What Causes Gravitational Time Dilation? A Physical Explanation.

[Alan Grayson]

https://www.youtube.com/watch?v=DjwQsKMh2v8

[Alan Grayson]

On Saturday, June 7, 2025 at 9:36:55 PM UTC-6 Alan Grayson wrote:

https://www.youtube.com/watch?v=DjwQsKMh2v8

I just watched this video again. It's provocative to say the least, although it doesn't explain the physical mechanism of why space flows into the center of masses, and what happens to "space" at that point. The answer is promised in subsequent videos. I like opinions on this videos, from any expert or quasi expert on GR. Is it really just a coincidence that gravitational time dilation in GR can be explained using the same concept of time dilation in SR? AG 

[Brent Meeker]

No.  GR is just SR in non-flat spacetime.  Geodesics replace straight-lines as the longest paths between two events.

Brent

[Alan Grayson]

Isn't geodesic motion in non-flat spacetime a postulate of GR? If so, I don't see it as particularly enlightening as an explanation gravity. For example, as a test particle moves in free fall, how does it "know" that any departure from geodesic isn't allowed? How does it know to conform to some extremal principle? AG

[Brent Meeker]

On 6/10/2025 9:47 PM, Alan Grayson wrote:

On Tuesday, June 10, 2025 at 9:49:40 PM UTC-6 Brent Meeker wrote:

On 6/10/2025 8:41 PM, Alan Grayson wrote:

On Saturday, June 7, 2025 at 9:36:55 PM UTC-6 Alan Grayson wrote:

https://www.youtube.com/watch?v=DjwQsKMh2v8

I just watched this video again. It's provocative to say the least, although it doesn't explain the physical mechanism of why space flows into the center of masses, and what happens to "space" at that point. The answer is promised in subsequent videos. I like opinions on this videos, from any expert or quasi expert on GR. Is it really just a coincidence that gravitational time dilation in GR can be explained using the same concept of time dilation in SR? AG

No.  GR is just SR in non-flat spacetime.  Geodesics replace straight-lines as the longest paths between two events.

Brent

Isn't geodesic motion in non-flat spacetime a postulate of GR? If so, I don't see it as particularly enlightening as an explanation gravity.

It explains why falling bodies take accelerated paths thru space.  It doesn't explain why massive bodies warp spacetime.

For example, as a test particle moves in free fall, how does it "know" that any departure from geodesic isn't allowed? How does it know to conform to some extremal principle? AG

Same way as in Newtonian mechanics.

Brent

[John Clark]

On 6/10/2025 8:41 PM, Alan Grayson wrote:

> https://www.youtube.com/watch?v=DjwQsKMh2v8

 just watched this video again. It's provocative to say the least, although it doesn't explain the physical mechanism of why space flows into the center of masses, and what happens to "space" at that point. The answer is promised in subsequent videos. I like opinions on this videos, 

Yeah, you're right. I've watched videos from that "Dialectic" guy before and he loves to be provocative, he's always saying everybody else is wrong and I'm going to tell you what's really true. BUT NOT NOW. I've come to the conclusion that the man is full of shit. 

 John K Clark    See what's on my new list at  Extropolis

ez1

 

[John Clark]

On Tue, Jun 10, 2025 at 11:49 PM Brent Meeker <meeke...@gmail.com> wrote:

> GR is just SR in non-flat spacetime.

Yes. If a gravitational field does not make a significant contribution to the outcome then using the full power of General Relativity to solve a problem would be overkill, Special Relativity would be sufficient. 

 John K Clark    See what's on my new list at  Extropolis

tzp

[Brent Meeker]

No, I'm saying more than that.  If you take into account the different metric of spacetime induce by gravitation the motion of small object "test particles" is just SR on a lumpy background.  Of course it this doesn't extend to how the spacetime gets to be lumpy in the presence of mass-energy.  That takes the full mechanism of GR.  But since lots of gravity is associated with astronomical sized stuff, we're often just interested in what can be regarded as "test particles".

