Hijack from Jumping out of the black hole, What about the event horizon? From nowhere to everywhere.

[StringJunky]

4 hours ago, MigL said:

When people, or Physicists, speak of 'geometry' or 'fabric', are they referring to the model or the actual space-time ?

All we know is that a model, incorporating 'geometry', or curvature if you will, manages to very accurately predict what happens with test masses in actual space-time.
We have no idea whether the 'reality' of actual space-time, or its 'fabric', incorporates such curvature. But the mathematical model, which is GR, does utilize geometry, also mathematical, to make its extremely accurate predictions.

Are you maybe mistaking the model for any undelying rality, Lorentz Jr. ( which we may possibly never know ) ?

Is the curvedenature of spacetime just a mathematical abstraction that happens to model mathematically as a curve on paper, its actual manifestation is something competely different and not mirrored verbatim enough in our 'commonsense' view.

[Genady]

1 hour ago, StringJunky said:

Is the curvedenature of spacetime just a mathematical abstraction that happens to model mathematically as a curve on paper, its actual manifestation is something competely different and not mirrored verbatim enough in our 'commonsense' view.

Here is a guru's answer (Thorne, Kip. Black Holes & Time Warps: Einstein's Outrageous Legacy (pp. 400-401):

Quote

Isn’t it conceivable that spacetime is actually flat, but the clocks and rulers with which we measure it, and which we regard as perfect in the sense of Box 11.1, are actually rubbery? Might not even the most perfect of clocks slow down or speed up, and the most perfect of rulers shrink or expand, as we move them from point to point and change their orientations? Wouldn’t such distortions of our clocks and rulers make a truly flat spacetime appear to be curved? 

Yes. 

Figure 11.1 gives a concrete example: the measurement of circumferences and radii around a nonspinning black hole. On the left is shown an embedding diagram for the hole’s curved space. The space is curved in this diagram because we have chosen to define distances as though our rulers were not rubbery, as though they always hold their lengths fixed no matter where we place them and how we orient them. The rulers show the hole’s horizon to have a circumference of 100 kilometers A circle of twice this circumference, 200 kilometers, is drawn around the hole, and the radial distance from the horizon to that circle is measured with a perfect ruler; the result is 37 kilometers. If space were flat, that radial distance would have to be the radius of the outside circle, 200/π kilometers, minus the radius of the horizon, 100/π kilometers; that is, it would have to be 200/π – 100/π = 16 kilometers (approximately). To accommodate the radial distance’s far larger, 37-kilometer size, the surface must have the curved, trumpet-horn shape shown in the diagram.

If space is actually flat around the black hole, but our perfect rulers are rubbery and thereby fool us into thinking space is curved, then the true geometry of space must be as shown on the right in Figure 11.1, and the true distance between the horizon and the circle must be 16 kilometers, as demanded by the flat-geometry laws of Euclid. However, general relativity insists that our perfect rulers not measure this true distance. Take a ruler and lay it down circumferentially around the hole just outside the horizon (curved thick black strip with ruler markings in right part of Figure 11.1). When oriented circumferentially like this, it does measure correctly the true distance. Cut the ruler off at 37 kilometers length, as shown. It now encompasses 37 percent of the distance around the hole. Then turn the ruler so it is oriented radially (straight thick black strip with ruler markings in Figure 11.1). As it is turned, general relativity requires that it shrink. When pointed radially, its true length must have shrunk to 16 kilometers, so it will reach precisely from the horizon to the outer circle. However, the scale on its shrunken surface must claim that its length is still 37 kilometers, and therefore that the distance between horizon and circle is 37 kilometers. People like Einstein who are unaware of the ruler’s rubbery nature, and thus believe its inaccurate measurement, conclude that space is curved. However, people like you and me, who understand the rubberiness, know that the ruler has shrunk and that space is really flat. 

What could possibly make the ruler shrink, when its orientation changes? Gravity, of course. In the flat space of the right half of Figure 11.1 there resides a gravitational field that controls the sizes of fundamental particles, atomic nuclei, atoms, molecules, everything, and forces them all to shrink when laid out radially. The amount of shrinkage is great near a black hole, and smaller farther away, because the shrinkage-controlling gravitational field is generated by the hole, and its influence declines with distance. 
The shrinkage-controlling gravitational field has other effects. When a photon or any other particle flies past the hole, this field pulls on it and deflects its trajectory. The trajectory is bent around the hole; it is curved, as measured in the hole’s true, flat spacetime geometry. However, people like Einstein, who take seriously the measurements of their rubbery rulers and clocks, regard the photon as moving along a straight line through curved spacetime. 

