Is There Perfection in Physical Laws?

[Avichal]

Newton's laws, coulomb's law are all very neat but are they totally accurate? According to modern instruments which can measure up-to remarkable precision, do these laws behave perfectly?
I haven't studied quantum mechanics yet but as far as I have heard it's all about probabilities ... we can't predict anything, all we can say is about the probability of a certain event happening. So how come there exists such precise relations among physical things when underneath there is so much randomness? I can only think that these laws are only an approximation and don't behave perfectly.

Further how do we even test these laws? There are so many variables to consider but I suppose that's a different question.

 

[phinds]

If physical laws were not accurate they would not be called laws, they would called approximations.

I can't quote you a source, but I'm sure General Relatively has been found accurate to beyond our ability to make measurements.

As much as 30 years ago, Richard Feynman was fond of telling folks that quantum mechanics had been found accurate to the equivalent of measuring the width of the United States and getting an answer that fit to within the width of a human hair (and I doubt we could make measurements any more refined than that at the time).

 

[Avichal]

If physical laws were not accurate they would not be called laws, they would called approximations.

I can't quote you a source, but I'm sure General Relatively has been found accurate to beyond our ability to make measurements.

As much as 30 years ago, Richard Feynman was fond of telling folks that quantum mechanics had been found accurate to the equivalent of measuring the width of the United States and getting an answer that fit to within the width of a human hair (and I doubt we could make measurements any more refined than that at the time).

Okay, wow! But how does this happen if underneath all the particles are behaving randomly? How does that translate to laws? (I have never studied quantum mechanics before so I might be wrong about the whole random thing)

 

[WannabeNewton]

Newton's 2nd law is approximate; it is really only valid in the non-relativistic domain and non-quantum mechanical domain so you are correct. AFAIK the most scientifically accurate theory we have (with regards to experimental prediction power) is quantum electrodynamics.

 

[dipole]

Okay, wow! But how does this happen if underneath all the particles are behaving randomly? How does that translate to laws? (I have never studied quantum mechanics before so I might be wrong about the whole random thing)

It's "random" in the technical sense of the word, which essentially means it's impossible to know the outcome of a measurement regardless of how much information you know before you make it.

However, "random" doesn't mean anything can happen. The laws govern what a particle can do, and what the probability of that happening is. This can include a zero probabability, in which case it's impossible for the particle to behave in such a way.

For example, in a piece of metal there are an enormous number of "free" electrons moving about inside it, and quantum mechanics tells us that the probability of any two of these electrons occupying the same state is zero. When we do measurements on metals, this prediction is in perfect agreement with the experiment, as far as anyone can tell.

 

[Jorriss]

Okay, wow! But how does this happen if underneath all the particles are behaving randomly? How does that translate to laws? (I have never studied quantum mechanics before so I might be wrong about the whole random thing)

Because that random behavior that is present in our theory is present in nature itself.

 

[Avichal]

But there might be some modified version of Newton's second law given by QED theory or some other, right?

 

[Avichal]

Because that random behavior that is present in our theory is present in nature itself.

I didn't get that.
EDIT: Are you saying that theories are approximate because of the randomness in nature?

 

[phinds]

But there might be some modified version of Newton's second law given by QED theory or some other, right?

No, Newton's law is a very deterministic, fixed, classical physics "law" that happens to have been (and still is) a VERY good predictor of mechanics at small scales ("small" = measured in miles, not millions of miles). It is "wrong" in that it is a localized approximation of what General Relatively predicts. It isn't going to be "updated" by anything (other than GR, by which it has already BEEN updated).

This whole "random" thing is at a sub-atomic level. If you measure something in feet or more, the error produced is trivial besides, this is below our ability to measure.

 

[utpalashu]

Like the value of PIE = 22/7 is just a certain approximation but used everywhere.
These laws are the best yet approached approximations.

So, if we take Newton Law of Gravitation it was more clarified by Einstein in his general relativity. (Describing Gravitation as curvature of Space-Time). I read somewhere that when some people did an experiment with Newton's law by applying it on moon's path.. They found a difference in the current position of moon and what it was predicted by using Newton's law.

 

[Dale]

Newton's laws, coulomb's law are all very neat but are they totally accurate?

Newton's laws and Coulomb's law are both approximations which are measurably incorrect in certain regimes. Specifically, Newton's laws are incorrect as v approaches c, and Coulomb's law is incorrect any time charges are moving.

According to modern instruments which can measure up-to remarkable precision, do these laws behave perfectly?

No, but there are other laws which are accurate to the best precision we can reach experimentally.