Brent

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[Alan Grayson]

The Newtonian postulate of inertia is inherently simpler than the GR postulate of geodesic motion on curved spacetime, but your point is well taken. It shows me we've got a lot of work ahead, before we really understand gravity. AG

As for muon half-life, you and Clark are in agreement that measuring the half-life requires the lab frame to be at rest wrt the muons being measured. But how can this be? A lab atop a mountain sees the muons flying by, same as the lab at rest on the Earth. So perhaps you could elaborate on how this half-life is measured, and where I have made an error. AG

 

[John Clark]

On Thu, Jun 12, 2025 at 4:49 AM Alan Grayson <agrays...@gmail.com> wrote:

> The Newtonian postulate of inertia is inherently simpler than the GR postulate of geodesic motion on curved spacetime

A good theory should be as simple as possible, but not simpler. Newton couldn't explain or predict that starlight passing near the sun will be bent by 1.75 arcseconds or that Mercury's orbit would precess by 43 arcseconds per century or that gravity could produce a redshift. But Einstein could. 

> A lab atop a mountain sees the muons flying by, same as the lab at rest on the Earth. 

No it is not the same! I don't understand why you believe that muons are always moving at close to the speed of light relative to us.  Muons are routinely made in the lab by smashing protons into carbon, and they can be moving at any speed. And muons have a negative electrical charge just like the electron so they can be easily manipulated; in fact the muon is identical to the electron except it is 207 times as massive and has a half-life of 1.56 *10^-6 seconds, which is very very long by particle physics standards. 

John K Clark    See what's on my new list at  Extropolis

7x=

[Alan Grayson]

On Thursday, June 12, 2025 at 5:36:15 AM UTC-6 John Clark wrote:

On Thu, Jun 12, 2025 at 4:49 AM Alan Grayson <agrays...@gmail.com> wrote:

> The Newtonian postulate of inertia is inherently simpler than the GR postulate of geodesic motion on curved spacetime

A good theory should be as simple as possible, but not simpler. Newton couldn't explain or predict that starlight passing near the sun will be bent by 1.75 arcseconds or that Mercury's orbit would precess by 43 arcseconds per century or that gravity could produce a redshift. But Einstein could. 

What do you think you've established? That GR is superior to NM? We already knew that! But what we don't understand about gravity is truly mind boggling, but only for those with imagination. AG 

> A lab atop a mountain sees the muons flying by, same as the lab at rest on the Earth. 

No it is not the same! I don't understand why you believe that muons are always moving at close to the speed of light relative to us.  

Where did I make that claim? Nowhere. Never. AG 

Muons are routinely made in the lab by smashing protons into carbon, and they can be moving at any speed. And muons have a negative electrical charge just like the electron so they can be easily manipulated; in fact the muon is identical to the electron except it is 207 times as massive and has a half-life of 1.56 *10^-6 seconds, which is very very long by particle physics standards. 

So if we have two labs, one atop a mountain and another on the Earth's surface, will they measure different half-lifes? AG 

[John Clark]

On Thu, Jun 12, 2025 at 8:10 AM Alan Grayson <agrays...@gmail.com> wrote:

> So if we have two labs, one atop a mountain and another on the Earth's surface, will they measure different half-lifes? AG 

Of course they will! One will detect muons that were produced when cosmic ray protons hit air molecules in Earth's upper atmosphere and are moving at near the speed of light; if it wasn't for time dilation caused by their  very high speed no muons would be detected by that guy on the mountain at all because the muons would've all decayed before they reached him. But the guy in the lab is measuring the half-life of muons that he had just made that were not moving, or were moving very slowly, relative to him.

>> A good theory should be as simple as possible, but not simpler. Newton couldn't explain or predict that starlight passing near the sun will be bent by 1.75 arcseconds or that Mercury's orbit would precess by 43 arcseconds per century or that gravity could produce a redshift. But Einstein could. 

