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

[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.

 

[Dale]

No. If you throw coin many times, it will lands on both sides.

That would be a different theory.

Staying with my theory that the coin always lands “tails”, how many throws would you require to show “tails” before you would consider my theory “proven”?

Clearly 1 experiment with “tails” did not satisfy you. How about if it landed “tails” 10 times, then would you say my theory was “proven”? How about 100? 1000? What is the exact minimum number of “tails” that you would require to “prove” my theory?

 

[jbriggs444]

No. If you throw coin many times, it will lands on both sides.

Not necessarily. The probability depends on how many times you throw.

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.

That is not quite correct either. Torque, by itself is just a number. It has no physical consequences. If we have a force $\vec{F}$ applied to a moment arm of $\vec{r}$ then that force results in a torque $\tau$ given by $\vec{r} \times \vec{F}$. That is true. By definition.

We need to tie that number ($\tau$) to something physical if we are going to make a prediction.

We can do that. We can start by defining another number, angular momentum ($L$), as the sum of $\vec{r} \times \vec{p}$ across the incremental mass elements that make up an object.

We can can next assert that $\sum \tau = \frac{dL}{dt}$

Now for a continuously unmoving object we are in a position to predict that the sum of the torques on that object is zero. And for an object subject to a net torque, we can predict its angular acceleration.

Though we might need some more definitional axioms for "rigid object", "angular velocity" and "angular acceleration"

 

[user079622]

That would be a different theory.

Staying with my theory that the coin always lands “tails”, how many throws would you require to show “tails” before you would consider my theory “proven”?

Clearly 1 experiment with “tails” did not satisfy you. How about if it landed “tails” 10 times, then would you say my theory was “proven”? How about 100? 1000? What is the exact minimum number of “tails” that you would require to “prove” my theory?

Neither once, because I know from logic/experience that this experiment doesn't make sense. Experiment will shows that theory is wrong in first few throws.

So everything in Physics=maybe, I am disappointed by that fact, disappointed that everything what we learn is maybe wrong.

 

[jbriggs444]

I am disappointed by that fact, disappointed that everything what we learn is maybe wrong.

Welcome to the real world.

 

[fresh_42]

So everything in Physics=maybe, I am disappointed by that fact, disappointed that everything what we learn is maybe wrong.

I am totally satisfied with Newton when I start my car, although I know he was wrong.

 

[user079622]

Welcome to the real world.

Not necessarily. The probability depends on how many times you throw.

If coin is thrown every time with same initial condition(ex. machine) it will land always on same side. Determinism can't be fooled. Indeed from my pure logic, randomness can't exist, just appear to us to exist.(In my beliefs even in atomic world, now when we conclude that physics doesn't have to be correct, no one can't prove me that my belief is 100% wrong.)

I am totally satisfied with Newton when I start my car, although I know he was wrong.

Even if he was wrong, considering what he had at his disposal at the time, he discovered great things.
It seems Einstein is also wrong at atomic level.

 

[jbriggs444]

Indeed from my pure logic, randomness can't exist

You might be disheartened to learn that plain old Newtonian mechanics is not deterministic in all cases. John Baez points out some problems with the continuum model here.

 

[user079622]

You might be disheartened to learn that plain old Newtonian mechanics is not deterministic in all cases. John Baez points out some problems with the continuum model here.

Now I can always say, maybe he is wrong..

 

[Dale]

Neither once, because I know from logic/experience that this experiment doesn't make sense. Experiment will shows that theory is wrong in first few throws.

OK.

So now let’s change it. Now let’s suppose that we have just encountered a flubnubitz for the first time. Like a coin a flubnubitz has two sides but unlike a coin it feels somewhat asymmetrical. We accidentally drop it and it lands with a “tails”. I drop it 9 more times and each time it lands “tails”.

Based on my initial experience I make a theory that unlike coins, a flubnubitz always lands “tails”.

With my 10 experiments all showing “tails”, have I proved my theory? What about with 100 or 1000?

 

[user079622]

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

Did Dayton Miller conduct Michelson-Morley experiments in 1930's, and find some difference in light speeds, and prove speed of light depend of source speed?
Is this true?
at 8:20

So now let’s change it. Now let’s suppose that we have just encountered a flubnubitz for the first time. Like a coin a flubnubitz has two sides but unlike a coin it feels somewhat asymmetrical. We accidentally drop it and it lands with a “tails”. I drop it 9 more times and each time it lands “tails”.

Based on my initial experience I make a theory that unlike coins, a flubnubitz always lands “tails”.

With my 10 experiments all showing “tails”, have I proved my theory? What about with 100 or 1000?

For same initial condition, object will land always on same side.
Yes, if you've never seen black swan, it doesn't mean it doesn't exist.