Black holes

[DeiRenDopa]

A couple of posts by Farsight, with responses to mine have appeared in this thread today*. I'll get to them later.

For now, just this, which will begin to get at Farsight's apparent misunderstanding of GR (well, one of them):

I think you need to go read a good textbook on relativity, Farsight. The only way you can tell if a 'clock runs slower' is by comparing it with another clock in the same reference frame!

Let's see now. I can see my clock, and I can see my other clock. One's lower than the other, and it's running slower, just like Einstein said. Then I can open up my clocks and see them in action. I can see the cogs whirring, or the crystals oscillating, or using my gedeanken microscope I can the electrons flipping or the electromagnetic waves propagating. And in the lower clock I can see all those things moving slower than the upper. But then you lean over my shoulder and say No Farsight, they're moving at the same speed, they're just in different reference frames. What reference frames? Two little rectangles, one around each clock? And then you say you need to read the good book, Farsight. The last time I heard stuff like that was when I was having a dingdong with the YECs.

Let's start, Farsight, by going diving. We will carry with us a pressure gauge, and the water we will dive in has a nice, vertical ruler, marked in meters, with zero being the water's surface.

We will also carry with us a nice, miniature, (physical) chemistry lab. As we descend, we keep a record of the pressure gauge readings, the depth (per the ruler), and the results of experiments we do with our lab, concerning pressure-sensitive reactions (including phase changes); our lab is a pretty snazzy one in that it does an excellent job of holding other physical conditions (such as temperature) constant. We take with us a team of observers, equipped with appropriate recording devices, so there is an objective, independently verifiable, record of our experimental results.

What we find is not all that surprising, and may be summarized by saying that depth correlates with pressure, and the various parameters of our chemistry experiments do too.

As we live in the far future, we are able to repeat this set of experiments in many bodies of water, at different locations on Earth, and on other bodies in our solar system.

With me so far? Any questions or comments?

For our next series of experiments, we travel the world with a gravitometer, an altimeter, and our usual cast of observers. We keep a very careful record of the output of the gravitometer. In one set of experiments, we climb, with our instruments, up a tall, strong, low-mass tower.

Again, this being the far future, we are able to repeat our experiments on, and above, the surfaces of many solar system bodies.

What we find is also not very surprising, and may be summarized by saying that the local g correlates with altitude (or, as you like to say, elevation) on any particular solar system body, and with the estimated mass of that body.

With me so far? Any questions or comments?

For the next set of experiments we carry with us a standard clock, a standard ruler (i.e. devices which measure time and length, per the SI definitions), and a parallel-mirror light clock. We also have pressure gauges, temperature gauges, gravitometers, ... This time we have some friends along, each of whom has their own clock, and each clock is of a different kind; one has a grandfather clock, another a quartz crystal clock, a third an optical clock, a ... Oh, and our usual retinue of observers.

We visit all the places we went to on our 'gravitometer tour'.

This time we find something strange and wonderful (or not): at each location, all the clocks tell the same time (within their error bars/uncertainties)!

With me so far? Any questions or comments?

This being the very far future, we repeat all our experiments, in environments considerably more extreme than any we'd visited previously, like near the photosphere of the Sun, in deep space, just above the surface of a white dwarf star, ditto of a neutron star.

Do any of our findings (experimental results) change?

Once you've had a chance to comment, I'll continue.

* YMMV, depends where in the world you are ...

 

[DeiRenDopa]

Oh, one more thing we need to agree on: how to measure the speed of light.

Can you please describe how we can do this, using devices/equipment/techniques/etc which incorporate - at whatever critical point necessary - the definitions of the second and the meter?

 

[Brian-M]

The rate at which light moves. It moves at the speed that it does. We use that to define the second and the metre and then we label that speed 299,792,458 m/s.

That's funny, I thought we were defining the second by how long it takes a microwave signal tuned to the resonant frequency of cesium to oscillate 9,9,192,631,770 times, not on the speed of light.


(And then we take the distance that a photon can travel in a vacuum during that time, and label that distance 299,792,458 meters.)

And those clocks don't actually measure time. There is no time flowing through those clocks. Can you see it whooshing through? No. What they actually do is clock up some form of regular motion, and display a cumulative total that you call the time.