>What do you think you've established? That GR is superior to NM? We already knew that! But what we don't understand about gravity is truly mind boggling, but only for those with imagination. AG 

So I'm supposed to believe that your confusion is the result of your vast intelligence?  

John K Clark    See what's on my new list at  Extropolis

&#(

[Alan Grayson]

You're confusing confusion with an interest in asking some deep questions, like how the half life of muons is effected by being observed. Is the Moon there when it's not being observed? True intelligence is knowing what you don't know, and with you it's obvious that you have virtually zero understanding of gravity, but lack the integrity to simply admit it. Moreover, generally speaking, without any contact with the White Light, you clearly fall into the category of a fool with a big mouth. AG

[John Clark]

On Thu, Jun 12, 2025 at 2:25 PM Alan Grayson <agrays...@gmail.com> wrote:

>  without any contact with the White Light, you clearly fall into the category of a fool with a big mouth. AG

I don't know about a white light but several years ago I had contact with the light of a different color. I was in a Kmart and somebody on the PA said "Attention Kmart Shoppers" and then a blue light started flashing.  

 John K Clark    See what's on my new list at  Extropolis

abl

[Brent Meeker]

I provided a graphic and text already.  You obviously paid no attention to it since you keep referring a lab atop a mountain an muons "flying" by.  

Frisch-Smith experiment

A much more precise experiment of this kind was conducted by David H. Frisch and Smith (1963), who measured approximately 563 muons per hour in six runs on Mount Washington. By measuring their kinetic energy, mean muon velocities between 0.995 c and 0.9954 c were determined. The target was located in Cambridge, Massachusetts with a difference in height of 1907 m, which should be traversed by the muons in about 6.4 µs. Assuming a mean lifetime of 2.2 µs, only 27 muons would reach this location if there were no time dilation. However, approximately 412 muons per hour arrived in Cambridge, resulting in a time dilation factor of 8.8±0.8.



Frisch and Smith showed that this is in agreement with the predictions of special relativity: The time dilation factor for muons on Mount Washington traveling at 0.995 c to 0.9954 c is approximately 10.2. Their kinetic energy and thus their velocity was diminished until they reached Cambridge to 0.9881 c and 0.9897 c due to the interaction with the atmosphere, reducing the dilation factor to 6.8. So between the start (≈ 10.2) and the target (≈ 6.8) an average time dilation factor of 8.4±2 was determined by them, in agreement with the measured result within the margin of errors (see the above formulas and the image for computing the decay curves).

Notice that the speed was inferred from the measured energy.  The decay rate of muons at rest was known from laboratory measurements of muons that were at rest or in slow (non-relativistic) motion.

Brent

[Brent Meeker]

On 6/12/2025 5:10 AM, Alan Grayson wrote:

On Thursday, June 12, 2025 at 5:36:15 AM UTC-6 John Clark wrote:

On Thu, Jun 12, 2025 at 4:49 AM Alan Grayson <agrays...@gmail.com> wrote:

> The Newtonian postulate of inertia is inherently simpler than the GR postulate of geodesic motion on curved spacetime

A good theory should be as simple as possible, but not simpler. Newton couldn't explain or predict that starlight passing near the sun will be bent by 1.75 arcseconds or that Mercury's orbit would precess by 43 arcseconds per century or that gravity could produce a redshift. But Einstein could. 

What do you think you've established? That GR is superior to NM? We already knew that! But what we don't understand about gravity is truly mind boggling, but only for those with imagination. AG 

The problem is you don't even have a proper conception of "understanding".  You're like Faraday who conceived of the electric and magnetic fields as lots of masses and springs.  If it was just equations it wasn't understood.  It had to be masses and springs.  When you saw the infalling space model of gravity you thought it provided you "understanding", but it wouldn't even allow for orbits.  In graduate school, if not earlier, physicists learn to let equations speak for themselves.  Examples are good to develop intuition.  But every example is incomplete.  And every made-up visualization is misleading in some respect.  So think about what counts as "understanding".   Knowing the equations and how to apply them is the real understanding.

