I My lecturer says "Special relativity is absolutely wrong"

[vanhees71]

I'm hoping that this philosophy of physics course isn't the one at my "one of the top universities in Australia"!

Well, before you study the philosophy of physics you should study physics. That's more or less trivial, but unfortunately many philosophers try to do philosophy of physics without having a clue about physics.

The apparent "faster-than-light neutrinos" measured by the OPERA colaboration are gone for some time now. It turned out to be an error in the setup of the measurement (some issue with the connection of glass fibers and some time-measuring oscillator, if I remember right). So there's not the slightest hint for tachyons so far, and if there were, theorists have a huge problem to solve, because today there's no consistent theory of interacting tachyons. Free tachyons can be theoretically described to a certain point, but they are not observable, because they don't interact with any detector by definition. So it's useless to study them too.

 

[haushofer]

It depends how you define motion and momentum, in either theory. If you define motion via 4-velocity, itself defined as derivative with respect to proper time, then tachyonic motion is ruled out by definition (as are massless classical particles).

I'm not seeing this directly. Could you elaborate? Massless classical particles are described by an action using an auxiliary field, and I don't see why this action cannot also be used for tachyons. :)

 

[PAllen]

I'm not seeing this directly. Could you elaborate? Massless classical particles are described by an action using an auxiliary field, and I don't see why this action cannot also be used for tachyons. :)

That's why I said it depends on definitions you adopt. I gave one definition, you immediately changed definitions. For 4-velocity defined as derivative by proper time, it fails to exist for null paths because the differential interval is zero. For spacetime paths, it fails to exist because the differential interval is proper distance rather than proper time.

 

[Charles Kottler]

Well, before you study the philosophy of physics you should study physics. That's more or less trivial, but unfortunately many philosophers try to do philosophy of physics without having a clue about physics.

It goes without saying that a professor teaching philosophy of physics must have a thorough understanding of the maths. However, while I agree that it would be useless to study the philosophy of physics without also studying physics, I don't see the necessity of learning the physics first. Often these days students are drilled to 'internalize the maths' to avoid getting sucked into the much harder challenge of understanding what it actually means. I would argue that studying the maths without also studying the reasoning behind it would be a waste of time. The following article outlines the need for philosophy far more eloquently than I ever could:

http://www.pbs.org/wgbh/nova/blogs/physics/2015/04/physics-needs-philosophy/

Every course on relativity should include a discussion of the implications and the weaknesses of the theory. Students need to be taught to look for the purpose of what they are learning before being taught the detail.

 

[PeterDonis]

The following article outlines the need for philosophy far more eloquently than I ever could

Unfortunately, I think this article unintentionally illustrates why philosophy contributes so little to physics. The writer says that "physicists strongly discourage questions about the nature of reality". Yet he never considers the possibility that the reason physicists discourage such questions is that "reality" is too vague a term to be used when formulating questions that can actually be answered. If philosophy were really doing its job, it would either give a precise meaning to the term "reality"--a meaning that could actually be used in understanding physical theories--or admit that the term is too vague and drop it, and find better terms.

Another example of unintentionally illustrating the limits of philosophy is the article's discussion of the twin paradox. The writer asserts that the explanation given in the Feynman lectures is incorrect. But he never says what the "correct" explanation is. He also asserts that "it is easy to describe cases where the opposite is true, and even cases where neither twin accelerates but they end up different ages". This is simply incorrect when working within the limits of special relativity--which is what the chapter of the Feynman lectures that the article refers to was discussing. Scenarios where the unaccelerated twin ages less, or where two unaccelerated twins can end up aging differently, can only be set up in curved spacetime, which is beyond the scope of SR. Within the scope of SR, the rule Feynman gives works fine, so calling it "incorrect" is, well, incorrect.

I could go on, but I think you get the idea.

Every course on relativity should include a discussion of the implications and the weaknesses of the theory. Students need to be taught to look for the purpose of what they are learning before being taught the detail.

I agree with these statements, but they are not arguments for learning philosophy before learning physics. They are arguments for learning physics. Physics includes the implications and weaknesses of theories, and understanding the overall purpose of a theory--what domain it is supposed to cover--before learning its details.