You keep going on about not being able to literally see time flowing through clocks. So what? You can't see time any more than you can see gravity. But I don't hear you complaining that there's no gravity flowing through gravimeters, so that gravimeters don't actually measure gravity. Or that a gravimeter simply compares the difference between the strain on it's internal components from it's "zero" setting to display a value of acceleration we call gravity.

In a gravitational field the speed of light demonstrably varies. So the impedance of space must be varying too.

Since the impedance of space is defined as the product of the speed of light and vacuum permeability, you're saying that the vacuum permeability of space is higher in regions of higher gravity?

This apparent change in the speed of light in would also be explained if time passed more slowly in regions of higher gravity.

But there's no reason to guess. If you're right, we should be able to measure a difference in vacuum permeability in regions of different gravity. If you're wrong, we should be able to measure a difference in the passage of time in regions of different gravity.

ETA: Of course, a change in the speed of light would also result in a change in the impedance of space, but I'm assuming you're not arguing that C has changed because of a change in impedance due to the change in C.

 

[ctamblyn]

(...snip...)
In a gravitational field the speed of light demonstrably varies. So the impedance of space must be varying too. It isn't constant either.
(...snip...)

You are using "the speed of light" in two different senses above, and you have commited an equivocation fallacy of sorts.

The Shapiro delay experiment is a non-local measurement which measures the time taken for light to get from one point to another, distant point and back again. This is not the value which is denoted by the symbol "c" in the formula Z₀ = μ₀c for the vacuum impedance.

In any freely-falling laboratory small enough that tidal forces are irrelevant, light always goes at the same speed. It this universal constant which "c" denotes in that formula.

Of course, even if c did vary from point to point your argument above would be a non-sequitur. The value of c by itself is insufficient to determine Z₀; you must also specify how μ₀ changes from place to place. Obviously it is constant in standard classical physics, but since you have already claimed that other fundamental constants vary, perhaps you should be clear on your position with regard to μ₀.

Nevertheless, let's suppose you manage to cook up a vacuum in which the speed of light truly varies; suppose that light is refracted in some manner as it moves through space. Theories of gravitation based on a scalar (in your case, c) that varies through space are not mathematically equivalent to GR. Therefore, if there is nothing else to your model, whatever you are discussing here is not GR and you at least have to show that it is equivalent as far as experimental observations go. Look up "scalar theories of gravitation" to get an idea of what problems you will need to overcome.

The closest thing I've found to a decent attempt at what you're proposing is the "polarisable vacuum" model of Puthoff. His model of gravitation, based on a varying ε₀ and μ₀, matches the predictions of GR in some areas (redshift, light deflection, precession of the perihelion of planetary orbits) but not in others (particularly those relating to gravitational radiation and frame-dragging).

I'll quickly mention one more problem with this whole idea. You have placed a lot of emphasis on vacuum impedance, as though it could be an explanation for gravitational time dilation and the like. However, not all phenomena are electromagnetic in nature. Even if you did have a model in which the vacuum impedance varies from point to point, somehow reducing the speed of photons passing through that space, how does that affect weak and strong nuclear interactions? In detail, I mean, rather than just vaguely alluding to electroweak unification (which would not help you with strong interactions, anyway).

 

[Brian-M]

Really? Because there are lots of things which do. If I point a flashlight at the moon and pass my hand across it quickly, the shadow of my hand on the moon will travel across the moon faster than c.

Your shadow across the moon can carry information, such as shape and direction.

But what is a shadow? It's a perceived shape, an illusion. The shadow is no more moving across the surface of the moon than a televised object is really moving across your TV screen. The shadow may look like it's moving, that's simply an artifact of human perception.

All that's really happening is that light from the torch is lighting up different areas of the moon in sequence (the exact sequence being determined by the passage of your hand) in the same way that a televised image lights up different areas of the screen in sequence to create the illusion of movement.

Basically, you're only creating the illusion of faster than light lateral movement on the moon when in reality no lateral movement on the moon is occurring. You could get the same effect by pointing a laser at the moon and waving it around. Sure, it appears the dot is moving faster than light, but in reality the light from the laser is simply lighting up different areas of the moon in sequence, creating the illusion of movement.

