a truth? No it is not.

 

[fresh_42]

I think this is 100% correct. Isn't it?

You have first to decide what correct means. It may refer to

1. a definition, in which case it is correct in the sense of an abbreviation. We call it as such.
2. a deduction, i.e., a logically correct chain of implications. This depends on the logical set-up in which correct is defined.
3. an observation or measurement. The apple falls downwards from the tree, and we have never observed the opposite. This is a physical truth, provided that Newton was "correct". We have no reason for doubt, but that does not imply we couldn't theoretically be wrong.
4. an unconditioned true statement. Those do not exist. Either we have a setup in which the truth value of a statement relies on, or it is a vacuously true statement, like in a definition, or it is a probability approaching 100% as in the case of the apple.

The words true, right, and correct all depend on the surroundings in which they are used. Philosophers might have even different approaches but I'm not familiar with them.

 

[Dale]

Result is correct but assumption of air movement in theory is not what happen in real life. I dont know why..

How can the result be correct? If the result says lift is generated by the air moving in this pattern and lift is generated by air not moving in that pattern then what do you mean when you claim that it is correct?

Suppose that I have a theory. My theory says if scenario A then result X. Now I attempt to test my theory and I find only if scenario B then result X, then in what way can I claim that my theory is correct?

 

[hutchphd]

Now I attempt to test my theory and I find only if scenario B then result X, then in what way can I claim that my theory is correct?

How does one do an "only if" test without "infinite" repetitions? You can put limits on it but how does one do it absolutely? I don't see it.

 

[Dale]

How does one do an "only if" test without "infinite" repetitions? You can put limits on it but how does one do it absolutely? I don't see it.

Sure, that’s poor wording. It should have been “I only find if scenario B then result X” rather than “I find only if scenario B then result X”. The point is that how can I claim a theory is correct if I don’t test the scenario that the theory covers.

 

[user079622]

The definition of torque? It does doesn't make sense to ask whether a definition is correct or not. You could say that a definition is always correct, per definition. But that is an empty statement.

You have first to decide what correct means.

Correct mean if you put weight of 50N at 2m lever arm, on other side you put weight of 100N at 1m lever arm, seesaw will stay in balance. That mean theory is correct, because it fits with experiment.
Definition of torque must fits with experiment, if definition of torque was T= F + lever arm, it will not fit with reality.
Isn't obvious what mean correct?

How can the result be correct? If the result says lift is generated by the air moving in this pattern and lift is generated by air not moving in that pattern then what do you mean when you claim that it is correct?

I don't know. I think every theory don't care about what really happen physically, only important is that result is same as experiment.

 

[renormalize]

I don't know. I think every theory don't care about what really happen physically, only important is that result is same as experiment.

Can you state clearly what you perceive as the difference between "what really happen(s) physically" and "(the theory) result is same as experiment"?

 

[user079622]

Can you state clearly what you perceive as the difference between "what really happen(s) physically" and "(the theory) result is same as experiment"?

"result is same as experiment" mean experiment and theory both show same result, ex. Lift=200N
"what really happen(s) physically", mean in this case how airflow flow at wing, we all know that air don't circulate/"revolve" around wing.
Circulation is a mathematical concept used to explain the motion of air from a frame of reference bound to the wing, but this is not what happen in reality.
So how can assumption that is not physically correct, gives correct result, that is my question..

 

[fresh_42]

Isn't obvious what mean correct?

No, because you describe a probability: the outcome of many measurements. This is what I call a physical truth. It isn't an absolute truth in a philosophical sense. Physics cannot provide such truths, only measurements, relying on the "postulate" that the outcome doesn't change with time or location. It is a probability, even though close to one.

 

[user079622]

No, because you describe a probability: the outcome of many measurements. This is what I call a physical truth. It isn't an absolute truth in a philosophical sense. Physics cannot provide such truths, only measurements, relying on the "postulate" that the outcome doesn't change with time or location. It is a probability, even though close to one.

1. T = F x r
2. T = F + r

You dont agree that 2. formula for torque don't represent what nature/experiment do?
why 1. formula is not 100% correct?

 

[Dale]

I think every theory don't care about what really happen physically, only important is that result is same as experiment.

That statement doesn’t make sense.