What is the real, genuine truth? Is spacetime really flat, as the above paragraphs suggest, or is it really curved? To a physicist like me this is an uninteresting question because it has no physical consequences. Both viewpoints, curved spacetime and flat, give precisely the same predictions for any measurements performed with perfect rulers and clocks, and also (it turns out) the same predictions for any measurements performed with any kind of physical apparatus whatsoever. For example, both viewpoints agree that the radial distance between the horizon and the circle in Figure 11.1, as measured by a perfect ruler, is 37 kilometers. They disagree as to whether that measured distance is the “real” distance, but such a disagreement is a matter of philosophy, not physics. Since the two viewpoints agree on the results of all experiments, they are physically equivalent. Which viewpoint tells the “real truth” is irrelevant for experiments; it is a matter for philosophers to debate, not physicists. Moreover, physicists can and do use the two viewpoints interchangeably when trying to deduce the predictions of general relativity.

 

[StringJunky]

20 minutes ago, Genady said:

Here is a guru's answer (Thorne, Kip. Black Holes & Time Warps: Einstein's Outrageous Legacy (pp. 400-401):

 

Thanks. Is the problem of understanding spacetime curvature analogously similar to that of whether wave functions are considered real, rather than just an abstract means to describe the phenomonolgy presented to the observer in a shareable, consensus-built format?

Edited March 12, 2023 by StringJunky

[Genady]

16 minutes ago, StringJunky said:

Thanks. Is the problem of understanding spacetime curvature analogously similar to that of whether wave functions are considered real, rather than just an abstract means to describe the phenomonolgy presented to the observer in a shareable, consensus-built format?

Yes, they are similar, IMHO.

[MigL]

How would we know what the properties of space-time actually are ?
Is it flat, curved or inside-out ?
Remember, I'm in the camp that claims Physics does not tell us what 'reality is, only how it behaves ( see Physics and 'Reality' thread ).

All we can say for sure, is that the mathematical model, including geometric curvature, makes extremely accurate predictions about gravity, and how test masses behave when affected by it.

Anyone who claims to know more about the actual 'reality' is simply confused and deluding themselves.

[Markus Hanke]

16 hours ago, Lorentz Jr said:

The problem is when people deny that any mechanism ("fabric") exists or formulate principles (no preferred frame) that are incompatible with the existence of any mechanism.

Ok, but in order to discuss this we need to clarify just what “mechanism” actually means here, or else we won’t know whether or not anyone is denying its existence. So how do you define this term, exactly? 

16 hours ago, Lorentz Jr said:

I don't, and what I question is why you keep knocking down these straw men.

It isn’t a straw man, it was merely my interpretation of what it is you are trying to say, because that is not at all clear to me. Since I evidently missed the actual point you were trying to make, it would be helpful if you could summarise it clearly and concisely.

16 hours ago, Lorentz Jr said:

Boundary conditions are a mathematical concept, not a physical one.

They are a description of your physical scenario, and thus both mathematical and physical.

16 hours ago, Lorentz Jr said:

If two systems have different outcomes between the same two points in spacetime, there must have been some physical difference between their environments.

The physical difference is the path these clocks are taking. 

16 hours ago, Lorentz Jr said:

But at least it's scientifically valid.

I disagree. The ether you are referring to here is undetectable and has no physical consequences whatsoever. I might as well postulate an Invisible Pink Unicorn in my back garden, for all the difference it makes. It’s philosophically permissible precisely because it has no detectable consequences - but it’s not science, because it isn’t amenable to the scientific method. Besides, if you do this, you are going to have to explain a “mechanism” for why that ether has the properties it has, why it behaves the way it does, and where it came from - so in the end you haven’t actually explained anything, you have just kicked the can down the road.

16 hours ago, Lorentz Jr said:

physical mechanisms than appeals to boundary conditions and "paths through spacetime"

Again, I think you need to define for us exactly what you mean by “mechanism”.

 

[Lorentz Jr]

16 hours ago, Lorentz Jr said:

There's nothing wrong with shallow theories if there's no clear evidence for specific mechanisms. The problem is when people deny that any mechanism ("fabric") exists or formulate principles (no preferred frame) that are incompatible with the existence of any mechanism.

