Time and relativity (split from The Nature of Time)

[Markus Hanke]

15 hours ago, DanMP said:

It is different.

No. It’s not. You are asking about relativistic motion through a gravity well other than the Earth’s, and electromagnetic radiation propagating to/from Venus, Mercury, as well as various probes we have sent out, provides a perfect example for that.

[DanMP]

5 hours ago, Markus Hanke said:

No. It’s not. You are asking about relativistic motion through a gravity well other than the Earth’s, and electromagnetic radiation propagating to/from Venus, Mercury, ...

No, I'm asking about the effect (if any) of the motion of a gravity well on a clock co-travelling with that gravity well.

 

17 hours ago, zapatos said:

What is it about the difference that makes the moon a better platform than a satellite?

It is not about better or worse, it is about doing something that we don't.

 

17 hours ago, swansont said:

18 hours ago, DanMP said:

Did you make GR calculations, as you should, or you just applied Special Relativity? 

How is this an answer to my question: The moon is moving relative to us. How does kinematic time dilation not occur?

Your statement sounds like: "I can see the Sun rotating every day around the Earth, how can you say that it is not rotating?". Without GR calculations and/or experimental test you are just hand waving. And please stop comparing apples and oranges, GPS satellites around the Earth are not on another massive object, nor orbiting it.

 

18 hours ago, swansont said:

Relativity is well-tested. We’re past the point of having the necessary confidence that it’s valid within the levels of precision we’ve tested. Confident that gravity behaves the same on the moon as on earth (which we’ve tested in a number of ways)

Of course, "gravity behaves the same on the moon as on earth", but, again, this is not what I want to investigate. I'm interested about the effect (if any) of the motion of a gravity well on/to a clock co-travelling with that gravity well.

 

18 hours ago, swansont said:

18 hours ago, DanMP said:

Also, the Earth is moving relative to the Moon, so according to the Moon observer the clock on Earth should be slower.

That symmetry only applies to inertial frames of reference.

Moon's frame is less inertial than Earth's frame? Why?

You said "The moon is moving relative to us. How does kinematic time dilation not occur?". Why someone on the Moon cannot say "The Earth is moving relative to me. How does kinematic time dilation not occur?"?

 

18 hours ago, swansont said:

No, I don’t think it would necessarily be cheap. Hafele-Keating was cheap because the incremental cost was plane tickets; they already had the clocks. What you’re proposing needs space-qualified clocks, which are generally not sitting around, and more expensive. And the cost of launching payloads is significantly higher than getting on a plane.

What do you mean by "space-qualified clocks"? Why not any atomic clock?

Yes, the cost of launching payloads is significantly higher than getting on a plane, but much lower than sending a mission with the sole purpose of doing my GR test, or the cost of building and running the Large Hadron Collider. You consider General Relativity less important than quantum physics, or quantum physics not enough tested/validated?

 

18 hours ago, studiot said:

I don't know the exact speed of light in Earth's frame ?

What rubbish are you trying to blow to obscure ....

I didn't say anything about the speed of light. Read again.

Rubbish you say. Ok, let's try again:

You stated:

On 1/6/2023 at 5:00 PM, studiot said:

So what is a line spectrum from Sol and Sirius if it is not a comparison to two clocks in different widely separated gravity wells ?

"two clocks" really? Where are the two clocks situated? How do you know their exact altitude in order to calculate gravitational time dilation? How do you know their exact speed in order to calculate kinematic time dilation?

And you are throwing it like this is already done. Offer a link or something.

What is the accuracy of such a method, based on spectrum lines? If you get a spectrum from the Moon surface, you can calculate (using GR - time dilation) the speed of the Moon around the Earth? To what degree of confidence? It was done?

 

16 hours ago, Ghideon said:

This may be of interest to @DanMP; testing GR in the context of solar gravity by using a Viking spacecraft that landed on Mars. 

Thank you, it is interesting, but not what I proposed (see above), nor contested in any way.

[joigus]

On 12/27/2022 at 4:44 PM, MigL said:

It isn't the 'ultimate theory, but it is the one best supported by observational evidence.
Do I need to go through the 100 years of evidence accumulated in support of GR ?

Theories don't explain why, they explain how.
And IIRC, your 'theory' did neither, other than conjecture, and had no supporting observational evidence.

Exactly. It's always a why from a how, or a how from a further how. And an initial how --what to assume-- is always susceptible of a further why.

That's why there's always a how in the last analysis. How about that?