I haven't studied quantum mechanics yet but as far as I have heard it's all about probabilities ... we can't predict anything, all we can say is about the probability of a certain event happening. So how come there exists such precise relations among physical things when underneath there is so much randomness? I can only think that these laws are only an approximation and don't behave perfectly.

The laws give very precise predictions for the expected probability distributions, so you perform thousands or millions of experiments and use those to set very precise limitations on the actual probability distribution.

Further how do we even test these laws? There are so many variables to consider but I suppose that's a different question.

Laws are generally tested using a test theory which is more general than the actual theory in question. The test theory has some unknown parameters and, for certain values of the parameters, it reduces to the actual theory. Then you use the test theory to make an experiment to measure the parameter and put constraints on the possible deviations from the actual theory.

 

[ModusPwnd]

AFAIK the most scientifically accurate theory we have (with regards to experimental prediction power) is quantum electrodynamics.

This is what I usually hear too. I went to a talk by Freeman Dyson and he claimed that GR is more accurate because it has more digits/significant figures of predictive power.

 

[ModusPwnd]

I can only think that these laws are only an approximation and don't behave perfectly.

Right, I agree. I think that the use of the word "law" in science is usually a misnomer. Its an old school way of thinking of science from before we developed our modern philosophy of science. In the past they viewed science as though they were looking for "truth" or "reality". With this way of thinking, unfalsified conclusions naturally seem like laws. But now we have a modern way of looking at science where we construct models (mathematical or otherwise) that describe and predict our observations. All conclusions are considered tentative with respect to new observations and evidence. These days new theories are not called laws for this reason.

You might also consider the mathematical equation the law. If you consider the equation alone as the law then it makes no difference what experimental evidence you have, coulombs equation is coulombs law. The theory is then that the law describes and predicts our observations. I see this as a ad-hoc way of defending sloppy language, but its an interpretation.

 

[WannabeNewton]

This is what I usually hear too. I went to a talk by Freeman Dyson and he claimed that GR is more accurate because it has more digits/significant figures of predictive power.

Ah that's quite interesting to hear. At least we can appreciate that both theories are both theoretically beautiful and experimentally powerful

 

[phinds]

Like the value of PIE = 22/7 is just a certain approximation but used everywhere.

Uh ... "used everywhere"? Really? I don't think so. I take it you don't do any calculations that require more than a couple of significant digits.

 

[sophiecentaur]

Strange. It takes just one fewer keystrokes to type 22/7 than it does to type the number 3.142, which the near f that simple fraction equivalent - but its rounded value is 3.143 - so you can only rely on 3.14 - same number of keystrokes. I wonder why it ever caught on.

 

[Jorriss]

I didn't get that.
EDIT: Are you saying that theories are approximate because of the randomness in nature?

No, what I mean is that, say, our theories predict that we'll get result X 50% of the time and result Y 50% of the time, but we can't be more certain than that. But this is a reflection of nature where, upon conducting a large number of experiments we find the result of the experiments match that distribution.

 

[mfb]

Strange. It takes just one fewer keystrokes to type 22/7 than it does to type the number 3.142, which the near f that simple fraction equivalent - but its rounded value is 3.143 - so you can only rely on 3.14 - same number of keystrokes. I wonder why it ever caught on.

The approximation is older than computers.


It is expected that general relativity is not exact, as it does not include quantum mechanics.
It is expected that quantum field theory is not exact, as it does not include gravity.

Therefore, our current "laws of physics" are probably just very good approximations. That is not a fundamental problem - if the universe follows some laws (and it looks like it does), it should be (in theory) possible to discover those laws. Those laws would be exact.

 

[Nugatory]

Strange. It takes just one fewer keystrokes to type 22/7 than it does to type the number 3.142, which the near f that simple fraction equivalent - but its rounded value is 3.143 - so you can only rely on 3.14 - same number of keystrokes. I wonder why it ever caught on.

If you're doing it the hard way, using pencil and paper while you're dodging the velociraptors... You can multiply by 22 in your head (double and add ten percent) and then you just have to do a long division by seven. That's way less work than multiplying by a four-digit number.

 

[mrspeedybob]

Strange. It takes just one fewer keystrokes to type 22/7 than it does to type the number 3.142, which the near f that simple fraction equivalent - but its rounded value is 3.143 - so you can only rely on 3.14 - same number of keystrokes. I wonder why it ever caught on.