18 minutes ago, Markus Hanke said:

Ok, but in order to discuss this we need to clarify just what “mechanism” actually means here, or else we won’t know whether or not anyone is denying its existence. So how do you define this term, exactly? 

I don't think there's anything unusual about my use of the term. A mechanism is something that makes something happen. If someone says something "just happens", or "It's just a matter of geometry", they're denying the existence of a mechanism for whatever phenomenon they're discussing.

16 hours ago, Lorentz Jr said:

I hold people ... accountable for using the idea of "geometry" as a way to suggest that no mechanism is required [for relativistic phenomena]. They use it as a "magic wand" to create confusion between physical mechanisms and mathematical descriptions.

I'm not criticizing the theories, I'm criticizing people who interpret the theories in confusing or unscientific ways.

18 minutes ago, Markus Hanke said:

Since I evidently missed the actual point you were trying to make, it would be helpful if you could summarise it clearly and concisely.

I summarized it in three sentences, Markus. I don't think I can boil it down any more than that.

18 minutes ago, Markus Hanke said:

The physical difference is the path these clocks are taking. 

No, it's not physical. The "path" you're referring to is the path through Minkowski space, and Minkowski space is a mathematical abstraction, not real physical geometry. And there's nothing about the spaceship's real path through 3D space that explains time dilation.

16 hours ago, Lorentz Jr said:

Lorentz's ether interpretation says there's an ether with its own reference frame, and time dilation is caused by motion through that mediuim. Not that there aren't problems with that idea, like why is there no experimental evidence for what the preferred frame is? But at least it's scientifically valid. Trying to "explain" the frame-independent time dilation in the twin paradox through paths and boundary conditions is not.

18 minutes ago, Markus Hanke said:

I disagree. The ether you are referring to here is undetectable and has no physical consequences whatsoever.

You can't prove a negative, Markus. The ether hasn't been detected in the past, but that doesn't mean it can't possibly be detected in the future or that it doesn't exist.

It potentially provides a mechanism for time dilation, and no one in the early 21st century can say what other physical consequences it might have.

18 minutes ago, Markus Hanke said:

I might as well postulate an Invisible Pink Unicorn in my back garden, for all the difference it makes. It’s philosophically permissible precisely because it has no detectable consequences - but it’s not science

But there is  a consequence. The astronaut is younger than the twin who stayed on Earth. That's a real, physical, frame-invariant consequence. It's a consequence of something, and an ether is a reasonable candidate for that something. Boundary conditions and paths through abstract mathematical spaces are not.

18 minutes ago, Markus Hanke said:

if you do this, you are going to have to explain a “mechanism” for why that ether has the properties it has, why it behaves the way it does, and where it came from - so in the end you haven’t actually explained anything, you have just kicked the can down the road.

Nonsense, Markus. You're making excuses. An ether can potentially explain time dilation, and explaining the ether itself can be left for future generations. There's nothing unusual about "kicking the can down the road". All science works that way. The behavior of one turtle is explained in terms of the one holding it up, the behavior of the lower turtle is explained in terms of the next one down, and so on and so on and so on.

16 hours ago, Lorentz Jr said:

That's not unique to simulation theories. It's a fundamental question about reductionism. What are quarks and leptons made of? What are their constituents made of? Does the tower go down infinitely far, in which case even the smallest actions entail infinite amounts of information processing? Or is there a swamp of nondeterminism underneath it, in which case the universe is ultimately founded on magic? It's one of the questions I've given up on trying to answer, because I'm not sure it's possible to answer it.

[Eise]

19 minutes ago, Lorentz Jr said:

I don't think there's anything unusual about my use of the term. A mechanism is something that makes something happen.

Nope, not quite. A 'mechanism' supposes physical, causal relationships. that means this mechanism exists, and all observers agree on it, no matter in what coordinate system, moving or in a gravitational field, independent of direction or orientation etc etc. Of course one might have to do a few coordinate transformations, so that all observers agree on the mechanism. But what if the coordinate transformation explains the observations without any reference to physical, dynamic processes?

If I look at the top of a glass from an angle, I see an ellipse, instead of a circle. Must I now look for a 'mechanism', i.e. a dynamical law, that distorts the circle to an ellipse? Or does the geometrical explanation suffice?