 

[haushofer]

I like Feynman's quote on this issue:

"We can't define anything precisely. If we attempt to, we get into that paralysis of thought that comes to philosophers, one saying to the other: 'you don't know what you are talking about!'. The second one says: 'what do you mean by talking? What do you mean by you? What do you mean by know?"

:P

 

[haushofer]

Another example of unintentionally illustrating the limits of philosophy is the article's discussion of the twin paradox. The writer asserts that the explanation given in the Feynman lectures is incorrect. But he never says what the "correct" explanation is.

He also includes this in his "Philosophy of physics: space and time". The corrext explanation Maudlin means is the fact that according to him only the ratio of both lengths of the worldlines should enter the explanation of the twin 'paradox', and not the acceleration. (page 83) But I consider that a bit of nitpicking: I think a lot of physicists would understand bending of the worldline as being caused by acceleration. Maudlin likes to rephrase SR in purely geometric terms.

The cleavage between physicists and philosophers of physics is also something that fascinates me.

 

[atyy]

I can't agree that physics and philosophy don't go together. The concept of reality is absolutely fundamental in physics. The best physicists have always been interested in philosophy - Landau and Lifshitz, Dirac and Weinberg. And of course, Feynman made so many comments on philosophy, he must have thought it important. Late in his career, Feynman made a statement that is equivalent to saying that the violation of Bell's inequality sums up quantum weirdness.

So I would contend that the teacher is doing bad physics and bad philosophy.

 

[vanhees71]

Well, concerning Weinberg I'd cite

http://www.pitt.edu/~mem208/courses/phph_s15/documents/weinberg_against_philosophy.pdf

 

[atyy]

Well, concerning Weinberg I'd cite

http://www.pitt.edu/~mem208/courses/phph_s15/documents/weinberg_against_philosophy.pdf

He wrote a really long philosophical essay :)

 

[gjonesy]

I think philosophy has its place in physics, the illustration of paradox, the illustration of certain concepts and its an overall good way of expressing specific ideas. BUT to inject ones own opinion into accepted science could lead to misunderstanding and then misinformation.

 

[Ben Niehoff]

Only Sith deal in absolutes.

 

[RockyMarciano]

I agree with these statements, but they are not arguments for learning philosophy before learning physics. They are arguments for learning physics. Physics includes the implications and weaknesses of theories, and understanding the overall purpose of a theory--what domain it is supposed to cover--before learning its details.

A study of the implications and weaknesses of theories and the overall purpose of physical theories is pretty much the definition of phylosophy of physics, you would be calling physics the sum of the two subjects which would be quite non-standard. I know very few physics textbooks that include it(and none when moving to the more advanced or technical texts that of course start off with a fixed philosophical position that is never made totally explicit) so I tend to think philosophy is not generally included in physics as discipline.

 

[peety]

When Einistein was moving towards his General theory and realized that there had to be something inadequate in giving priority to certain reference bodies or their state of motion wasn't this a kind of philosophical insight? Maybe we could view physics as an extraordinarily precise and empirical form of philosophy.

 

[PeterDonis]

A study of the implications and weaknesses of theories and the overall purpose of physical theories is pretty much the definition of phylosophy of physics

I disagree. Physicists are supposed to study the implications and weaknesses and overall purpose of theories--that's pretty much the main purpose of peer review.

 

[gjonesy]

My understanding of "philosophy" when it comes to physics it that is a practical way of illustrating theory as it pertains to reality. The math doesn't paint a picture, the philosophy and concepts they are based on does. Its practical an applicable for the layman to help understand such concepts (when presented accurately). For the Physicists Math is the language they speak therefore philosophical review on the nature and reality of physics doesn't necessarily help or hinder a physicists because they already have a deeper understanding of the material. The nature of reality and those concepts is the language they use to communicate theory to non-physicist.

 

[vanhees71]

I disagree completely. If anything general can be concluded from our experience about physics since Newton it's that the only adequate picture is painted by math!