Brent

> A lab atop a mountain sees the muons flying by, same as the lab at rest on the Earth. 

No it is not the same! I don't understand why you believe that muons are always moving at close to the speed of light relative to us.  

Where did I make that claim? Nowhere. Never. AG 

Muons are routinely made in the lab by smashing protons into carbon, and they can be moving at any speed. And muons have a negative electrical charge just like the electron so they can be easily manipulated; in fact the muon is identical to the electron except it is 207 times as massive and has a half-life of 1.56 *10^-6 seconds, which is very very long by particle physics standards. 

So if we have two labs, one atop a mountain and another on the Earth's surface, will they measure different half-lifes? AG 

John K Clark    See what's on my new list at  Extropolis

7x=

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[Alan Grayson]

On Thursday, June 12, 2025 at 1:56:20 PM UTC-6 Brent Meeker wrote:

On 6/12/2025 5:10 AM, Alan Grayson wrote:

On Thursday, June 12, 2025 at 5:36:15 AM UTC-6 John Clark wrote:

On Thu, Jun 12, 2025 at 4:49 AM Alan Grayson <agrays...@gmail.com> wrote:

> The Newtonian postulate of inertia is inherently simpler than the GR postulate of geodesic motion on curved spacetime

A good theory should be as simple as possible, but not simpler. Newton couldn't explain or predict that starlight passing near the sun will be bent by 1.75 arcseconds or that Mercury's orbit would precess by 43 arcseconds per century or that gravity could produce a redshift. But Einstein could. 

What do you think you've established? That GR is superior to NM? We already knew that! But what we don't understand about gravity is truly mind boggling, but only for those with imagination. AG 

The problem is you don't even have a proper conception of "understanding". 

GR has many unexplained postulates, like the physical reason mass distorts spacetime. You're the one who has an improper concept of "understanding". You don't seem to have a clue of what you don't understand! Consider the muon. Why does applying the LT cause its half-life to dilate? It's not even being observed, just thought of as being observed. Yes, one can say it happens in order to preserve the invariance of light speed. Is that really enough? You just don't want to go deeper and are happy with your equations. Sad. AG 

 

You're like Faraday who conceived of the electric and magnetic fields as lots of masses and springs.  If it was just equations it wasn't understood.  It had to be masses and springs.  When you saw the infalling space model of gravity you thought it provided you "understanding", but it wouldn't even allow for orbits. 

No.You read worse than a Trumper. I wrote it didn't explain what happened to space when it reached the center of the gravitating mass, among other things unmentioned, like why does it flow. AG 

[Brent Meeker]

On 6/12/2025 4:33 PM, Alan Grayson wrote:

On Thursday, June 12, 2025 at 1:56:20 PM UTC-6 Brent Meeker wrote:

...

The problem is you don't even have a proper conception of "understanding". 

GR has many unexplained postulates, like the physical reason mass distorts spacetime. 

Yes, but what would count as an explanation for you?  Entropic gravity? 
https://en.wikipedia.org/wiki/Entropic_gravity

You're the one who has an improper concept of "understanding". You don't seem to have a clue of what you don't understand! Consider the muon. Why does applying the LT cause its half-life to dilate? 

I know that one.  It's because when going fast it takes an inertial spacetime path with more space and less time, as quantified by the Lorentz transformation.  In it's own frame it is decaying at the same rate as a stationary muon...which is good since otherwise we'd have absolute motion.

Brent

[Alan Grayson]

On Thursday, June 12, 2025 at 6:05:41 PM UTC-6 Brent Meeker wrote:

On 6/12/2025 4:33 PM, Alan Grayson wrote:

On Thursday, June 12, 2025 at 1:56:20 PM UTC-6 Brent Meeker wrote:

...

The problem is you don't even have a proper conception of "understanding". 