Special and general relativity show that time dilation, length contraction etc, and gravity can be explained geometrically as coordinate transformations, assuming 4-dimensional (curved) spacetime. Under this assumption there is nothing left to explain dynamically. The geometric explanation works wonderful well, as e.g. also MigL notices:

9 hours ago, MigL said:

All we can say for sure, is that the mathematical model, including geometric curvature, makes extremely accurate predictions about gravity, and how test masses behave when affected by it.

If the geometric explanation works, why would we even need a 'mechanism'? 

I think I understand why you took 'Lorentz' as your nickname.

40 minutes ago, Lorentz Jr said:

(...) Minkowski space is a mathematical abstraction, not real physical geometry.

What is a 'real physical geometry'? Wouldn't that be the geometry that turns out to be the most useful, i.e. helps most to generalise basic laws of physics?

44 minutes ago, Lorentz Jr said:

You can't prove a negative

True. But it can turn out to be superfluous.

[Markus Hanke]

2 hours ago, Lorentz Jr said:

I don't think there's anything unusual about my use of the term. A mechanism is something that makes something happen.

So if I understand you right, you are looking for a mechanism in spacetime that somehow acts on a clock to make it go slower? If so, then we are not talking about the same thing, because I’m looking for a mechanism for spacetime, in the sense of some system of dynamics the classical limit of which can be written as a semi-Riemannian manifold endowed as with a connection and a metric (ie GR). SR’s Minkowski spacetime is then just the local limit of that.

2 hours ago, Lorentz Jr said:

The "path" you're referring to is the path through Minkowski space, and Minkowski space is a mathematical abstraction, not real physical geometry.

Euclidean geometry is also a mathematical abstraction - one that ignores time, and doesn’t gel very well at all with the Standard Model. Why is Euclidean geometry scientific and physical, but Minkowski geometry is not? So far as I am concerned, the idea of the world being Euclidean is pretty much explicitly ruled out by existing observational data.

2 hours ago, Lorentz Jr said:

You can't prove a negative, Markus. The ether hasn't been detected in the past, but that doesn't mean it can't possibly be detected in the future or that it doesn't exist.

Sure, but that’s just as true for my IPU (Invisible Pink Unicorn). The point is that we have no reason to think that either of these things exist, or even need to exist.

2 hours ago, Lorentz Jr said:

It potentially provides a mechanism for time dilation

My understanding of the ether in LET is that is has no physically detectable consequences, ie there is no experiment - local or global - that you can perform to detect the presence of this ether. This seems to imply to me that it cannot provide the mechanism you are looking for.

2 hours ago, Lorentz Jr said:

It's a consequence of something

No, I don’t think there needs to be any “something” at all, other than the choice of how those twin clocks move.

To give a Euclidean analogy - it’s like connecting the same two cities by a group of airplanes. Let everything be the exact same - departure time, type of plane, ground speed, weather conditions, cruising altitude, laws of aerodynamics etc etc - except the route they take. One of the planes flies along the shortest possible route (great circle segment), whereas the others choose different routes, no two of which shall coincide.

What is the mechanism that “makes” the total flight time different for each of these planes? Is there an ether that “drags” on those planes (without being detectable!), thus making them arrive later than the shortest-route flight? Why would you expect planes that fly along different routes to always take the same amount of time, in the first place?

The only physically relevant mechanism here is that we need to apply measurable acceleration at some point in order to not make all the flight path coincide - and once you do, the flight times must necessarily diverge. This is entirely irrespective of the kind of mathematical description you give this situation. 

2 hours ago, Lorentz Jr said:

Nonsense, Markus. You're making excuses. An ether can potentially explain time dilation

Actually, the point I was trying to make was simply that this idea postulates an unnecessary mechanism that then requires an entire set of new mechanism to make it work. 

[swansont]

2 hours ago, Lorentz Jr said:

No, it's not physical. The "path" you're referring to is the path through Minkowski space, and Minkowski space is a mathematical abstraction, not real physical geometry. And there's nothing about the spaceship's real path through 3D space that explains time dilation.

That’s because kinematic time dilation is not a result of the physical path. 

2 hours ago, Lorentz Jr said:

The ether hasn't been detected in the past, but that doesn't mean it can't possibly be detected in the future or that it doesn't exist.