 

[Ziggurat]

Your shadow across the moon can carry information, such as shape and direction.

No. Information travels from my hand to the moon at light speed. No information travels across the moon as the shadow moves faster than c.

Basically, you're only creating the illusion of faster than light lateral movement on the moon when in reality no lateral movement on the moon is occurring.

Nonsense. Something is quite definitely moving, and it's moving faster than c. That's not an illusion. It's not the same sort of motion as an object (which can carry information) moving, but it's still real.

You could get the same effect by pointing a laser at the moon and waving it around.

Yes, you could.

Sure, it appears the dot is moving faster than light

"appears"? No, it would move faster than c. There's no "appears" involved.

but in reality the light from the laser is simply lighting up different areas of the moon in sequence, creating the illusion of movement.

That's not an illusion, unless you mistake the light spot itself for something it isn't.

But let's recall the context in which this came up. If I accelerate, and I choose to adopt the accelerating reference frame, then distant objects will immediately respond to my acceleration. That "effect" traveled faster than c. Farsight thought that this would be a problem that would invalidate my position. But no information was carried. This is no more problematic than a shadow (or a laser spot) moving across the moon at faster than c.

 

[Reality Check]

No, but we're talking GR here, and that hard scientific evidence is backed up by what Einstein said, see this post of mine on a previous thread.

You have not cited any "hard scientific evidence" other than the references to the effects predicted by GR .
this post of yours is a list of quotes from Einstein before the publication of GR in 1917. No surprising physics in what he states.


A bit of sceintific woo from you though " My particular position with GR is Einstein's position: that the speed of light varies and space is inhomogeneous":

1. Einstein's position in the quotes is that the speed of light varies
   It is unclear whether he is talking about proper or coordinate speed from your quotations but othe rposters point out that itis coordinate speed.
2. "space is inhomogeneous" is nonsense.

No. GR as taught today is no longer in line with Einstein's GR.

That statement is foolish on a couple of levels.
Firstly who cares about "Einstein's GR"?
What matters is GR. That is the scientific theory. You seem to want people to ignore almost 100 years of progress in science just to obsess on the original presentation of GR by Einstein.

Secondly: GR as taught today is exactly in line with Einstein's GR with the obvious exception of the use of a non-zero cosmological constant. The mathematics is the same aside from notational differences. The predictions from GR are the same.

 

[Brian-M]

No. Information travels from my hand to the moon at light speed. No information travels across the moon as the shadow moves faster than c.

Nonsense. Something is quite definitely moving, and it's moving faster than c. That's not an illusion. It's not the same sort of motion as an object (which can carry information) moving, but it's still real.

WHAT is moving across the surface of the moon?

Shadows are illusions, an absence given the illusion of form by illumination of the surrounding area. All you're seeing is light reflecting off the moon.

So when you say something is definitely moving, what is it that you think is moving across the surface?

All that's happening is that patterns of light are moving from your torch to the moon and bouncing off the moon again. Nothing is actually moving across the surface of the moon. The fact that some patterns make it appear as something is moving across the surface is only because the image-recognition portion of your brain interprets it as movement. It's an illusion, nothing more.

If anything detectable could actually travel faster than C, then it must also be able to carry information faster than C, because the fact that the observer can detect it conveys the information that it's there.

(And if something that's not detectable could actually travel faster than C, you'd never know because you can't detect it.)

That's not an illusion, unless you mistake the light spot itself for something it isn't.

Such as mistaking it for an actual spot or light source on the moon rather than simply a reflection of the laser at your location.

A laser doesn't really make a spot on the object it's pointed at^*, that's also an illusion. The "spot" that appears to exist on the object is really on the lens of the laser. When you wave the laser around, you're just seeing the light from the laser reflecting off different areas of the object. Nothing is moving across the object.

* Unless the object is photosensitive, or the laser is powerful enough to burn an actual spot into the object.

But let's recall the context in which this came up. If I accelerate, and I choose to adopt the accelerating reference frame, then distant objects will immediately respond to my acceleration. That "effect" traveled faster than c. Farsight thought that this would be a problem that would invalidate my position. But no information was carried. This is no more problematic than a shadow (or a laser spot) moving across the moon at faster than c.