Philosophy of physics is not part of physics itself but helps to analyse what physicists do in a larger context of all human experience. It can also analyse how physicists came to the knowledge from a historical and/or epistological point of view. Philosophy can hinder physicists (even the greatest geniuses of all times like Einstein) by establishing prejudices about how nature should behave by taking these epistomelogical findings as unchangeable truths rather than being subject to refinements (or even revolutionary paradigm shifts, which are however very rare in the history of physics; since the founding fathers of modern physics, Galilei and Newton, there was only one really revolutionary paradigm shift, which was the discovery of quantum theory in 1925).

In my opinion philosophy can only analyse the contemporary status of physics a posteriori but not help to enter new territory of physics itself.

 

[gjonesy]

I disagree completely. If anything general can be concluded from our experience about physics since Newton it's that the only adequate picture is painted by math!

That's only if you have a solid understanding of the math. I agree 110% math is the language of the physicist. Not all of us speak math. At least not very complex math. I speak some algebra some geometry. Everything else has to be explained by the comparison of movement of bodies or nature of reality.

edit: when they say (question) in the philosophy, only the formulation of such can give rise to concepts that a laymen can understand, example Einstein's " space time", and concept of time travel, it being compared to a flat sheet of paper, how do you get to the other end of the paper? A straight line ...but what if we fold the paper? ...that type of thing.

 

[PeterDonis]

Everything else has to be explained by the comparison of movement of bodies or nature of reality.

But such "explanations" are heuristic at best, and outright misleading at worst. Only the math gives an explanation that is precise enough to not be heuristic and not be misleading. So if you don't speak math, you have to accept the fact that the explanations you can follow will not be that precise.

 

[gjonesy]

@PeterDonis,
I fully except it. Only the simplest concepts are grasp at that level. But it gives us something to follow and try to make sense of at least.

And since being here its actually helped me distinguish between the worst and more misleading to the better and more informed explanations.

This place is great for that.

 

[andrew s 1905]

But such "explanations" are heuristic at best, and outright misleading at worst. Only the math gives an explanation that is precise enough to not be heuristic and not be misleading. So if you don't speak math, you have to accept the fact that the explanations you can follow will not be that precise.

Yes, but it can't just be mathematics. It has to include a description or interpretation of the objects (forces, fields, particles etc.) that the mathematics embodies so that they can be linked to the world they intend to describe and so they can be experimentally tested. I suspect it is the difference use of some of these terms in normal usage and in specific scientific usage that can lead to misunderstandings. Unfortunately, I think, that sometimes this is deliberately done for effect.

This was brought home to me when my daughter studied economics at university. The equations she was using were the same as the ones I had encountered in classical mechanics. The mathematics was the same but the subject matter was very different.

Regards Andrew

 

[PeterDonis]

It has to include a description or interpretation of the objects (forces, fields, particles etc.) that the mathematics embodies so that they can be linked to the world they intend to describe and so they can be experimentally tested.

I would say it has to include a description of which mathematical quantities correspond to direct observables, and how those observables are measured. Adding a description of the "objects" is not, strictly speaking, necessary, although it is practically always done; and descriptions in terms of "objects" are not necessarily precise, since the same words are often used to describe different mathematical quantities, or the same quantities are described using different words.

I suspect it is the difference use of some of these terms in normal usage and in specific scientific usage that can lead to misunderstandings.

Yes, and this is a key reason why the scientist's answer to questions about what a word means will ultimately be "look at the math". The math is unambiguous, whereas ordinary language is not.

 

[andrew s 1905]

I would say it has to include a description of which mathematical quantities correspond to direct observables, and how those observables are measured. Adding a description of the "objects" is not, strictly speaking, necessary, although it is practically always done; and descriptions in terms of "objects" are not necessarily precise, since the same words are often used to describe different mathematical quantities, or the same quantities are described using different words.

That may well be strictly correct but would leave a very sterile physics as so few "objects" are directly observable. No electrons, protons, Higgs. Unless I have misunderstood you.