It’s incumbent on the ones proposing an ether to do so. Until that happens, it’s provisional at best, and isn’t accepted until that experimental evidence exists. And one must acknowledge the experiments that have tried to detect an ether, and failed to do so.

[Lorentz Jr]

4 hours ago, Markus Hanke said:

My understanding of the ether in LET is that is has no physically detectable consequences, ie there is no experiment - local or global - that you can perform to detect the presence of this ether. This seems to imply to me that it cannot provide the mechanism you are looking for.

According to LET, no experiment can detect the ether's state of motion. That doesn't mean it's not there, any more than the fact that you don't know how to open the hood (bonnet) of your car means there's not an engine inside it. The fact that the car moves with no external propulsion implies that it must have an engine, and the fact that the astronaut is younger than his twin when he returns to Earth implies that something slowed down the time evolution of the astronaut's wave function.

4 hours ago, Markus Hanke said:

What is the mechanism that “makes” the total flight time different for each of these planes?

Air drag. There's a limit to how fast the planes can fly, so, if we assume they all fly at the same speed, which is physically reasonable if they have similar capabilities, then the ones taking less direct routes have to plow through larger quantities of air.

 

6 hours ago, Eise said:

If I look at the top of a glass from an angle, I see an ellipse, instead of a circle.

That's not a real effect. It's frame-dependent. The age difference in the twin paradox is the same to all observers.

6 hours ago, Eise said:

I think I understand why you took 'Lorentz' as your nickname.

🙂

 

4 hours ago, swansont said:

It’s incumbent on the ones proposing an ether to [detect it]. Until that happens, it’s provisional at best

That's why I don't insist that the ether exists. An alternative explanation is that the entire universe is some kind of simulation. As I said earlier, the speed of light as an absolute speed limit is suggestive of a CPU processing speed.

My only requirement is that real physical effects have real physical causes, and changing reference frames to analyze a problem (e.g. when the spaceship turns around) isn't a real physical cause.

Edited March 13, 2023 by Lorentz Jr

[Eise]

32 minutes ago, Lorentz Jr said:

That's not a real effect. It's frame-dependent. The age difference in the twin paradox is the same to all observers.

I think all observers agree that the circumference of my ellipse is smaller than the circumference of the circle. I know, it is an analogy, and maybe it does not apply exactly, but it looks quite similar to me: following 'the path' of the circle, it is longer than 'the path' of the ellipse. In the twin paradox the paths through spacetime differ, and with that their lengths.

[Lorentz Jr]

18 minutes ago, Eise said:

I think all observers agree that the circumference of my ellipse is smaller than the circumference of the circle.

No. To an observer viewing the glass from directly above, the rim is a circle and there is no ellipse. Observers will agree on the geometry of light rays reaching your eyes and creating elliptical images on your retinas, but that's not the rim of the glass itself or the surface of any liquid inside the glass. It's just your perception.

Edited March 13, 2023 by Lorentz Jr

[swansont]

6 hours ago, Lorentz Jr said:

According to LET, no experiment can detect the ether's state of motion.

Then how could it affect anything, like a clock?

6 hours ago, Lorentz Jr said:

My only requirement is that real physical effects have real physical causes, and changing reference frames to analyze a problem (e.g. when the spaceship turns around) isn't a real physical cause.

Time is a physical thing?

[Lorentz Jr]

9 hours ago, Lorentz Jr said:

According to LET, no experiment can detect the ether's state of motion.

2 hours ago, swansont said:

Then how could it affect anything, like a clock?

The effect is indistinguishable from the rules of SR. That's all the distinction means. It's not even absolute. It just means the ether's state of motion hasn't been detected yet, and it doesn't have to be detected for the ether to exist.

I'm not going to deny that this is a bit of a stretch. An invisible ether sounds like IPUs or monsters under the bed. Although apparently the observed combination of time dilation and length contraction minimizes some relevant action, so maybe that could explain why they're so closely coordinated. The ether is just an attempt to make sense of frame-independent time dilation, because none of the answers from SR make sense to me.

9 hours ago, Lorentz Jr said:

My only requirement is that real physical effects have real physical causes, and changing reference frames to analyze a problem (e.g. when the spaceship turns around) isn't a real physical cause.

2 hours ago, swansont said:

Time is a physical thing?