GR has many unexplained postulates, like the physical reason mass distorts spacetime. 

Yes, but what would count as an explanation for you?  Entropic gravity? 
https://en.wikipedia.org/wiki/Entropic_gravity

I'm not familiar with this theory, but I've heard of it. GR tells us how to calculate the effect of mass/ energy on spacetime curvature, but nothing about the physical mechanism upon which the effect depends. AG

You're the one who has an improper concept of "understanding". You don't seem to have a clue of what you don't understand! Consider the muon. Why does applying the LT cause its half-life to dilate? 

I know that one.  It's because when going fast it takes an inertial spacetime path with more space and less time, as quantified by the Lorentz transformation.  In it's own frame it is decaying at the same rate as a stationary muon...which is good since otherwise we'd have absolute motion.

I don't think you understand my question. In part I am asking how the dichotomy arises wherein the muon's half life implied by the LT, differs from what it measures internally? And how does the muon acquire a clock? And more. AG 

Brent

It's not even being observed, just thought of as being observed. Yes, one can say it happens in order to preserve the invariance of light speed. Is that really enough? You just don't want to go deeper and are happy with your equations. Sad. AG  

You're like Faraday who conceived of the electric and magnetic fields as lots of masses and springs.  If it was just equations it wasn't understood.  It had to be masses and springs.  When you saw the infalling space model of gravity you thought it provided you "understanding", but it wouldn't even allow for orbits. 

No. You read worse than a Trumper. I wrote it didn't explain what happened to space when it reached the center of the gravitating mass, among other things unmentioned, like why does it flow. AG 

In graduate school, if not earlier, physicists learn to let equations speak for themselves.  Examples are good to develop intuition.  But every example is incomplete.  And every made-up visualization is misleading in some respect.  So think about what counts as "understanding".   Knowing the equations and how to apply them is the real understanding.

That means you've de-facto given up on any model that explains the physical interaction of mass/energy with spacetime. AG

[Brent Meeker]

On 6/12/2025 6:22 PM, Alan Grayson wrote:

In graduate school, if not earlier, physicists learn to let equations speak for themselves.  Examples are good to develop intuition.  But every example is incomplete.  And every made-up visualization is misleading in some respect.  So think about what counts as "understanding".   Knowing the equations and how to apply them is the real understanding.

That means you've de-facto given up on any model that explains the physical interaction of mass/energy with spacetime. AG

No, it means that if I find a fundamental process underlying gravity, like entropic gravity, I will just have moved your problem down to a different one, why does matter produce this entropic gradient that produces gravity.  Physics doesn't answer "why" questions about fundamentals; otherwise they wouldn't be fundamental.

Brent

[Alan Grayson]

Whereas "why' questions always exist regardless of the depth of some theory, physics can and does answer some of these questions in a provisional way. You were taught to be satisfied with provisional theories which give good predictions. The problem with your perspective, is that it endorses the status quo, and is anathema to progress. AG 

[Alan Grayson]

On Thursday, June 12, 2025 at 7:17:31 AM UTC-6 John Clark wrote:

On Thu, Jun 12, 2025 at 8:10 AM Alan Grayson <agrays...@gmail.com> wrote:

> So if we have two labs, one atop a mountain and another on the Earth's surface, will they measure different half-lifes? AG 

Of course they will! One will detect muons that were produced when cosmic ray protons hit air molecules in Earth's upper atmosphere and are moving at near the speed of light; if it wasn't for time dilation caused by their  very high speed no muons would be detected by that guy on the mountain at all because the muons would've all decayed before they reached him. But the guy in the lab is measuring the half-life of muons that he had just made that were not moving, or were moving very slowly, relative to him.