[studiot]

5 minutes ago, DanMP said:

"two clocks" really? Where are the two clocks situated? How do you know their exact altitude in order to calculate gravitational time dilation? How do you know their exact speed in order to calculate kinematic time dilation?

And you are throwing it like this is already done. Offer a link or something.

What is the accuracy of such a method, based on spectrum lines? If you get a spectrum from the Moon surface, you can calculate (using GR - time dilation) the speed of the Moon around the Earth? To what degree of confidence? It was done?

I don't think you want to understand my points since your rendering is so far from what I actually said so how can I help you understand.

Your questions have very little to do with what I said.

The only question I can answer is I have said more than once there is light from Sol and light from Sirius.

Any source of light can be used as a clock in many different ways.

So we have two clocks, one on Sol and one on Sirius.

Since we can observe both clocks we can compare the two.

 

[swansont]

8 hours ago, DanMP said:

What do you mean by "space-qualified clocks"? Why not any atomic clock?

Clocks (and other hardware) that go to space must be able to withstand the vibrations and acceleration associated with launch, being in vacuum, temperature range/cycling, and the radiation they will be subjected to in space. (plus more) Not commercial off-the-shelf electronics.

One example

https://en.m.wikipedia.org/wiki/MIL-STD-883

 

8 hours ago, DanMP said:

Yes, the cost of launching payloads is significantly higher than getting on a plane, but much lower than sending a mission with the sole purpose of doing my GR test, or the cost of building and running the Large Hadron Collider. You consider General Relativity less important than quantum physics, or quantum physics not enough tested/validated?

Since electronics depends on QM being correct, we are already implicitly assuming that QM is correct if we send missions anywhere. But you aren’t suggesting that QM is in question on the moon, and needs to be tested.

 

[DanMP]

54 minutes ago, studiot said:

So we have two clocks, one on Sol and one on Sirius.

You are joking me right? The spectrum collected from one star is not from one atom! There are many many atoms/clocks, not all at the same altitude and with the same velocity. Now you get it?

Even if you can somehow deal with that, the problem is: what accuracy you can get, using spectrum lines and GR, regarding the speed of the star as a whole?

And again, it was done? How the speed of the star matched the speed determined using other methods? By the way, how did we know the speed of the star? And what frame of reference was used?

7 minutes ago, swansont said:

1 hour ago, DanMP said:

Yes, the cost of launching payloads is significantly higher than getting on a plane, but much lower than sending a mission with the sole purpose of doing my GR test, or the cost of building and running the Large Hadron Collider. You consider General Relativity less important than quantum physics, or quantum physics not enough tested/validated?

Since electronics depends on QM correct, we are already implicitly assuming that QM is correct if we send missions anywhere. But you aren’t suggesting that QM is in question on the moon, and needs to be tested.

You didn't understand, again. You said/implied that GR needs no more testing. I said that QM is still tested, with high costs, even it was validated time and time again. Why investing (big money) in QM tests is ok, but in GR tests is not?

[swansont]

42 minutes ago, DanMP said:

You didn't understand, again. You said/implied that GR needs no more testing.

No, I said you can’t justify spending money on an experiment without some expectation of a novel result. If you can test to a higher level of precision, that’s uncharted territory. Deviations from theory could be detected.

The moon does not represent a range of speed or gravitational potential that hasn’t been tested.

 

42 minutes ago, DanMP said:

I said that QM is still tested, with high costs, even it was validated time and time again. Why investing (big money) in QM tests is ok, but in GR tests is not?

What experiments with high costs, that are testing some data range that’s already been investigated, can you name?

[DanMP]

44 minutes ago, swansont said:

If you can test to a higher level of precision, that’s uncharted territory. Deviations from theory could be detected.

It's not about the level of precision. It is just a new scenario, not tested, not "charted". And we don't (as far as I know) really calculated, using GR, the outcome. Even that may offer surprising results, because what your "intuition" told you may be invalidated by proper calculations.

 

49 minutes ago, swansont said:

What experiments with high costs, that are testing some data range that’s already been investigated, can you name?

It is not about some data range, it is about not giving up testing QM although it was proven right time and time again.

[studiot]

3 hours ago, DanMP said:

You are joking me right? The spectrum collected from one star is not from one atom! There are many many atoms/clocks, not all at the same altitude and with the same velocity. Now you get it?

Even if you can somehow deal with that, the problem is: what accuracy you can get, using spectrum lines and GR, regarding the speed of the star as a whole?