Quantum wave functions represent real physical phenomena, and their time evolution is a physical process. LET and SR were developed before QM, so I tack that on as a sort of "neo-LET". I do believe there's such a thing as universal time, and I think it's required in LET for time dilation to be a real effect. As for what time itself ultimately is, as I mentioned earlier, that may be too hard of a question for science to answer. I leave it as a question for the Creator and limit myself to thinking about physical processes.

Edited March 13, 2023 by Lorentz Jr

[swansont]

1 hour ago, Lorentz Jr said:

Quantum wave functions represent real physical phenomena, and their time evolution is a physical process. LET and SR were developed before QM, so I tack that on as a sort of "neo-LET".

The phrase “Jack and Jill went up the hill” represents a real physical process, but is not actually a physical process.

 

1 hour ago, Lorentz Jr said:

I do believe there's such a thing as universal time, and I think it's required in LET for time dilation to be a real effect.

What you believe is immaterial. In science it’s what you can show.

 

1 hour ago, Lorentz Jr said:

As for what time itself ultimately is, as I mentioned earlier, that may be too hard of a question for science to answer. I leave it as a question for the Creator and limit myself to thinking about physical processes.

You say (in reference to time dilation) “real physical effects have real physical causes” but then refuse to back this up by explaining anything about this alleged physical process

You keep referring to an ether theory, but “don't insist that the ether exists”

You say time dilation is an effect on clocks, but then…nothing.

We have rules about soapboxing and arguing in good faith. If you can’t comply, then stop making the claims.

 

[Lorentz Jr]

1 hour ago, swansont said:

The phrase “Jack and Jill went up the hill” represents a real physical process

Except in nonrealist interpretations of quantum mechanics, where Jack and Jill don't actually go up the hill, they just have an increasing probability of being detected there! 😄

You get today's award for worst analogy, swanson. Congratulations. 🙂

1 hour ago, swansont said:

You say (in reference to time dilation) “real physical effects have real physical causes” but then refuse to back this up by explaining anything about this alleged physical process

So what? I don't have to know how the engine in my car works to know that it's there and it propels the car.

1 hour ago, swansont said:

You keep referring to an ether theory, but “don't insist that the ether exists”

So what? We don't have to know things exist to speculate about them.

1 hour ago, swansont said:

You say time dilation is an effect on clocks, but then…nothing.

Because we haven't finished with the first step yet. The next step is just Control Theory 101: You can't drive your car without turning the key in the ignition and operating the pedals and the shift lever and the steering wheel. You need to interact with your car in an absolute sense, not just wave your car keys in the air relative to the ignition switch or wiggle your toes near the gas pedal. An ether can affect a moving object, and the object can control the ether through its absolute motion. Not relative motion. Only absolute motion can have a real physical effect.

1 hour ago, swansont said:

We have rules about soapboxing and arguing in good faith.

All I'm doing is answering your questions, swanson. If you don't want me to soapbox, please stop provoking arguments with me with your false analogies and pointless comments. As for not arguing in good faith, you still haven't answered my question about your claim that "time moves at a slower pace in some reference frames". All you did was lecture me about derivations, cite generalities, refer to some "straw man" that I "fabricated" without specifying what it was, and ask some irrelevant question about "time" without specifying what you meant by it or what your question had to do with our discussion: 

On 3/12/2023 at 2:19 PM, swansont said:

I urge you to look at the derivation of time dilation. Without that as a common base, there is no discussion. And it just leaves you criticizing a theory you aren’t familiar with. I also note that you haven’t defended your claims at all, but expect me to defend a strawman of your fabrication. Which law of physics requires time to be the same in all frames?

Edited March 14, 2023 by Lorentz Jr

[Markus Hanke]

16 hours ago, Lorentz Jr said:

According to LET, no experiment can detect the ether's state of motion.

That means it cannot be the cause of the twin’s dilated proper time.

16 hours ago, Lorentz Jr said:

Air drag. There's a limit to how fast the planes can fly, so, if we assume they all fly at the same speed, which is physically reasonable if they have similar capabilities, then the ones taking less direct routes have to plow through larger quantities of air.

I stated in my analogy that they all fly at the same ground speed at all times - there is no difference in velocities-over-ground between these planes, nor is there any other physical difference between them. Thus air drag obviously isn’t the reason why they take differing amounts of time to reach their destination (you could perform the same experiment in vacuum, using rockets instead, with the same outcome) - the reason is that they take different routes, and thus have different distances (at the same ground speed) to travel. Therefore their flight times must necessarily differ. In that sense, the choice of route has causal efficacy so far as the total accumulated flight time is concerned, all other variables being equal.