OK. I was unaware of the scenario you were imagining. If the lab on the mountain was also creating muons, the half-lives would be the same as the Earth bound lab. I was imagining a case where both labs create muons, or both observe them falling. Nonetheless, I remain puzzled about the claim that muons have clocks, and that the LT somehow distinguishes between dilation in relative motion of clocks NOT being directly observed, just calculated, and rest clocks in the muon's frame of reference. I don't think you can deny there's an unsolved mystery in this dichotomy. AG  

[Alan Grayson]

I'll tell you something you don't know and surely won't appreciate; what the White Light Is. The White Light is You. AG 

abl

[John Clark]

On Thu, Jun 12, 2025 at 7:33 PM Alan Grayson <agrays...@gmail.com> wrote:

 

> GR has many unexplained postulates,

Many? General Relativity only has 3 postulates:
1)The speed of light is constant for all observers.
2) Gravitational mass and inertial mass are equivalent.

3) Equations expressing physical laws should say the same thing regardless of what coordinate system is used to describe 4D spacetime, even accelerating or rotating ones. 

Or if you're willing to tolerate a little inaccuracy and wanted to say the same thing more poetically you could say it only has one postulate. "matter tells spacetime how to curve". "Spacetime tells matter how to move" comes from the definition of spacetime. And the definition of "move" is a change in 4D spacetime coordinates.

And a postulate is not unexplained, it is unproven. A statement that cannot be explained is gibberish, but right or wrong "matter tells spacetime how to curve" is not gibberish. 

 

> like the physical reason mass distorts spacetime.

And if tomorrow somebody found that X is the physical reason that mass exists then you would immediately ask what is the reason that X exists. As I keep saying there are only two possibilities, an iterated chain of questions either goes on forever or ends in a brute fact.  

 

> Consider the muon. Why does applying the LT cause its half-life to dilate?

The same exact reason relative velocity causes ANY clock to slow down, the speed of light is constant for all observers. And time is what a clock measures.  

On Thu, Jun 12, 2025 at 3:56 PM Brent Meeker <meeke...@gmail.com> wrote:

 > You're like Faraday

Brent, you can't be talking about Alan Grayson! If somebody told me I was like Michael Faraday I would take that as a huge compliment. But I've read about Michael Faraday and Alan Grayson is no Michael Faraday.

> You read worse than a Trumper.

I'm a little jealous, I thought I was the only one Grayson accused of being a Trumper because of a scientific disagreement. 

John K Clark    See what's on my new list at  Extropolis

ez1

 

[John Clark]

On Fri, Jun 13, 2025 at 4:27 AM Alan Grayson <agrays...@gmail.com> wrote:

>>>  without any contact with the White Light, you clearly fall into the category of a fool with a big mouth. AG

>> I don't know about a white light but several years ago I had contact with the light of a different color. I was in a Kmart and somebody on the PA said "Attention Kmart Shoppers" and then a blue light started flashing.  

> I'll tell you something you don't know and surely won't appreciate; what the White Light Is. The White Light is You. AG

But that blue light had profound consequences, thanks to it I got a great deal on an electric can opener!

John K Clark    See what's on my new list at  Extropolis 

euu

[Alan Grayson]

I see. Not even a "thank you". I casted pearls before swine, and as expected you're condemned to be an ignorant fool. AG 

[spudb...@aol.com]

Meanwhile, an old idea gets more credit. Quanta Magazine

https://x.com/i/status/1933524373287137665

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[Brent Meeker]

On 6/12/2025 11:33 PM, Alan Grayson wrote:

On Thursday, June 12, 2025 at 7:17:31 AM UTC-6 John Clark wrote:

On Thu, Jun 12, 2025 at 8:10 AM Alan Grayson <agrays...@gmail.com> wrote:

> So if we have two labs, one atop a mountain and another on the Earth's surface, will they measure different half-lifes? AG 

Of course they will! One will detect muons that were produced when cosmic ray protons hit air molecules in Earth's upper atmosphere and are moving at near the speed of light; if it wasn't for time dilation caused by their  very high speed no muons would be detected by that guy on the mountain at all because the muons would've all decayed before they reached him. But the guy in the lab is measuring the half-life of muons that he had just made that were not moving, or were moving very slowly, relative to him.