Regards Andrew

 

[IllyaKuryakin]

In physics we can never say anything is "absolutely right". There could always be an experiment that we haven't thought of that could prove that the theory is wrong, or at least incomplete. Of course Einstein understood that Special Relativity was incomplete, but does that make it wrong? Very few theories can be said to be complete. Almost every theory will break down at some scale. We aren't even sure that General Relativity applies at the quantum scale, but probably not. Does that mean that almost every theory in physics is wrong? That's an extreme position to take. So then, what is "absolutely wrong"? Absolutely wrong would mean that a theory would not predict results that could be verified by experiment over any reasonable range of application. Given that definition, I'd have to say your lecturer is "absolutely wrong". Of course, there is nothing to be gained by making that point to her/him. If the grade is important enough, say the difference between getting the degree or not, I'd present my case to the head of the Department. Otherwise, I'd just let it go and move on.

 

[andrew s 1905]

I would say it has to include a description of which mathematical quantities correspond to direct observables, and how those observables are measured. Adding a description of the "objects" is not, strictly speaking, necessary, although it is practically always done; and descriptions in terms of "objects" are not necessarily precise, since the same words are often used to describe different mathematical quantities, or the same quantities are described using different words.
Yes, and this is a key reason why the scientist's answer to questions about what a word means will ultimately be "look at the math". The math is unambiguous, whereas ordinary language is not.

That can't be right as maths without context is just "maths" it must include some connection to the world - observables, objects

Do the equations describe a spaceship in flight or the stock exchange?

Regards Andrew

 

[gjonesy]

Only Sith deal in absolutes.

Definitely a Sith Lord! In disguise

 

[PeterDonis]

That may well be strictly correct but would leave a very sterile physics as so few "objects" are directly observable. No electrons, protons, Higgs.

The math certainly has quantities in it which can be labeled as "electrons", "protons", "Higgs particles", etc. But those quantities (for the most part) are not direct observables. Describing those quantities as "electrons", "protons", "Higgs", etc. is not necessary to predicting the values of the direct observables, which are what we actually compare with experiments; we do it because it helps us conceptualize what is going on, not because it is necessary to the model.

This also ties into the other issue you raised, about words having different meanings to scientists and non-scientists. When a non-scientist hears the word "electron", he probably thinks of a tiny little billiard ball zipping around. But the scientist actually means a quantity in the mathematical model--in our most fundamental current model, it's a quantum field. This mathematical quantity does not correspond to anything in an ordinary person's intuition, so calling it an "object" is already a stretch, and there is no other ordinary language word that captures it any better. So the best a scientist can do is to emphasize that all of the ordinary language descriptions are at best heuristic, and that the only precise description is the math. That's not "sterile" physics; it's precise physics. The fundamental quantities in our models are unlike anything in your ordinary experience, so physicists should not use language that suggests that they are--and there is no ordinary language that doesn't.

Do the equations describe a spaceship in flight or the stock exchange?

What actual observations do the direct observables in the mathematical model correspond to? If they correspond to the position, velocity, acceleration, mass, etc. of a space ship, then the equations are describing a space ship. If they correspond to stock prices, price changes, etc., then the equations are describing the stock exchange.

My point is that the link between scientific models and reality is not in the names we give to internal objects in the models; it is in the correspondence between the direct observables in the models and our actual observations. You can give names to internal objects all you want, but if you don't know what the direct observables correspond to, you don't know if your names for the internal objects are the right ones.

 

[bob012345]

His little schpiel about General Relativity allowing faster than light travel is absolute hokum.
Special Relativity is not wrong in the way that Newtonian mechanics is not wrong. They are just approximate theories - effective only within their domain of application.

GR doesn't allow FTL travel per se. It does, in principle, allow travel that effectively gets one between two points FTL to an outside observer but it requires exotic matter. This is the so-called Alcubierre drive.

 

[andrew s 1905]

You call it precise but to my mind it is also sterile. In your world the Higgs bosson and Gavitational waves were not discovered but just some aspects of the internals of the mathematical machinery of the Standard model of Particle Physics and General Relativity were confirmed. That maybe sufficient motivation to professional Physicists but I doubt it would attracted much funding or public interest.

We will have to agree to disagree on this.

Regards Andrew

 

[RockyMarciano]

I disagree.

About what?

Physicists are supposed to study the implications and weaknesses and overall purpose of theories--that's pretty much the main purpose of peer review.