The exact same principle holds in SR/GR as well, it’s just you’re now considering a path that goes through space and time, while holding the norm of your velocity 4-vectors equal. So the choice of path through spacetime has causal efficacy so far as total proper time is concerned, since all other physical parameters remain exactly equal between the twins, so only the distance through spacetime can differ. And that’s by definition precisely the total time physically accumulated on that clock.

[Lorentz Jr]

1 hour ago, Markus Hanke said:

you’re now considering a path that goes through space and time

How do you measure the length of the path?

In real space it's the number of meter sticks, laid end-to-end along the path, that are required to connect the two endpoints. What is the equivalent operation in Minkowski space?

Edited March 14, 2023 by Lorentz Jr

[Eise]

19 hours ago, Lorentz Jr said:

No. To an observer viewing the glass from directly above, the rim is a circle and there is no ellipse. Observers will agree on the geometry of light rays reaching your eyes and creating elliptical images on your retinas, but that's not the rim of the glass itself or the surface of any liquid inside the glass.

Yep. And in the twin 'paradox' all observers agree on the spacetime distance in Minkowskian spacetime.

20 hours ago, Lorentz Jr said:

Air drag. There's a limit to how fast the planes can fly, so, if we assume they all fly at the same speed, which is physically reasonable if they have similar capabilities, then the ones taking less direct routes have to plow through larger quantities of air.

This interpretation of Markus' example lets me doubt your sincerity. 

14 hours ago, swansont said:

My only requirement is that real physical effects have real physical causes, and changing reference frames to analyze a problem (e.g. when the spaceship turns around) isn't a real physical cause.

You are confused about causation. Without diving too deep, causation implies:

• the cause precedes its effect
• cause and effect are located closely to another

The first is a criterion in time, the second in space. You cannot apply 'causation' to time and space themselves. 

3 hours ago, Lorentz Jr said:

What is the equivalent operation in Minkowski space?

Proper time?

[Markus Hanke]

3 hours ago, Lorentz Jr said:

How do you measure the length of the path?

With your clock. That’s just the point - the entire geometry is such that the geometric length of a path between two events equals the accumulated time physically recorded on a clock that travels on that path (remember that’s a path through spacetime, not just space), so there is a very direct link between the theoretical formalism, and what physically happens. Once we adopt the empirical finding that c=invariant for all observers, and hold start and end points fixed, then the operation of varying the path leaves you with only one degree of freedom - its length, which is the total accumulated clock time. That’s how the times between the twins differ - they logically can’t be the same, unless either the paths coincide, or c is not an invariant. The former case is trivial, and the latter is so highly constrained by observational data as to be practically ruled out within the domain of our experimental capabilities.

[Lorentz Jr]

2 hours ago, Markus Hanke said:

there is a very direct link between the theoretical formalism, and what physically happens.

There's a direct link between the theoretical formalism and the elapsed time. So what? That's the thing we're trying to explain. You said something about "causal efficacy", but things can't cause themselves, so that was nonsense. Your earlier point about detecting the ether's motion is also nonsense, because that's not the same thing as having an effect. It was established way back in Einstein and Lorentz's time that, for whatever reason, time dilation and length contraction are coordinated in such a way that they have the same effect regardless of the ether's velocity. As for proving the ether's existence, I've tried to explain that time dilation is evidence of something that causes time dilation, and an ether is one conceivable explanation but not the only one.

So the relativistic argument seems to be that spacetime and real space are equally valid because they're both "models". But real space is simple, intuitive, and easy to explain. One can think of it as a network of little cells (Roger Penrose has called it a "spin network"), so proximity could be implemented as connections between cells, and distance along a path could be the number of cells on the path. And those cells could potentially be related to quantum-mechanical phenomena.

What is the equivalent structure for spacetime? What underlying physics could it possibly represent? Why should people accept the apparently ridiculous proposition that a structure combining such obviously different phenomena as duration and extent can be anything more than a mathematical convenience?

The final justification for relativity so far seems to be, not that spacetime provides a physical explanation for time dilation, but that theories in general don't have to provide explanations, because they're "just models". Which to me seems like blurring the distinction between science and religion.

Maybe this would be a good place to end the thread. I'm not sure I can stand reading these excuses anymore without getting uncivil.