 

[fresh_42]

1. T = F x r
2. T = F + r

You dont agree that 2. formula for torque don't represent what nature/experiment do?
why 1. formula is not 100% correct?

I agree that 2. is fantasy, but 1. depends on the environment in which you make your measurements. However, if you use the equation to define T then it is trivially true, by abbreviation of the RHS by the LHS.

 

[user079622]

1. depends on the environment in which you make your measurements.

You mean is not valid at atomic/particle level?

 

[A.T.]

Correct mean if you put weight of 50N at 2m lever arm, on other side you put weight of 100N at 1m lever arm, seesaw will stay in balance.

1. T = F x r

why 1. formula is not 100% correct?

Because we have not tested it under all possible circumstances with unlimited precision, so we cannot be 100% sure that it is always exactly correct.

 

[user079622]

Because we have not tested it under all possible circumstances with unlimited precision, so we cannot be 100% sure that it is always exactly correct.

But precision is just errors in measurements devices, 200N vs 200.000000000001N, is it proof that formula is not 100% correct?
"all possible circumstances" you mean physics theories only valid in some domain?

 

[fresh_42]

You mean is not valid at atomic/particle level?

We are constantly confusing several terms and understandings of what "correct" can mean. I tried to resolve this by distinguishing between deductive and inductive sciences, by providing three different setups in which the word is used in science, all without success, to clear up the discussion.

As long as we cannot agree on the context in which we use the word correct, as long it is senseless to continue this debate. Without defining what exactly you mean by T,F,r, it makes no sense to answer your questions because you happily jump from one context to another.

 

[Frabjous]

But precision is just errors in measurements devices, 200N vs 200.000000000001N, is it proof that formula is not 100% correct?
"all possible circumstances" you mean physics theories only valid in some domain?

You cannot prove a theory correct; you can only prove it wrong. The proper question is if the theory is useful.

 

[user079622]

You cannot prove a theory correct; you can only prove it wrong. The proper question is if the theory is useful.

Why don't the results from experiments not count as proofs?
You mean the theory cannot be mathematically proven, (like in math)?

 

[Herman Trivilino]

Does physics has axioms (like math), "fundamental blocks" from which we can build theory, laws and what are they?

Not usually. The special theory of relativity is based on two postulates. I can't think of any other examples of that.

1. How was it discovered that F=ma, do we know from mathematics that f=ma or only after we conducted an experiment?

It, like all laws of physics, is a generalization from observation. We see in many many different observations and experiments that the relation holds, and it's used to make successful predictions of how Nature behaves. Engineers and technicians are able to use it to invent and build new machines and other devices that have advanced civilization. For example, instead of relying on horses and row boats to move ourselves around, we have automobiles, trains, airplanes, machine-powered boats.

2. How do we know that light is constant in all reference frames, was it first shown to us by mathematics or by experiment?

That's a good question. Einstein claimed that it was shown to him by the mathematics of Maxwell's Equations. But it took experimental and observation (for example, the famous Michaelson-Morley experiment of 1887) for it to begin to be accepted by the vast majority of physicists.

Which experiment?

There are lots and lots of them.

3.If theory predict same results as experiment, even theory is not physical, is theory considered correct?

The theory is considered conditionally valid. More experiment and observation is usually needed before the theory is accepted. Or in your words, "considered correct".

4. Why often say, physics is never 100% correct, for example why moment= force x lever arm is not 100% correct?

You never know when a theory will need to be modified or even replaced when there are new observations or experiments.

You gave the example of F=ma. It's been known for over 100 years that that relation is not valid in many situations, yet it is still used in the many situations in which it is valid. Strictly speaking, F=ma is now seen as a very very good approximation in those situations where it's used and considered valid.

All physical theories have limits of validity. In many cases we don't know what those limits are because the theory has not been tested outside those limits of validity.

The history of physics is filled with examples of things that physicists "knew" to be valid but were then shown to be only approximations that are not valid outside certain limits.

Learning quantum physics, for example, is a very humbling experience for most people. We learn that our way of thinking about certain things that we knew to be obviously true, are not true. I heard the famous Nobel prize winning physicist Sheldon Glashow state that "quantum theory doesn't make sense". Yet it's one of the most successful theories ever invented by the human mind. For most people, it's quite a humbling experience to discover that many of the things we thought to be obviously true are in fact not true. So things that make sense aren't always valid, and things that don't make sense can be valid. It has a profound effect on how we form our worldview and belief system.