And again, it was done? How the speed of the star matched the speed determined using other methods? By the way, how did we know the speed of the star? And what frame of reference was used?

Apart from the insulting remark at the beginning, this is a perfect example of you choosing to argue with things I did not say, rather than ask for clarification about what I did say if you didn't understand it.

I said nothing whatsoever about any velocities or atoms.

In fact velocity doesn't appear explicitly in GR in the way it does in SR.

Not in fact does it care whether atoms exist or matter appears in some other form.

 

I have already explained the how and why effect on GR on the observed frequency of light and given you a reference to a NASA artcle on the subject.

Since and I have observed that frequency measurement can be used to measure time, though I did not explicitly say say how it is simply because frequency is the reciprocal of time. I actually credited you with the intelligence to understand this without baby steps.

Argument from incredulity is unbecoming from someone who claims to know more than the experts. (I am not an expert in this, I follow them, I don't preach to them)

So here is, plain as a pikestaff, what I am talking about

 

 

It can be clearly seen that lambda emitted is not the same as lambda observed.

I suggest a good place to go and study such things would be

An Introduction to Galaxies and Cosmology

Jones and Lambourne

Cambridge University Press

You will find plenty of formulae, derivations, explanations and examples such as the one in the attachment.

Edited January 10, 2023 by studiot

[swansont]

58 minutes ago, DanMP said:

It's not about the level of precision. It is just a new scenario, not tested, not "charted". And we don't (as far as I know) really calculated, using GR, the outcome. Even that may offer surprising results, because what your "intuition" told you may be invalidated by proper calculations.

 

It is not about some data range, it is about not giving up testing QM although it was proven right time and time again.

But it is about the data range. When you see experimental GR or QM results reported, it’s invariably because the new results cover that new ground.

As far as the “proper” calculation goes, you are free to do it.

[zapatos]

5 hours ago, DanMP said:

It is not about better or worse, it is about doing something that we don't.

 

So if we do the test on a small satellite, that should be followed by a test on a medium satellite? Then a large satellite? Then a satellite by a different manufacturer? Then a satellite launched next year instead of this year? There are an infinite number things that are different from what we are doing now. If you want someone to do something different you need to provide a reason for doing so that is more robust than "doing something that we don't."

[Markus Hanke]

18 hours ago, DanMP said:

No, I'm asking about the effect (if any) of the motion of a gravity well on a clock co-travelling with that gravity well.

Motion with respect to what, exactly? 

Motion is not an intrinsic feature of a physical system, it’s simply a relationship to some external point of reference. As such, the local geometry of spacetime around an isolated gravitational source does not depend on whether that source happens to be moving with respect to some external reference point, unless this source is itself embedded in a region of curved spacetime (eg a binary system of some sort). 

As I’ve said before, in binary systems you cannot neatly separate the effects of the two bodies, because their gravity combines in highly non-linear ways. 

14 hours ago, DanMP said:

And we don't (as far as I know) really calculated, using GR, the outcome.

Of course we have. If you combine ordinary Schwarzschild geometry with relative motion, you get the Aichlburg-Sexl ultraboost. This is the same geometry as Schwarzschild, but expressed in different coordinates to reflect relative motion.

If you want to see the effects of a binary system, then this can also be done, but only numerically on a computer (it’s too complicated to write down and solve on a piece of paper). 

[DanMP]

19 hours ago, studiot said:

... frequency measurement can be used to measure time, though I did not explicitly say say how it is simply because frequency is the reciprocal of time. I actually credited you with the intelligence to understand this without baby steps.

Now you are insulting me. And this is the second time (remember rubbish).

You are also wrong. I knew that "frequency is the reciprocal of time" from the beginning, that's why I asked:

On 1/9/2023 at 4:46 PM, DanMP said:

What 2 clocks? The lines in the spectrum are not from individual emitters. You don't know the exact position (altitude) in order to calculate gravitational time dilation. You don't know the exact speed in order to calculate the kinematic time dilation. And what accuracy you can get using this approach? What speed, perpendicular on the line between us and Sirius, was detected using this method that you claim it covered the test I proposed? And what other metod was used to determine that speed, in order to say that GR predicted the exact same speed?

 

19 hours ago, studiot said:

I said nothing whatsoever about any velocities or atoms.

In fact velocity doesn't appear explicitly in GR in the way it does in SR.

Your spectral lines are shifted for both gravitational reasons (as you said) and kinematic reasons (see here: Relativistic Doppler effect and Transverse Doppler effect).