I'd contend that the change in the distant objects is also an illusion. The distant objects haven't changed in the slightest, it's you that's changed, and as a consequence of this you now perceive and interact with the light, gravity, etc, from these objects in a different manner.

It's still the same information as to distance, speed, etc, that traveled to your position at light speed, just viewed in a different context.

They've always been the way you perceive them after you accelerate, and still are the way you perceived them them before you accelerated. The only thing that has changed is you, and the reference frame by which you measure the rest of the universe.

 

[Farsight]

You confirmed pretty much what I suspected; it seems you don't really understand how the cesium fountain clock works, in terms of determining, as a standard, one second, do you?

Yes I do.

I'll guess that you have no problem with "maximizes their [the cesium atoms'] fluorescence", but you do seem to have difficulty with "a microwave frequency is found", as in "the microwave signal in the cavity is tuned to different frequencies".

I don't have any difficulty with it at all. I explained how it's like you twiddling the knob on your radio.

So let's start with this: what do you think a "microwave cavity" is? And how do you think you "tune" the microwave signal in such a cavity to different frequencies? To quote you, "this one is hugely important".

No it isn't. Everybody knows what a microwave cavity is, you've got one in your kitchen. Don't waste my time with evasion, go and look at what the NIST clock actually does, and go and think through the issue of finding a frequency when you're defining the second. It's a counting exercise, not some clever circular magic.

Um, you do realize, don't you, that the ideas you express, in your posts in the threads in this part of JREF (at least the ones I'm actively participating in, on GR) are at considerable variance to standard, textbook GR?

Yes. Those textbooks are wrong in some respects. Have a read of the Golden age of general relativity and note the "paradigm shifts". I'm shifting them back to Einstein's original. Hacking through the thicket to the sleeping beauty and all that.

That being so, if you wish others to understand you - and that's why, or one important reason why, you post here, right?

I tend to post here to correct some of the pseudoscience bandied about. There's a degree of "Emperors New Clothes" to it, wherein there's no supporting evidence, and if anybody probes deeper they essentially get told you don't understand the maths dear boy. I started posting on this thread because sol was trotting out the waterfall analogy, which paints a picture of a black hole as an object surrounding by inward moving space, flowing like some aether. As it happens Max Tegmark appeared in a Horizon program in front of a waterfall promoting this analogy.

then those who seek to understand you need to be confident your understanding of key terms you use is the same as their own, right?

No. You need to be confident that the scientific evidence I present is correct, and then you should be confident in your own ability to think for yourself and follow the reasoning I offer. If you find an issue we'll discuss it, but don't be some textbook groupie who dismisses evidence because it doesn't match what he's had drummed into him.

From our exchanges so far I've learned that you have some very different understandings of key terms and concepts than what I find in standard textbooks. To be sure I do not misunderstand you, I will - often - ask you to define key terms, in your own words. If you reply by pointing to definitions that are standard (or nearly so as never mind), I can be confident of at least that commonality in our mutual understanding.

I don't mind putting some time into this, but if it turns into evasion and distraction on your part, forget it.

Now that I know - with some degree of certainty - what you mean by "the parallel-mirror light clock", I can proceed to try to understand other things you've posted.

You shouldn't have needed any explanation from me about the paralel-mirror light clock.

Well, on this we may have to agree to disagree.

OK.

Some philosophers may care, and to the extent to which a nice mental picture may help some physicists develop new tests, models, hypotheses, etc, they may too.

No problem.

But if the word pictures all produce the same results - in terms of quantitative matches between theory and experiment - they're equivalent, right?

No. Have a read of The Other Meaning of Special Relativity by Robert Close. The maths is the same and the quantitative predictions are the same. But the different interpretation delivers understanding that directs endeavour and facilitates scientific progress.

 

[DeiRenDopa]

Three posts in this thread by you now Farsight, responding to mine, that I will get to in due course.

Just so you - and other readers - know, that'll be after you've responded to my two most recent, #381 and #382.

 

[Farsight]

Really? Because there are lots of things which do. If I point a flashlight at the moon and pass my hand across it quickly, the shadow of my hand on the moon will travel across the moon faster than c. Pick the right medium, and you can also get a phase velocity for light which is faster than c. Plenty of things travel faster than c. But none of them carry information. That's all we need to preserve causality.

