I Know the Math Says so, but Is It Really True?

[BWV]

Well that's an interesting observation. I have enjoyed music my whole life without ever playing piano, guitar, or anything. I believe musicians appreciate some of the details more than I do. But, nobody is promoting the idea that concert-going is a waste of time for non-musicians.

Indeed, the analogy is the more you learn about music as a listener or amateur musician, the more appreciation you have for people who do it at a very high level

 

[bhobba]

How many hours of study does it take to become proficient in, say, QFT at a professional level?

You mean after you have done something like Susskind? Well he claims to take you to a level where you at least understand the jokes. To take you to more advanced QM that would be about 1 university course which is about 150 hours. Then 2 subjects on QFT or a further 300 hours. But it depends on how hard you find Susskind. If it was about average difficulty for you then I would say that 450 hours is reasonable. Let's be generous about this and you study about an hours per day with weekends free - then I would say about 2 years.

But if you are interested in professional level understanding you will be better going to university for a graduate degree like the following:
https://my.uq.edu.au/programs-courses/plan.html?acad_plan=PHYSCX2321

That will also take about 2 years part time - but with about 2-3 hours study each night.

Thanks
Bill

 

[BWV]

[

You mean after you have done something like Susskind? Well he claims to take you to a level where you at least understand the jokes. To take you to more advanced QM that would be about 1 university course which is about 150 hours. Then 2 subjects on QFT or a further 300 hours. But it depends on how hard you find Susskind. If it was about average difficulty for you then I would say that 450 hours is reasonable. Let's be generous about this and you study about an hours per day with weekends free - then I would say about 2 years.

But if you are interested in professional level understanding you will be better going to university for a graduate degree like the following:
https://my.uq.edu.au/programs-courses/plan.html?acad_plan=PHYSCX2321

That will also take about 2 years part time - but with about 2-3 hours study each night.

Thanks
Bill

but that would assume a good foundation in basic physics and math, if your only introduction to classical mechanics was Susskind, that would likely not be a good enough foundation. Also there is a large gap between understanding the math conceptually, which is really what Susskind requires, vs being proficient at using the math to solve problems. Then once you get there, its ‘use it or lose it‘ otherwise you will just forget it all

 

[bhobba]

but that would assume a good foundation in basic physics and math, if your only introduction to classical mechanics was Susskind, that would likely not be a good enough foundation. Also there is a large gap between understanding the math conceptually, which is really what Susskind requires, vs being proficient at using the math to solve problems. Then once you get there, its ‘use it or lose it‘ otherwise you will just forget it all

Susskind covers a lot more than just classical mechanics. Of course it depends on your preparation and what you recall. If you just read Susskings 3 books then yes I think one hour each night for 2 years is enough. If you did a degree with not much math, or do not remember much, then a prior diploma in math would be of value:
https://my.uq.edu.au/programs-courses/plan.html?acad_plan=MATHEX2321

That would take it to 3-4 years. But you are asking for professional level knowledge. Really is that want you want - or just to get the jokes as Susskind says. That's all the general citizen really needs.

Thanks
Bill

 

[swampwiz]

I had thought that someone falling into black hole would have time being so dilated from the mass that he would observe the universe evolving very rapidly, even to the point of seeing stars form, go into giant phase, supernova, etc. very quickly; OTOH, anyone observing him would observe his watch as almost not ticking at all.

 

[PeterDonis]

I had thought that someone falling into black hole would have time being so dilated from the mass that he would observe the universe evolving very rapidly, even to the point of seeing stars form, go into giant phase, supernova, etc. very quickly

No, this is not correct. An observer hovering at a constant altitude above the hole's horizon, not falling in, will see what you describe. But an observer free-falling into the hole will actually see the outside universe redshifted, not blueshifted, with the redshift increasing as he falls.

OTOH, anyone observing him would observe his watch as almost not ticking at all.

This is correct (at least as long as the observer is outside the horizon, so light signals from him can get back out to distant observers). But that is because, for an observer free-falling into the hole, the time dilation between him and an observer who is far away is symmetric, like time dilation in SR--each observer sees the other's clock running slow. This is a key difference between this case and the case of a hovering observer.

 

[LieToMe]

Why are people making this weird assumption that "math" says anything? People are the ones making arguments. No matter what you write it will only ever be an approximation of relative observations. The only reason we take an interest in it is for practical applications in being able to predict the evolution of systems to some arbitrary degree of certainty in some arbitrary consideration of variables.