And the spectra you get are coming from individual atoms, with different speeds and positions. The fact that you didn't say anything about their velocities and altitude doesn't mean that they are not important. Ok, you may work with average velocities and average altitude, but this is an approximation, not at all like in the Moon-Earth experiment I'm proposing. I asked you about accuracy and you never answered.

 

19 hours ago, swansont said:

But it is about the data range. When you see experimental GR or QM results reported, it’s invariably because the new results cover that new ground.

In the experiment I'm proposing is just a different scenario: 2 clocks on 2 different massive objects, not about a new level of accuracy, since there is no "first/older" level/range in this particular scenario.

 

18 hours ago, zapatos said:

So if we do the test on a small satellite, that should be followed by a test on a medium satellite? Then a large satellite? Then a satellite by a different manufacturer? Then a satellite launched next year instead of this year? There are an infinite number things that are different from what we are doing now.

An artificial satellite is not a massive object. The Moon is. That's the big difference.

 

5 hours ago, Markus Hanke said:

Motion with respect to what, exactly? 

Motion is not an intrinsic feature of a physical system, it’s simply a relationship to some external point of reference. As such, the local geometry of spacetime around an isolated gravitational source does not depend on whether that source happens to be moving with respect to some external reference point, unless this source is itself embedded in a region of curved spacetime (eg a binary system of some sort). 

Both Moon and Earth observer are seeing the other moving. Swansont said: "The moon is moving relative to us. How does kinematic time dilation not occur?". I responded that someone on the Moon can say "The Earth is moving relative to me. How does kinematic time dilation not occur?". Obviously, if there is any kinematic effect, it should be agreed by both.

5 hours ago, Markus Hanke said:

Of course we have. If you combine ordinary Schwarzschild geometry with relative motion, you get the Aichlburg-Sexl ultraboost. This is the same geometry as Schwarzschild, but expressed in different coordinates to reflect relative motion.

If you want to see the effects of a binary system, then this can also be done, but only numerically on a computer (it’s too complicated to write down and solve on a piece of paper). 

So you know if there is (should be) any kinematic effect in this particular scenario? Consider the clocks on the ground, at one pole (in order to be locally static).

[swansont]

53 minutes ago, DanMP said:

In the experiment I'm proposing is just a different scenario: 2 clocks on 2 different massive objects, not about a new level of accuracy, since there is no "first/older" level/range in this particular scenario.

Yes, it’s just a different scenario, but this range has been tested. Slower and faster speeds, and deeper and shallower locations in a gravitational potential. No new physics is proposed that this would reveal, and no new limits are going to be tested. No compelling reason to spend from a limited budget since that could mean some other science would not take place.

 

[zapatos]

2 hours ago, DanMP said:

An artificial satellite is not a massive object. The Moon is. That's the big difference.

 

I don't mean to be picky, but you seem to be all over the place. When I asked you what the difference was earlier you said:

On 1/10/2023 at 6:56 AM, DanMP said:

...it is about doing something that we don't.

Now that I've suggested an infinite number of different scenarios you claim it is because the moon has mass..

 

2 hours ago, DanMP said:

An artificial satellite is not a massive object. The Moon is. That's the big difference.

But an artificial satellite DOES have mass. So again, why choose the moon over the satellite?

Edited January 11, 2023 by zapatos

[studiot]

http://gamelab.mit.edu/games/a-slower-speed-of-light/

 

Have fun folks

[DanMP]

3 minutes ago, zapatos said:

But an artificial satellite DOES have mass. So again, why choose the moon over the satellite?

By massive object I mean a star, a planet or a moon.

The reason: because it was not done and it may be interesting.

 

1 hour ago, swansont said:

Yes, it’s just a different scenario, but ...

 

Ok, I get it, you don't find it interesting enough. No problem.

[studiot]

1 hour ago, DanMP said:

By massive object I mean a star, a planet or a moon.

And just who are you to use abnormal definitions of scientific terms.

The term massive refers to those bodies which possess the property of mass and distinguishes it from those that do not.

[zapatos]

1 hour ago, studiot said:

http://gamelab.mit.edu/games/a-slower-speed-of-light/

 

Have fun folks

That looks pretty cool!!!

[Markus Hanke]

16 hours ago, DanMP said:

So you know if there is (should be) any kinematic effect in this particular scenario? Consider the clocks on the ground, at one pole (in order to be locally static).