Yeah yeah, and a mexican wave can travel faster than c too, see this physicsworld article on pulsars. A shadow isn't some thing, it's just an absence of light. Information isn't some thing, it's just some pattern in things that we deem to be information. Light is the thing, it moves, and causality is preserved becase negative motion does not exist.

That doesn't mean it's not real. The relativity of velocity is just an observer effect too, under this logic. Yet if I'm on a train and you're on the ground, you really are moving. It's not an illusion, unless all motion is an illusion.

Motion is relative. In the end it's relative to the expanding universe. Now there's a thing. That's the thing we're trying to understand. And in some respects the early universe can be likened to a black hole, so it's important that we understand the latter correctly.

ETA:

That's easy: accelerate towards the lower clock from above.

OK, I can see you accelerating towards the lower clock. And whaddyaknow, it's now ticking faster than the upper clock! Magic! You starting moving towards it and it started ticking faster just like that! Come on zig, get real. That clock didn't change at all, now did it? You changed. Your motion affected your observations, not the clock.

 

[Farsight]

Let's start, Farsight, by going diving. We will carry with us a pressure gauge, and the water we will dive in has a nice, vertical ruler, marked in meters, with zero being the water's surface.

No problem.

We will also carry with us a nice, miniature, (physical) chemistry lab. As we descend, we keep a record of the pressure gauge readings, the depth (per the ruler), and the results of experiments we do with our lab, concerning pressure-sensitive reactions (including phase changes); our lab is a pretty snazzy one in that it does an excellent job of holding other physical conditions (such as temperature) constant. We take with us a team of observers, equipped with appropriate recording devices, so there is an objective, independently verifiable, record of our experimental results.

Good. I like hard scientific evidence.

What we find is not all that surprising, and may be summarized by saying that depth correlates with pressure, and the various parameters of our chemistry experiments do too.

Uh huh.

As we live in the far future, we are able to repeat this set of experiments in many bodies of water, at different locations on Earth, and on other bodies in our solar system. With me so far? Any questions or comments?

I'm with you. No problems.

For our next series of experiments, we travel the world with a gravitometer, an altimeter, and our usual cast of observers. We keep a very careful record of the output of the gravitometer. In one set of experiments, we climb, with our instruments, up a tall, strong, low-mass tower.

OK.

Again, this being the far future, we are able to repeat our experiments on, and above, the surfaces of many solar system bodies.

Again, no problem. We're all happy with gedankenexperiments.

What we find is also not very surprising, and may be summarized by saying that the local g correlates with altitude (or, as you like to say, elevation) on any particular solar system body, and with the estimated mass of that body. With me so far? Any questions or comments?

I'm with you. No questions.

For the next set of experiments we carry with us a standard clock, a standard ruler (i.e. devices which measure time and length, per the SI definitions), and a parallel-mirror light clock. We also have pressure gauges, temperature gauges, gravitometers, ... This time we have some friends along, each of whom has their own clock, and each clock is of a different kind; one has a grandfather clock, another a quartz crystal clock, a third an optical clock, a ... Oh, and our usual retinue of observers.

OK.

We visit all the places we went to on our 'gravitometer tour'. This time we find something strange and wonderful (or not): at each location, all the clocks tell the same time (within their error bars/uncertainties)! With me so far? Any questions or comments?

I'm with you. No questions. But do note that all those clocks feature some kind of regular cyclical motion which they accumulate and display. This display might be a counter in say YYYYMMDD HHMMSS base form, or as moving metal pointers on a clock face.

This being the very far future, we repeat all our experiments, in environments considerably more extreme than any we'd visited previously, like near the photosphere of the Sun, in deep space, just above the surface of a white dwarf star, ditto of a neutron star.

No problem.

Do any of our findings (experimental results) change? Once you've had a chance to comment, I'll continue.

Yes. We find that our clock readings change subtlely with elevation. We cannot detect this by comparing one of the clocks we're carrying with another of the clocks we're carrying, because all local clocks are similarly affected. Instead we detect it using a distant pulsar. In addition our measurement of the fine structure constant changes with elevation. This is no surprise, because we know already that it is a "running" constant.