Ok, that means you think they are supposed to learn philosophy of science. That is what makes possible to critically assess how the math symbols are best interpreted. The most usual alternative is just swallow others' philosophies without even realizing it.

 

[shintashi]

When I was at Columbia, we had a Physics and Philosophy course taught by the guy who appeared on "What the Bleep do we Know?". It was my understanding from other students that the quantum mechanics professor didn't have the highest opinion of his interpretation of QM. Ergo, as Russ says, go speak with another professor if you have one, who knows more about the topic.

Nevertheless, remember the golden rule of academia: the guy grading your papers is always right, especially when they are wrong.

 

[gjonesy]

There is one thing I know about the mind, a picture is worth a thousand words, a value and vector a quantity, numbers and symbols on a black board or sheet of paper or computer screen. All of these "things" paint a picture in the mind of the physicist. You can look at every equation and data point for the double slit but is it only the numbers you see? Or do you see the filters the detectors the screen the wave like pattern formed? Do you visualize? Do you conceptualize? How would you create a real world experiment, with just numbers? The particle accelerator at CERN LHC isn't constructed of numbers and equations...its made of metal. There has to be a picture beyond the equations...there has to be real vision IMHO.

 

[PeterDonis]

In your world the Higgs bosson and Gavitational waves were not discovered but just some aspects of the internals of the mathematical machinery of the Standard model of Particle Physics and General Relativity were confirmed.

No, in my world observations were made that matched the predictions for particular direct observables in the Standard Model of particle physics and General Relativity, and those things can be described, in ordinary language, as "discovering the Higgs boson" and "observing gravitational waves". But the meaning I give to those ordinary language descriptions might be different from the meaning you give to them.

The question is: are you comfortable with knowing that you only have a heuristic, approximate, possibly misleading understanding of what those terms actually mean? If your answer is yes, then we have no disagreement.

That maybe sufficient motivation to professional Physicists but I doubt it would attracted much funding or public interest.

Same question here: are you comfortable with knowing that your interest in, and willingness to fund, basic research in physics is based on a heuristic, approximate, and possibly misleading understanding of what the physicists are doing? If your answer is yes, then we have no disagreement.

Btw, plenty of physicists would apparently answer "yes" to this as well, since they spend considerable time giving heuristic, approximate, possibly misleading descriptions in ordinary language of what they are doing, for the express purpose of stimulating public interest and obtaining funding.

 

[PeterDonis]

that means you think they are supposed to learn philosophy of science.

No, it means that I draw the boundary between "science" and "philosophy of science" differently than you do.

 

[andrew s 1905]

The question is: are you comfortable with knowing that you only have a heuristic, approximate, possibly misleading understanding of what those terms actually mean? If your answer is yes, then we have no disagreement.

Strange as it may seem to you I do my best to understand many areas of Physics. I study the recommended texts, linked articles and follow the discussions on this forum as best as I can. I have to accept that given my age and abilities this quest will never be fully realized. So no I am not comfortable with a heuristic, approximate, possibly misleading understanding. I continue to strive to improve it.

Regards Andrew

 

[PeterDonis]

Strange as it may seem to you

It doesn't seem strange to me at all. I'm simply trying to get clear about your position.

So no I am not comfortable with a heuristic, approximate, possibly misleading understanding.

Then you should not be comfortable with descriptions like "the Higgs boson was discovered" or "gravitational waves were detected" by themselves; you should want to understand the math beneath them (and you say you do), which will tell you things that are very different from the ordinary language meanings of those phrases, and certainly are not conveyed by those phrases. Which means that, by your own stated preference, it is the ordinary language phrases that are "sterile", since they don't give you all the much richer underlying meaning that is contained in the math.

 

[Ernest S Walton]

I don't go along with this business of 'ordinary language' being sterile whereas math has some 'rich underlying meaning'.

In reality, what that means is that physicists don't have a sufficiently eloquent grasp of language to enable them to translate their mathematical symbols into the appropriate and corresponding terminology. Which is not surprising as it's difficult to wield expertise in two disparate subjects.

At the end of the day every mathematical concept can be expressed linguistically, but not vice versa.

 

[Vanadium 50]

Science needs philosophers of science like birds need ornithologists.