I’m still not sure what you are actually suggesting. Do you mean you want to have two clocks, one stationary on the moon and one stationary on the Earth, and then compare them?

If so, then yes, you’d get a gravitational and a kinematic component to the total time dilation - though the kinematic contribution will be very small. This is in no way different from the GPS receiver in your car - the software installed on it will correct for both the gravitational as well as kinematic time dilation between yourself and the satellite. If it didn’t, your position would be off by a whopping 10km per day!

Honestly, I don’t see the point in all this? We have known these principles for a long time, and are using them every day in some commonly available technologies. There’s no mystery in it. Why would you expect things to be any different on the moon, as opposed to a satellite? It’s not like either gravity or motion function any differently there than they do here. There’s nothing wrong in principle with performing such an experiment, but I don’t think anyone will throw loads of money at this, since we have no reason whatsoever to expect that anything special would happen. If there was some physical difference between gravity on Earth and elsewhere in the solar system, then we’d have already noticed this in other ways.

[DanMP]

8 hours ago, Markus Hanke said:

I’m still not sure what you are actually suggesting. Do you mean you want to have two clocks, one stationary on the moon and one stationary on the Earth, and then compare them?

Yes, two clocks, one stationary on the Moon and one stationary on the Earth. How many times I need to repeat this? 😄

 

8 hours ago, Markus Hanke said:

If so, then yes, you’d get a gravitational and a kinematic component to the total time dilation - though the kinematic contribution will be very small.

Did you make (or read) proper GR calculations, or you are just guessing?

What reference frame was used and why?

 

8 hours ago, Markus Hanke said:

Why would you expect things to be any different on the moon, as opposed to a satellite? It’s not like either gravity or motion function any differently there than they do here.

With one clock on the Moon surface and the other on a Moon artificial satellite, yes, things would be exactly as expected. No reason to be different.

The test with one clock on the Moon surface and the other on the Earth surface was never done, nor any similar, so you don't really know the outcome. It is a dangerous thing, both in physics and in life, to be sure that you know something, when in fact you never really checked it.

 

8 hours ago, Markus Hanke said:

If there was some physical difference between gravity on Earth and elsewhere in the solar system, then we’d have already noticed this in other ways.

Gravity is not different, that's not the issue, we simply have not enough/accurate information about "kinematic time dilation" caused by the movement of a planet/star/moon. If you do have such information, please share it here.

 

8 hours ago, Markus Hanke said:

There’s nothing wrong in principle with performing such an experiment, but I don’t think anyone will throw loads of money at this, since we have no reason whatsoever to expect that anything special would happen.

Loads of money? Tiny, compared to LHC, JWST, or gravitational-wave detectors.

So you don't expect that anything special would happen. I hope you are aware that a theory must pass any kind of test related to it. This kind of test (able to check with accuracy the "kinematic time dilation" caused by the movement of a planet/star/moon in relation with another planet/star/moon) is highly related to GR and never performed. If the test is not passed, GR would have to be adjusted or abandoned. You are denying that?

[swansont]

40 minutes ago, DanMP said:

Did you make (or read) proper GR calculations, or you are just guessing?

Did you? One can’t help but notice you haven’t provided any calculations in support of your proposal.

43 minutes ago, DanMP said:

So you don't expect that anything special would happen. I hope you are aware that a theory must pass any kind of test related to it. This kind of test (able to check with accuracy the "kinematic time dilation" caused by the movement of a planet/star/moon in relation with another planet/star/moon) is highly related to GR and never performed.

Must pass all tests, yes. Must conduct all tests, no.

As Markus has already noted, there are other ways to test GR, and we would have noticed issues.

 

43 minutes ago, DanMP said:

If the test is not passed, GR would have to be adjusted or abandoned. You are denying that?

Nobody has denied this, or even hinted at it.

[Markus Hanke]

15 hours ago, DanMP said:

Did you make (or read) proper GR calculations, or you are just guessing?

Calculating the total time dilation when there is a combination of differences in gravitational potential, as well as relative motion, is a standard exercise that’s done in most undergrad courses on GR. It’s not that hard so long as you can use the Schwarzschild metric, which is highly symmetric. Usually it’s done in the context of GPS satellites, because the software on your GPS receivers has to explicitly account for both these effects. At an orbital height of ~20000km and a relative speed of ~3.9km/s wrt to the ground observer, the gravitational contribution works out to about \(38 \mu s \), and the kinematic contribution is roughly \(7 \mu s \). Because of the symmetries of the Schwarzschild metric, you can just add these together to get total time dilation.