 

[Farsight]

Oh, one more thing we need to agree on: how to measure the speed of light. Can you please describe how we can do this, using devices/equipment/techniques/etc which incorporate - at whatever critical point necessary - the definitions of the second and the meter?

We measure the speed of light with light and mirrors, like Fizeau did. We already know something about relativity, so we constrain our measurements to horizontal measurements to avoid radial length contraction and keep our experiment simple. However we are not so stupid as to use our parallel-mirror light clock to time the back-and-forth travel time. Or our atomic clock, because that employs the electromagnetic hyperfine transition and microwaves. Or the optical clock which employs UV light. Or the quartz wristwatch, because that's electromagnetic like light. Or the mechanical clock, because that's made of electrons and protons etc, which have an electromagnetic nature. We time it using the distant pulsar.

 

[ben m]

Yes. We find that our clock readings change subtlely with elevation. We cannot detect this by comparing one of the clocks we're carrying with another of the clocks we're carrying, because all local clocks are similarly affected.

Amazing! Not only "all local clocks" but all local physics experiments whatsoever. Why, it's almost as there were some "law of relativity", in which the laws of physics do not care what time-coordinates the observer has chosen to use!

Instead we detect it using a distant pulsar.

.... But I, Farsight, will designate the correct coordinates anyway! Just for the heck of it! Using a mythical pulsar, at Absolute Rest, in Flat Space at Zero Gravitational Potential. Heck, let's put it at the Geometric Center of the Universe, and we'll have it spinning Right-Side Up.

 

[DeiRenDopa]

Oh, one more thing we need to agree on: how to measure the speed of light. Can you please describe how we can do this, using devices/equipment/techniques/etc which incorporate - at whatever critical point necessary - the definitions of the second and the meter?

We measure the speed of light with light and mirrors, like Fizeau did.

As far as I know, Fizeau used several different experimental setups, each with light and mirrors.

And we need to be pretty specific, I think, so would you mind spelling out the actual setup you recommend, in more detail?

We already know something about relativity, so we constrain our measurements to horizontal measurements to avoid radial length contraction and keep our experiment simple.

OK, but as we will be doing our experiments in many different environments, including in deep space, we need a way to establish what "horizontal" is; how do you recommend we do that?

However we are not so stupid as to use our parallel-mirror light clock to time the back-and-forth travel time. Or our atomic clock, because that employs the electromagnetic hyperfine transition and microwaves. Or the optical clock which employs UV light. Or the quartz wristwatch, because that's electromagnetic like light. Or the mechanical clock, because that's made of electrons and protons etc, which have an electromagnetic nature. We time it using the distant pulsar.

We may have a problem here Houston.

Or not; can you explain how we "time it [the back-and-forth travel time, in some Fizeau-like set-up] using the distant pulsar"?

 

[Farsight]

That's funny, I thought we were defining the second by how long it takes a microwave signal tuned to the resonant frequency of cesium to oscillate 9,9,192,631,770 times, not on the speed of light.

It's like you're sitting in a boat with water waves coming at you. Up down, up down, you count the oscillations. When you get to 9,192,631,770 you say that's a second. Then you say that the frequency of those waves was 9,192,631,770 Hertz.

(And then we take the distance that a photon can travel in a vacuum during that time, and label that distance 299,792,458 meters.)

Yes. If the light is going at speed X the second has a value Y. If light is going at half X the second has value 2Y. And so on. Regardless of how fast the light is moving, you use it and the second you defined using it, to define the metre. So the metre is always the same.

You keep going on about not being able to literally see time flowing through clocks. So what? You can't see time any more than you can see gravity. But I don't hear you complaining that there's no gravity flowing through gravimeters, so that gravimeters don't actually measure gravity. Or that a gravimeter simply compares the difference between the strain on it's internal components from it's "zero" setting to display a value of acceleration we call gravity.

We can open up those clocks and see things moving inside them, be they cogs or crystals or other things. We can also see things fall down instead of staying put. When that happens, we label it "gravity", and everybody here is happy with that, including me.

Since the impedance of space is defined as the product of the speed of light and vacuum permeability, you're saying that the vacuum permeability of space is higher in regions of higher gravity?

Not quite. I'm saying vacuum impedance changes with gravitational potential. It's higher where gravitational potential is lower. The "force" of gravity depends on the local slope in gravitational potential.