"Three point one four" is 4 syllables when you say it out loud. "Twenty-two sevenths" is 5, "twenty-two over seven" is even worse at 7 syllables. In addition, if you learn pi as 3.14 then it is easy to add more digits later if they are needed. If you want to upgrade 22/7 to something more precise your next good option is 311/99. If you likewise add 2 digits to 3.14 you have 3.1416 which is ≈24 time more accurate then 311/99.

 

[sophiecentaur]

If you're doing it the hard way, using pencil and paper while you're dodging the velociraptors... You can multiply by 22 in your head (double and add ten percent) and then you just have to do a long division by seven. That's way less work than multiplying by a four-digit number.

Good point.
I also learned 355/113 to use pi on my Sinclair Cambridge.

 

[sophiecentaur]

"Three point one four" is 4 syllables when you say it out loud. "Twenty-two sevenths" is 5, "twenty-two over seven" is even worse at 7 syllables. In addition, if you learn pi as 3.14 then it is easy to add more digits later if they are needed. If you want to upgrade 22/7 to something more precise your next good option is 311/99. If you likewise add 2 digits to 3.14 you have 3.1416 which is ≈24 times more accurate then 311/99.

Nothing personal here (and you are only the tip of a massive iceberg which is floating past me this morning) but where did this form of notation come from and why is it so popular these days? How can the concept of 'twenty four times less' be meaningful and, more important, unambiguous? Is it because people started with Percent Discount (but we know that most people can't 'do Percents') and it just 'growed' from there? There is always a way of putting things in a better way than using the 'times less' construction - like 'the error is 1/24th'. We surely can't be struggling with fractions, can we? The blessed Michael Gove would have us believe that five year old can cope with fractions. It isn't just a matter of style.

 

[Darryl]

I always have considered a law to be something beyond a theory and is fully consistent in that it consistently (without exception) allow predictions and analysis to take place.

Using Ohm's Law for example..

You know if you have 1 amp flowing through 1 ohm you will have 1 volt drop across the resistor. If your measurements differ from this it is your measurement that is incorrect. V=IR is more that a theory, or a hypotheses, it is a continuously proven RULE. The rule of law.

 

[sophiecentaur]

Actually, Ohm's Law is not a good example of a 'Law' because it is a description of a pattern of behaviour of certain conductors. A Metal will follow Ohm's Law under conditions of constant temperature (which are the specified conditions of that 'Law'). In fact, a thermistor or tungsten filament can follow 'Ohm's Law under the proper conditions although, colloquially, they is referred to as a non-ohmic devices. Non Ohmic conductors will still have a ratio V/I but that can change as V or I change but you can still assign then a value of instantaneous resistance.
It is not accurate to say that "Ohm's Law is R = V/I".

 

[phinds]

I always have considered a law to be something beyond a theory and is fully consistent in that it consistently (without exception) allow predictions and analysis to take place.

.

Uh ... have you ever heard of Newton's Law of Gravity? TOTALLY fails outside of local distances, so I'd say your understanding is flawed.

 

[Dale]

Modern science doesn't make a big deal about "laws" vs "theories". I think that "law" is simply an archaic term that is rather haphazardly applied to some specific equations.

 

[mrspeedybob]

...where did this form of notation come from and why is it so popular these days? ...

I don't really like it either for exactly the reason you mentioned. Few people can say exactly what it means mathematically. I use it because other people are accustomed to reading/hearing it and so it usually goes unnoticed. This is desirable when the point I am trying to make is more general and I want my audience thinking about the main point (3.1416 is far more precise then 311/99) instead of the odd way I choose to say it. I think if I had said "the difference between 311/99 and pi is ≈24 times the difference between 3.1416 and pi" I would have been saying it more precisely but less clearly.

 

[Claude Bile]

Modern science doesn't make a big deal about "laws" vs "theories". I think that "law" is simply an archaic term that is rather haphazardly applied to some specific equations.

Exactly. Either it is backed by evidence or it's not; that's the important thing.

Claude.

 

[Khashishi]

Quantum electrodynamics is accurate (in some calculations) to at least 15 digits, and possibly more. But it probably will fail to be correct to 36 digits because the strength of gravity is about 10^-36 of the strength of electromagnetism (for an electron), and gravity isn't included in QED.

 

[Naty1]

The laws 'behave perfectly'...but that doesn't mean they are absolutely precise representations of nature.

Newton's laws and Coulomb's law are both approximations which are measurably incorrect in certain regimes.

Likewise, quantum mechanics, and GR.
And quantum mechanics was 'updated' so the Standard Model, another very accurate model, utilizes relativistic quantum mechanics.

So how come there exists such precise relations among physical things when underneath there is so much randomness?