 

[A.T.]

But precision is just errors in measurements devices

And because all measurements will have those errors, we cannot prove that any physics formula is exactly correct.

"all possible circumstances" you mean physics theories only valid in some domain?

There are infinitely many possible circumstances, and we can only make a finite number of experiments. So we cannot show that some law always holds true.

Why don't the results from experiments not count as proofs?

The results could be a coincidence.

 

[Frabjous]

Why don't the results from experiments not count as proofs?
You mean the theory cannot be mathematically proven, (like in math)?

An experiment only shows that a theory works for that experiment. You never know if there is an edge case.

 

[Herman Trivilino]

You mean the theory cannot be mathematically proven, (like in math)?

Correct. Math uses deductive reasoning to reach conclusions. Science uses inductive reasoning.

Of course, inductive reasoning doesn't always lead to valid conclusions, whereas deductive reasoning does.

The thing about deductive reasoning is that the conclusions reached contain nothing that isn't already present in the assumptions used to reach the conclusion. I consider this something of a shortcoming, and whether you agree with that or not, it's something that's not present in the conclusions reached by inductive reasoning.

 

[jbriggs444]

Correct. Math uses deductive reasoning to reach conclusions. Science uses inductive reasoning.

While true, this is also somewhat incomplete.

Science uses inductive reasoning to guess at broadly applicable principles and equations -- hypotheses, postulates, axioms and laws.

Scientists then use deductive reasoning to explore the consequences of those principles and equations. Some of those consequences will be experimentally testable predictions.

If experiment differs from the predictions then the guessed at principles and equations are wrong.

If experiment agrees with the predictions then we gain confidence in the correctness of the guessed at principles and equations.

The thing about deductive reasoning is that the conclusions reached contain nothing that isn't already present in the assumptions used to reach the conclusion. I consider this something of a shortcoming, and whether you agree with that or not, it's something that's not present in the conclusions reached by inductive reasoning.

Agree!

 

[user079622]

Correct. Math uses deductive reasoning to reach conclusions. Science uses inductive reasoning.

Of course, inductive reasoning doesn't always lead to valid conclusions, whereas deductive reasoning does.

The thing about deductive reasoning is that the conclusions reached contain nothing that isn't already present in the assumptions used to reach the conclusion. I consider this something of a shortcoming, and whether you agree with that or not, it's something that's not present in the conclusions reached by inductive reasoning.

The conclusion must be true if the premises are true. If conclusion is not true that mean some or all premises are not true.

 

[Dale]

Why don't the results from experiments not count as proofs?

I have an ordinary coin. I make a theory that says this coin always lands “tails”. I perform an experiment and it lands “tails”. Have I “proven” my theory to your satisfaction?

 

[user079622]

Science uses inductive reasoning to guess at broadly applicable principles and equations -- hypotheses, postulates, axioms and laws.

What are axioms in science? Didn't we conclude that physics don't have axioms?

 

[jbriggs444]

What are axioms in science? Didn't we conclude that physics don't have axioms?

I regard "axiom", "law", "postulate" and "hypothesis" as functionally identical terms. We can use different terms to reflect different levels of confidence or different types of supporting evidence. But if I am working within a theory and have a set of given propositions to work from, the name by which I call those propositions is irrelevant.

Some commonly accepted axioms of Newtonian mechanics include the existence of inertial frames, Galilean relativity and conservation of momentum.

It turns out that Galilean relativity has been falsified in favor of special relativity. But it remains an excellent approximation within its realm of applicability.

 

[user079622]

I have an ordinary coin. I make a theory that says this coin always lands “tails”. I perform an experiment and it lands “tails”. Have I “proven” my theory to your satisfaction?

No. If you throw coin many times, it will lands on both sides.
If you measure torque, it will show the result T=Fxr absolutely every time..(if we neglect devices measurement error).
If the formula is not correct, bridges, houses, etc. would collapse on a regular basis.

 

[fresh_42]

What are axioms in science? Didn't we conclude that physics don't have axioms?

It doesn't have. Axioms is certainly the wrong word.