 

[PeterDonis]

In reality, what that means is that physicists don't have a sufficiently eloquent grasp of language to enable them to translate their mathematical symbols into the appropriate and corresponding terminology.

No, what it means is that the words that are used to refer to concepts in our scientific theories can't have their intended meanings to someone who does not understand those concepts. And ultimately the only way to be sure someone understands those concepts is to look at the math.

To put it another way: the meanings of words in ordinary language ultimately depend on ostensive definitions. If you want to know what a "cat" is, ultimately you have to get directly acquainted with some cats. But when you're talking about abstract concepts, the analogue of getting directly acquainted with cats is getting acquainted with those concepts, which can only be done by abstract thought. Sometimes concrete models can be used to help--for example, in learning set theory we can use concrete sets of things to illustrate the axioms and theorems. But nobody has a concrete model that works exactly like the quantum fields describing the fundamental particles in the Standard Model. So the only way to get acquainted with those concepts is to look at the math. Words can't help unless you have the mathematical concepts already in your head for the words to refer to.

 

[strangerep]

Science needs philosophers of science like birds need ornithologists.

 

[Warp]

The simple version of the situation is: Nothing can travel faster than c, but under certain circumstances the distance between two points can increase faster than c. (At first glance they might sound like the same thing, but they are not.)

 

[PAllen]

The simple version of the situation is: Nothing can travel faster than c, but under certain circumstances the distance between two points can increase faster than c. (At first glance they might sound like the same thing, but they are not.)

Correct observation. Note that this is as true in SR as in GR. Consider the simple case of an inertial frame in SR, with object A moving to the left at .9999...c and B moving to the right at .999...c. Then the distance between them grows by 1.9999...c [despite their relative velocity being <c]. Using a flat space analog of cosmological coordinates, you can get a separation speed between inertially moving bodies of any multiple of c. Note, this distance is integrated proper distance so it is not a matter of coordinate units. It is instead, a matter of how flat spacetime is foliated by the coordinates. In particular, each spatial slice being hyperbolic in geometry is what allows this result.

 

[Warp]

Note that this is as true in SR as in GR.

I don't see how. SR states that nothing can travel faster than c, no matter what. It doesn't matter what the relative velocities are between the observer and the object, when the observer measures the velocity of the object, it will always be under c.

The reason why under certain circumstances the distance between two points can genuinely grow faster than c is because of non-linear spacetime geometry, a concept that only GR introduced.

Consider the simple case of an inertial frame in SR, with object A moving to the left at .9999...c and B moving to the right at .999...c. Then the distance between them grows by 1.9999...c [despite their relative velocity being <c].

I don't think that's how SR works at all. You can't just sum velocities like that.

 

[PAllen]

I don't see how. SR states that nothing can travel faster than c, no matter what. It doesn't matter what the relative velocities are between the observer and the object, when the observer measures the velocity of the object, it will always be under c.

Wrong. While the velocity of A relative to B, measured by B, or vice versa, is < c, the growth rate of separation between A and B can approach arbitrarily close to 2c in a given inertial frame. This is exactly why comparing separation rate to relative velocity is a category error, like comparing temperature to energy.

I

The reason why under certain circumstances the distance between two points can genuinely grow faster than c is because of non-linear spacetime geometry, a concept that only GR introduced.

This is false. I made my observation because a surprising number of cosmology presentations make this error. If you take the limit of FLRW solutions to a massless universe, you end up with flat spacetime (i.e. pure SR) in Milne coordinates. These foliate the flat spacetime with hyperbolic spatial slices. The growth of proper distance (along these hyperbolic spatial slices) between inertial world lines that are part of the homogeneous congruence of the solution can by any multiple of c whatsoever (if they are far enough apart). Yet, this is pure SR minkowski spacetime.

I

I don't think that's how SR works at all. You can't just sum velocities like that.

The velocity addition formula applies to relative velocities. Separation rate (= recession rate) is a completely different category, that is just as unbounded in SR as it is in GR. I highlight this because of the large number of false statements in this regard by cosmologists making a category error. Note that Sean Carroll who has written a great GR text as well as being a notable cosmologist, has written on this point, and does not make this mistake.