This apparent change in the speed of light in would also be explained if time passed more slowly in regions of higher gravity.

That's how it is explained. And it's wrong. You can see light moving. But you can't see time passing.

But there's no reason to guess. If you're right, we should be able to measure a difference in vacuum permeability in regions of different gravity. If you're wrong, we should be able to measure a difference in the passage of time in regions of different gravity.

Vacuum impedance is a combination of vacuum permittivity and permeability. Light is considered to be a transverse wave. In mechanics a transverse or shear wave travels at a speed determined by the stiffness and density of the medium: v = √(G/ρ). The G is the shear modulus of elasticity, and the ρ is the density. In electrodynamics the c = √(1/ε₀μ₀) expression is somewhat similar. Permittivity is like the reciprocal of density and permeability is like the modulus of elasticity. (ETA: duh, try the other way around). They combine together as impedance. Note there's an element of circularity in the definitions, and that they're "defined" to be constant like the speed of light is.

ETA: Of course, a change in the speed of light would also result in a change in the impedance of space, but I'm assuming you're not arguing that C has changed because of a change in impedance due to the change in C.

No. I'm saying a concentration of energy, usually in the form of matter like a star, alters the surrounding space imparting a gradient in its vacuum impedance. Einstein used the phrase "conditions the surrounding space" or words to that effect.

Sorry, I have to go.

 

[DeiRenDopa]

No problem.

Good. I like hard scientific evidence.

Uh huh.

I'm with you. No problems.

OK.

Again, no problem. We're all happy with gedankenexperiments.

I'm with you. No questions.

OK.

We visit all the places we went to on our 'gravitometer tour'. This time we find something strange and wonderful (or not): at each location, all the clocks tell the same time (within their error bars/uncertainties)! With me so far? Any questions or comments?

I'm with you. No questions. But do note that all those clocks feature some kind of regular cyclical motion which they accumulate and display. This display might be a counter in say YYYYMMDD HHMMSS base form, or as moving metal pointers on a clock face.

Yes, we do need something like that.

Oh, and by "gravitometer" I meant gravimeter (just in case any reader was confused).

No problem.

Do any of our findings (experimental results) change? Once you've had a chance to comment, I'll continue.

Yes. We find that our clock readings change subtlely with elevation. We cannot detect this by comparing one of the clocks we're carrying with another of the clocks we're carrying, because all local clocks are similarly affected. Instead we detect it using a distant pulsar.

Indeed.

And it's this sort of thing I'm keen to get to, in the next round of experiments.

And that next round will begin once we have agreed on how to measure the speed of light (because we're already on the same page otherwise).

In addition our measurement of the fine structure constant changes with elevation. This is no surprise, because we know already that it is a "running" constant.

Hmm, maybe.

In any case, let's put that off for a while, and focus on getting the basics agreed - and done - first.

 

[DeiRenDopa]

Here's the next round of experiments I'd like to propose.

It's really just a modification of the first sets ...

Let's start, Farsight, by going diving. We will carry with us a pressure gauge, and the water we will dive in has a nice, vertical ruler, marked in meters, with zero being the water's surface.

We will also carry with us a nice, miniature, (physical) chemistry lab. As we descend, we keep a record of the pressure gauge readings, the depth (per the ruler), and the results of experiments we do with our lab, concerning pressure-sensitive reactions (including phase changes); our lab is a pretty snazzy one in that it does an excellent job of holding other physical conditions (such as temperature) constant. We take with us a team of observers, equipped with appropriate recording devices, so there is an objective, independently verifiable, record of our experimental results.

What we find is not all that surprising, and may be summarized by saying that depth correlates with pressure, and the various parameters of our chemistry experiments do too.

As we live in the far future, we are able to repeat this set of experiments in many bodies of water, at different locations on Earth, and on other bodies in our solar system.

In this round, our aim is to develop a model. We want the model to be able to 'explain' (I'll explain in a minute) all our detailed, objective, independently verifiable, quantitative results.

To do this we may need to have along with us quite a bit more equipment than just the pressure gauge, ruler, and miniature chemistry set; for example, our chemistry set may need to be able to give us a detailed analysis of the water, we will certainly need to have a thermometer, we may need to have a gravimeter along with us, and so on.