Things are not so simple as you imply:

FROM THE ROAD TO REALITY. Roger Penrose, page 528

The Schrodinger wave equation is a deterministic equation: the time evolution is completely fixed once the state in known at anyone time….and provides for the evolution of a quantum particle in a very precise way- until some measurement is performed on the system.

This may come as a surprise to some people, who may well have heard of quantum uncertainty, and of the fact that quantum systems behave in non deterministic ways.

[Non deterministic means limited to ‘statistical’ observational measurements.]and the following quote, with some additional detail, is also from Roger Penrose celebrating Stephen Hawking’s 60th birthday in 1993 at Cambridge England...from a talk to world famous scientists...

Either we do physics on a large scale, in which case we use classical level physics; the equations of Newton, Maxwell or Einstein and these equations are deterministic, time symmetric and local. Or we may do quantum theory, if we are looking at small things; then we tend to use a different framework where time evolution is described... by what is called unitary evolution...which in one of the most familiar descriptions is the evolution according to the Schrodinger equation: deterministic, time symmetric and local. These are exactly the same words I used to describe classical physics.

However this is not the entire story... In addition we require what is called the "reduction of the state vector" or "collapse" of the wave function to describe the procedure that is adopted when an effect is magnified from the quantum to the classical level...quantum state reduction is non deterministic, time-asymmetric and non local...The way we do quantum mechanics is to adopt a strange procedure which always seems to work...the superposition of alternative probabilities involving w, z, complex numbers...an essential ingredient of the Schrodinger equation. When you magnify to the classical level you take the squared modulii (of w, z) and these do give you the alternative probabilities of the two alternatives to happen...it is a completely different process from the quantum (realm) where the complex numbers w and z remain as constants "just sitting there"...in fact the key to keeping them sitting there is quantum linearity...

Penrose goes on to say in ROAD TO REALITY

My own view is that quantum theory is an approximate theory and we have to seek some new theory which supplants all three procedures.. classical, reduction and quantum...

 

[Avichal]

The laws 'behave perfectly'...but that doesn't mean they are absolutely precise representations of nature.

Likewise, quantum mechanics, and GR.
And quantum mechanics was 'updated' so the Standard Model, another very accurate model, utilizes relativistic quantum mechanics.

Really? Even the more modern theories are not accurate? Have we found some error in measurements or is it your own personal view?

 

[Delta Kilo]

Penrose goes on to say in ROAD TO REALITY

You have to be careful with this book, it's heavy :)

While the math part seems to be rock solid, when it comes to physics, especially QM and beyond, there are quite a few disclaimers stating that this or that bit is his personal view different from the mainstream. For example, the bit you quoted about classical, reduction and quantum is one of those. To be fair, every now and then he does the reverse and presents the mainstream view while making it clear he himself does not share it.

I mean the book is great, really great, but I wouldn't take quotes from it as a gospel without careful examination of the context.

 

[sophiecentaur]

Really? Even the more modern theories are not accurate? Have we found some error in measurements or is it your own personal view?

Why would you expect them to be accurate just because they are the latest? Surely, all you can hope for is that they are possibly 'more accurate' or cover a bigger range of circumstances. Can you really believe there is an 'ultimate answer', somewhere?

At a very basic level, you could never hope to 'measure' pi accurately because all measurement has a limited accuracy so you couldn't hope to produce a trancscendental number by using a ratio of two quantised values. But that wouldn't spoil anyone's day because it's real life.

 

[Avichal]

Why would you expect them to be accurate just because they are the latest? Surely, all you can hope for is that they are possibly 'more accurate' or cover a bigger range of circumstances. Can you really believe there is an 'ultimate answer', somewhere?

At a very basic level, you could never hope to 'measure' pi accurately because all measurement has a limited accuracy so you couldn't hope to produce a trancscendental number by using a ratio of two quantised values. But that wouldn't spoil anyone's day because it's real life.

I don't know about there being an 'ultimate answer' but surely I thought whatever we know currently is very much accurate and correct (as far as we can measure it).
It feels nice to have nature behave according to simple mathematical laws but of course I cannot tell the nature how to behave.

 

[sophiecentaur]

I don't know about there being an 'ultimate answer' but surely I thought whatever we know currently is very much accurate and correct (as far as we can measure it).
It feels nice to have nature behave according to simple mathematical laws but of course I cannot tell the nature how to behave.

It does feel nice when we find it behaves close to simple mathematical laws. But should be expect it to follow them to an infinite degree? The Maths we use assumes continuity in the set of numbers we use but there's no reason to assume that Nature is not granular. We made that mistake before, several times, in history.