People happen to choose some level of tolerance in the statistical correlation of their measurements and there happens to be a relativistic space-time model with the highest correlation to patterns we observe in astronomical objects. According to our best understanding of the standard model, it is astronomically unlikely that the pattern of observations can be explained by a capacity to measure "infinite" time, so the point was moot to begin with, just like asking for the frame of reference of a photon.

 

[romsofia]

Why are people making this weird assumption that "math" says anything?

Why do people make this weird assumption that "English" says anything? People are the ones who give words meaning. No matter what you write it will only ever be an approximation of how society interprets it. The only reason we take an interest in it is so for practical applications in being able to communicate with others to some arbitrary degree of certainty in some arbitrary consideration of intent.

People happen to choose some level of tolerance in the statistical correlation of their definitions, and there happens to be a book with the highest amount of definition to words we observe in society. According to our best understanding on English, one cannot define "the point of LieToMe's post" so the point was moot to begin with, just like asking for the definition of the word "obagooba".

 

[LieToMe]

Why do people make this weird assumption that "English" says anything? People are the ones who give words meaning. No matter what you write it will only ever be an approximation of how society interprets it. The only reason we take an interest in it is so for practical applications in being able to communicate with others to some arbitrary degree of certainty in some arbitrary consideration of intent.

That's something I've actually found to be true. Even now, all we have are statistical measurements, so to a certain degree, you can't be entirely certain about anything. That inability to be entirely certain is how scientific models appear to perpetually evolve.

You can make an argument that logic is independent of observable results, but then such an assumption would only be relative to an individual's construct of reality as a reiteration of past interactions.

 

[Imager]

As one of the people who haven't taken the time to understand the math, I think Peter's points are correct. When I first came to this site, one of my big problem was not getting simple answers like "Youtube" videos.

My other big problem was terminology. For example, using the term universe when they mean observable universe. It took me a while to figure out that those where different things. It's hard for us to ask the right questions, when we don't even understand the differences in terminology.

What makes this forum Great is that people like @PeterDonis, @Dale and many others showing massive amounts patience to walk people like me through the basic concepts!

 

[joeh3rd]

The mathematical models you refer to in other disciplines are still subject to the same test as mathematical models in physics: either they make predictions that match the data, or they don't. Models that don't make predictions at all aren't the kind of "math" I am talking about in the article.

Also, your post implies that mathematical models in physics don't have the characteristics you describe--simplifying complex processes, modeling domains where inputs are not fully knowable. That is quite wrong. There are plenty of domains in physics where the same issues arise. In fact, it's hard to find a domain even in physics where those issues don't arise.

Perhaps there is an example of predictive models containing non-existent or at least non-intuitive features. In electrical engineering Fourier transforms and convolution are used extensively in radio transmitter and receiver design. The heterodyning used for frequency shifting of modulated signals up for transmission and down for audio routinely use the negative frequency component of frequency shifting. I don’t believe that there have been tests for the existence of such however in application they are definitely present as symmetrical side bands of upshifted modulation.
Here we have a mathematical construct that emerges in transformation from the time domain to the frequency domain and back again that works mathematically but has a seemingly non-detectable real world component. Are we sometimes taking a mathematical model that when used may have non-existent internal characteristics yet when used in a series of operations yields measurable results and mistakenly assuming it is what occurs in reality?
Perhaps “virtual particles” are the same just as for modeling purposes we assume the atomic model and things called particles which may be side-effects of our means of measurement and perception — no tiny balls that behave similar to things we perceive by immediate sight and other senses on a much larger scale?

The positive frequency side of a modulated signal. More properly shown, it is symmetric when along the zero frequency axis.

The result when frequency shifted by multiplying with a sinusoid centered at 30kHz. Note the formerly negative frequency lower side and.

 

[PeterDonis]

I don’t believe that there have been tests for the existence of such however in application they are definitely present as symmetrical side bands of upshifted modulation.

You're contradicting yourself. First you say there are no tests for the existence of such, then you say they are definitely present. They can only be definitely present if we have a way of testing for their presence, and the test says they are. If the test is "symmetrical side bands of upshifted modulation", then if those things are present, "such" is present.

Are we sometimes taking a mathematical model that when used may have non-existent internal characteristics yet when used in a series of operations yields measurable results and mistakenly assuming it is what occurs in reality?

In order to even ask this question, you must assume that you can somehow distinguish "non-existent internal characteristics" from internal characteristics that aren't "non-existent". But that would require some kind of experimental test for such characteristics, and if such a test exists, the characteristics aren't "internal" to begin with.