A simplified approach may be to build our own tank - one which keeps its contents at a constant temperature - fill it with pure water, and do our diving in that. We take our tank to all sorts of interesting (and not so interesting) places ...

While our model may refer to theories of physics or chemistry which have sweeping domains of applicability, our aim is more modest: the model simply needs to account for all the experimental results in terms of inputs such as depth (as measured by our ruler); it may be nothing more than a small set of relatively simple functions derived from statistical fits to the data (i.e. formulae). Of course, our model will explicitly state its formal uncertainties.

OK?

For our next series of experiments, we travel the world with a gravitometer, an altimeter, and our usual cast of observers. We keep a very careful record of the output of the gravitometer. In one set of experiments, we climb, with our instruments, up a tall, strong, low-mass tower.

Again, this being the far future, we are able to repeat our experiments on, and above, the surfaces of many solar system bodies.

What we find is also not very surprising, and may be summarized by saying that the local g correlates with altitude (or, as you like to say, elevation) on any particular solar system body, and with the estimated mass of that body.

Here too this round of experiments aims to produce a model with the same sort of explanatory power. And again we may need to have a few more pieces of equipment along with us.

OK?

For the next set of experiments we carry with us a standard clock, a standard ruler (i.e. devices which measure time and length, per the SI definitions), and a parallel-mirror light clock. We also have pressure gauges, temperature gauges, gravitometers, ... This time we have some friends along, each of whom has their own clock, and each clock is of a different kind; one has a grandfather clock, another a quartz crystal clock, a third an optical clock, a ... Oh, and our usual retinue of observers.

We visit all the places we went to on our 'gravitometer tour'.

This time we find something strange and wonderful (or not): at each location, all the clocks tell the same time (within their error bars/uncertainties)!

Since the outcome of this experiment was so simple, there's no need to do a more elaborate version, in this round.

This being the very far future, we repeat all our experiments, in environments considerably more extreme than any we'd visited previously, like near the photosphere of the Sun, in deep space, just above the surface of a white dwarf star, ditto of a neutron star.

Do any of our findings (experimental results) change?

Once you've had a chance to comment, I'll continue.

Ditto.

 

[DeiRenDopa]

Addressing the first of Farsight's responses (one's I've been putting off).

Electrons move by doing a spin-flip. This emits electromagnetic waves, which move away.

The context here is important. Here it is:

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
F: The optical clock uses aluminium rather than caesium, and a UV frequency rather than a microwave frequency, but it works along the same lines, and employs electromagnetic phenomena. When these move at a lower rate,

DRD: When what moves? The optical clocks? The electromagnetic phenomena? A UV frequency?

And what does "at a lower rate" mean?

F: Electrons move by doing a spin-flip. This emits electromagnetic waves, which move away. It means when they move slower.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

So, re-writing F's original sentence with these clarifications, and adding back the full context (I've had to do some paraphrasing):

F: The optical clock uses aluminium rather than caesium, and a UV frequency rather than a microwave frequency, but it works along the same lines, and employs electromagnetic phenomena. When electrons move by doing a spin-flip, they emit electromagnetic waves, which move away more slowly from an optical clock at an elevation of a foot (or so) above an otherwise identical optical clock.

Right?

I kinda wondered if this gross misunderstanding was at the root of your assertion ("It's based on the hard scientific evidence that the speed of light varies with gravitational potential" - the "it" is not important here), now you've confirmed my suspicion, thanks.

It's no gross misunderstanding. The evidence for it is right there under your nose.

Well, we'll see (that's partly what my Gedankenexperiments are intended to shine light on, so to speak).

And so for the rest of this post by Farsight.

 

[Ziggurat]

Motion is relative.

Not according to you.

That clock didn't change at all, now did it? You changed. Your motion affected your observations, not the clock.

Suppose that we start out standing next to each other. Apparently you believe that if I start moving and you remain stationary, and I only perceive that you are moving, even though you are not in fact moving. Thus your motion is not relative to mine: you really are stationary, and I'm wrong to believe that you are now moving. Your motion is absolute, according to your own reasoning.

You are simultaneously grasping onto and rejecting central aspects not just of general and special relativity, but even Galilean relativity.