Edited March 14, 2023 by Lorentz Jr

[swansont]

 

11 hours ago, Lorentz Jr said:

So what? I don't have to know how the engine in my car works to know that it's there and it propels the car.

An engine propelling a car isn’t a proposition that’s contrary to accepted science.

 

11 hours ago, Lorentz Jr said:

So what? We don't have to know things exist to speculate about them.

At SFN there are requirements for such speculation.

 

11 hours ago, Lorentz Jr said:

Because we haven't finished with the first step yet. The next step is just Control Theory 101: You can't drive your car without turning the key in the ignition and operating the pedals and the shift lever and the steering wheel. You need to interact with your car in an absolute sense, not just wave your car keys in the air relative to the ignition switch or wiggle your toes near the gas pedal. An ether can affect a moving object, and the object can control the ether through its absolute motion. Not relative motion. Only absolute motion can have a real physical effect.

Another unsupported claim.

11 hours ago, Lorentz Jr said:

All I'm doing is answering your questions, swanson. If you don't want me to soapbox, please stop provoking arguments with me with your false analogies and pointless comments.

You made the claim before I called you out on providing support for it. (An application of causality here - the cause must precede the result)

 

11 hours ago, Lorentz Jr said:

As for not arguing in good faith, you still haven't answered my question about your claim that "time moves at a slower pace in some reference frames". All you did was lecture me about derivations, cite generalities, refer to some "straw man" that I "fabricated" without specifying what it was, and ask some irrelevant question about "time" without specifying what you meant by it or what your question had to do with our discussion: 

“My” claim is that of mainstream physics, and you appear to be familiar with the existence of time dilation. I pointed you to the derivation, because that’s the evidence that supports my claim. So yes, as far as the existing evidence goes, I did answer your question.

Your position here is in stark contrast to your other posts where you imply that you know what you’re talking about.

56 minutes ago, Lorentz Jr said:

As for proving the ether's existence, I've tried to explain that time dilation is evidence of something that causes time dilation, and an ether is one conceivable explanation but not the only one.

But it’s not, because you can arrive at the result without assuming an ether. 

[Eise]

2 hours ago, Lorentz Jr said:

Maybe this would be a good place to end the thread. I'm not sure I can stand reading these excuses anymore without getting uncivil.

Why would you get uncivil? Give the arguments. I think we are all civil here, aren't we? 

I am especially curious why you think it needs 'a real physical effect', i.e. imply that there must be a causal explanation. I notice sometimes people are disappointed when I explain e.g. time dilation: people miss a 'mechanism'. This is the same problem Lorentz and Poincaré had, if I understand history correctly: Lorentz e.g. hypothesised that the ether is expressing a pressure on objects moving in it (that would be a 'dynamical solution', and I suppose what you call  'a real physical effect'); Poincaré never got rid of the idea that there must be a preferred inertial frame, like the ether, but there is no method to find out with any physics experiment. But long since then, the physics community opted for Einsteinian relativity. It explains all relativity effects without reference to an ether. Ockham's razor at work: when the ether does not contribute anything to an explanation, we can drop it.

Edited March 14, 2023 by Eise

[Markus Hanke]

16 hours ago, Lorentz Jr said:

(Roger Penrose has called it a "spin network")

Spin networks are mathematical objects that are now used to construct certain classes of models of quantum gravity, such as LQG for example. The classical limit of such models must always be SR/GR. Right at the beginning of this thread I mentioned once or twice that it is just this - a model for the emergence of classical spacetime from quantum gravity - which I consider to be the “mechanism” for all relativistic effects. So it appears we have come full circle.

Why you brought an ether into all this is strange to me - it has no explanatory power or utility, because its presence or absence has no physical consequences whatsoever. It cannot provide the mechanism you are looking for, which is why it never became part of established physics (as Eise has explained). This entire discussion has already been had a century ago.

16 hours ago, Lorentz Jr said:

You said something about "causal efficacy", but things can't cause themselves, so that was nonsense. Your earlier point about detecting the ether's motion is also nonsense, because that's not the same thing as having an effect.

I wish you would refrain from misrepresenting what I actually said, in the context of when I said it. So far as I am concerned, you have, over the time you have been here, made very valuable contributions to the forum across many different threads and discussions - but this here, I’m sorry to say, is really beneath you. Disappointing 😕