15 hours ago, DanMP said:

The test with one clock on the Moon surface and the other on the Earth surface was never done, nor any similar, so you don't really know the outcome.

That’s like saying we have never been on the surface of the sun, so we don’t really know it’s hot. It’s a silly argument. We have had a large number of crafts of different kinds both on the surface of the moon, and in orbit around it. We have also bounced lasers and radar signals off the moon’s surface. All of these things explicitly take into account time dilation - it affects orbital mechanics, it affects light travel times, and it affects frequency shifts. No discrepancies with expected physics have ever been observed in that regard. True, we haven’t done that specific experiment you are suggesting - but we have done many, many others where time dilation plays a role too, so if anything unexpected was going on, we would have seen it long ago. 

15 hours ago, DanMP said:

we simply have not enough/accurate information about "kinematic time dilation" caused by the movement of a planet/star/moon.

Why is the movement of a planet/star/moon different from the movement of a satellite?

15 hours ago, DanMP said:

Gravity is not different, that's not the issue

Then why do you insist that this experiment must be conducted on the moon?

15 hours ago, DanMP said:

Loads of money? Tiny, compared to LHC, JWST, or gravitational-wave detectors.

It’s not the total amount that’s the problem, but the cost/benefit ratio. All the above were designed to observe specific phenomena, which our models indicated should be there, so these are direct tests of specific predictions. On the other hand, what you are suggesting is a wild goose chase - there is nothing whatsoever to suggest that anything out of the ordinary will happen if we perform that experiment of yours, because motion and gravity isn’t any different on the moon than it is in Earth orbit. Research funding in fundamental physics is a very limited resource, so we are careful where we invest it. 

Like I said, if you want to test time dilation on the moon’s surface with respect to an Earth observer, then bounce a laser or a radar echo off it, and compare propagation times and frequency shifts to what our models say they should be. It’s a much easier test that addresses the same issue of time dilation, and it’s been done many times since 1946 - Earth-Moon-Earth communications is in fact an entire sub-discipline of aeronautical engineering.

15 hours ago, DanMP said:

I hope you are aware that a theory must pass any kind of test related to it.

Sure. I’m not opposed to performing such ann experiment, if anyone wants to provide the necessary funds. The more tests of GR/SR the better, so far as I am concerned. I just think it would be a waste of money, since there are much easier ways to test the physics in question here.

15 hours ago, DanMP said:

and never performed

Wrong, see above. The radar echo “Moon bounce” is a direct test of this (radar echo goes Earth-Moon-Earth), because any discrepancies in predicted time dilations would show up as anomalous frequency shifts in the reflected signals. Needless to say, no such thing as ever been observed.

15 hours ago, DanMP said:

You are denying that?

Yes, I’m denying that, because it’s a pop-sci misconception.

Look at Newtonian gravity - there are any number of experiments that are in direct contradiction to what this model predicts. And yet, we are still using it very successfully, and we are even teaching it to our kids in school. The point here is that all models have a domain of applicability - a set of circumstances which they are able to model very well. So long as you stay within that domain, the model will continue to work for your purposes, just as Newtonian gravity continues to work for us within its domain of applicability, even though it’s been experimentally “disproven” in many different ways.

And so it is with GR - we have already know for a long time that its domain of applicability is limited; we’re just not entirely sure precisely where those limits are. So if some experiment comes along that contradicts GR, then in the first instance we will tighten those limits. But it won’t ever be abandoned - that’s never going to happen, because it has already proven far too accurate and useful.

15 hours ago, DanMP said:

It is a dangerous thing, both in physics and in life, to be sure that you know something, when in fact you never really checked it.

That’s true. But it’s also dangerous to become obsessed with a single tree, and forgetting the rest of the forest - which is what you seem to be doing here.

Edited January 13, 2023 by Markus Hanke

[studiot]

3 hours ago, Markus Hanke said:

That’s true. But it’s also dangerous to become obsessed with a single tree, and forgetting the rest of the forest - which is what you seem to be doing here.

Your patience is exemplary. +1

[zapatos]

7 hours ago, studiot said:

Your patience is exemplary. +1

I agree.

DanMP is better informed on this topic than I am, yet even I can see the folly of his arguments. I can only conclude that he is digging in his heels in order to avoid acknowledging (God forbid!) he may have overemphasized the importance of this test, or that he has a fundamental misunderstanding of how science is practiced.