 

[Warp]

This is false.

So what you are effectively saying is that the size of the universe is exactly the size of the observable universe, because the metric expansion of the universe cannot make distances between galaxies grow faster than c. After all, the claim that changes in the geometry of spacetime can cause distances to grow faster than c is "false".

Also ergospheres around rotating black holes do not exist, because the concept is "false".

You learn something new every day.

 

[PAllen]

So what you are effectively saying is that the size of the universe is exactly the size of the observable universe, because the metric expansion of the universe cannot make distances between galaxies grow faster than c. After all, the claim that changes in the geometry of spacetime can cause distances to grow faster than c is "false".

Also ergospheres around rotating black holes do not exist, because the concept is "false".

You learn something new every day.

No, you completely misunderstand (charitably; uncharitably, you deliberately and sarcastically distort) what I wrote. I wrote that distance between between inertial bodies can grow faster than c in both flat spacetime and curved spacetime, depending on the foliation. You state this somehow implies that distance cannot grow faster than c. This is the opposite of my claim - that distance can grow faster than c in either SR or GR.

 

[Warp]

No, you completely misunderstand (charitably; uncharitably, you deliberately distort) what I wrote. I wrote that distance between between inertial bodies can grow faster than c in both flat spacetime and curved spacetime, depending on the foliation. You state this somehow implies that distance cannot grow faster than c. This is the opposite of my claim - that distance can grow faster than c in either SR or GR.

I think there is a fundamental misunderstanding in all of this.

If I'm an observer and am measuring a (massive) object receding from me, according to SR I will never, ever measure said object to be receding from me faster than c, or even at c. It may approach c, and thus may red-shift to almost invisibility, but it will never reach c, and thus never become completely invisible.

However, according to GR the receding object can recede from me faster than c. It thus becomes completely unobservable from my perspective, effectively being beyond an observability horizon. And there is effectively no limit to how much faster than c it can recede. SR does not have this concept because it considers space to be linear and static.

 

[Ibix]

@Warp - you are depending on a particular simultaneity criterion (a flat foliation of flat spacetime) to make your statements. @PAllen is using a different, but still perfectly reasonable, simultaneity criterion (a curved foliation of flat spacetime). He's applying GR tools to SR, but he's still talking SR.

If I understand right, you can visualise spacetime as a block. You are slicing it into flat planes and calling each plane "the universe at time t". He's slicing the block into a stack of bowls and calling each bowl "the universe at time t". Spacetime is still the same 3d block, whichever way you slice it, but your definition of space is different so your definition of speed through space is different.

 

[martinbn]

Warp, you are confusing yourself. Shine light to the right and to the left. Each beam travels at speed c. What is the velocity (rate of change) of the separation of the fronts of the two beams? Let's calculate. After 1s, the right beam will be 300000km to your right, the left that much to your left. So the distance between the two has changed from 0 to 600000 in 1s, thus the speed is 2c.

 

[Battlemage!]

I don't go along with this business of 'ordinary language' being sterile whereas math has some 'rich underlying meaning'.

In reality, what that means is that physicists don't have a sufficiently eloquent grasp of language to enable them to translate their mathematical symbols into the appropriate and corresponding terminology. Which is not surprising as it's difficult to wield expertise in two disparate subjects.

At the end of the day every mathematical concept can be expressed linguistically, but not vice versa.

Even if you expressed an abstract mathematical concept linguistically, it could still be far beyond the ability for someone not mathematically inclined to grasp. They could recognize where the nouns and verbs are, but the idea being communicated in the words could still be inaccessible to them.

In fact, writing abstract mathematical ideas in words rather than math symbols would very likely make the concepts harder to understand, not easier.

Regardless, words won't help someone understand a concept they are unprepared to understand. This can be readily seen in the definition of a limit. When you PRECISELY describe it in words, using the epsilon-delta definition, the idea can be very difficult to grasp for someone not familiar with that sort of thing. But simply saying "some value this function approaches" is extremely imprecise. And then when you start making more abstract definitions that depend on previous ones things would get very confusing if written in everyday words. Regardless of the way they are written, if you don't have a good understanding of mathematics you aren't likely to grasp what you read.