OK. I was unaware of the scenario you were imagining. If the lab on the mountain was also creating muons, the half-lives would be the same as the Earth bound lab. I was imagining a case where both labs create muons, or both observe them falling. Nonetheless, I remain puzzled about the claim that muons have clocks, and that the LT somehow distinguishes between dilation in relative motion of clocks NOT being directly observed, just calculated, and rest clocks in the muon's frame of reference. I don't think you can deny there's an unsolved mystery in this dichotomy. AG  

The time dilation of the fast moving muons created in the upper atmosphere is inferred from the fact that they still exist at the lower altitude. Why don't you read what I posted with the diagram.  It has a plot of the number to have not decayed under a Newtonian model and one with Einstein's time dilation as a function of altitude.

Brent

>> A good theory should be as simple as possible, but not simpler. Newton couldn't explain or predict that starlight passing near the sun will be bent by 1.75 arcseconds or that Mercury's orbit would precess by 43 arcseconds per century or that gravity could produce a redshift. But Einstein could. 

>What do you think you've established? That GR is superior to NM? We already knew that! But what we don't understand about gravity is truly mind boggling, but only for those with imagination. AG 

So I'm supposed to believe that your confusion is the result of your vast intelligence?  

John K Clark    See what's on my new list at  Extropolis

&#(

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[Alan Grayson]

On Friday, June 13, 2025 at 4:54:35 PM UTC-6 Brent Meeker wrote:

On 6/12/2025 11:33 PM, Alan Grayson wrote:

On Thursday, June 12, 2025 at 7:17:31 AM UTC-6 John Clark wrote:

On Thu, Jun 12, 2025 at 8:10 AM Alan Grayson <agrays...@gmail.com> wrote:

> So if we have two labs, one atop a mountain and another on the Earth's surface, will they measure different half-lifes? AG 

Of course they will! One will detect muons that were produced when cosmic ray protons hit air molecules in Earth's upper atmosphere and are moving at near the speed of light; if it wasn't for time dilation caused by their  very high speed no muons would be detected by that guy on the mountain at all because the muons would've all decayed before they reached him. But the guy in the lab is measuring the half-life of muons that he had just made that were not moving, or were moving very slowly, relative to him.

OK. I was unaware of the scenario you were imagining. If the lab on the mountain was also creating muons, the half-lives would be the same as the Earth bound lab. I was imagining a case where both labs create muons, or both observe them falling. Nonetheless, I remain puzzled about the claim that muons have clocks, and that the LT somehow distinguishes between dilation in relative motion of clocks NOT being directly observed, just calculated, and rest clocks in the muon's frame of reference. I don't think you can deny there's an unsolved mystery in this dichotomy. AG  

The time dilation of the fast moving muons created in the upper atmosphere is inferred from the fact that they still exist at the lower altitude. Why don't you read what I posted with the diagram. 

 

I know that story, so it wasn't necessary to read it, though I eventually did. Was I supposed to assume your scenario and Clark's were identical? Now see if you can answer my questions, which you've conveniently ignored. What do you know about muon clocks? Anything? AG

[Brent Meeker]

On 6/13/2025 5:02 AM, John Clark wrote:

On Thu, Jun 12, 2025 at 7:33 PM Alan Grayson <agrays...@gmail.com> wrote:

 

> GR has many unexplained postulates,

Many? General Relativity only has 3 postulates:
1)The speed of light is constant for all observers.
2) Gravitational mass and inertial mass are equivalent.

3) Equations expressing physical laws should say the same thing regardless of what coordinate system is used to describe 4D spacetime, even accelerating or rotating ones. 

Or if you're willing to tolerate a little inaccuracy and wanted to say the same thing more poetically you could say it only has one postulate. "matter tells spacetime how to curve". "Spacetime tells matter how to move" comes from the definition of spacetime. And the definition of "move" is a change in 4D spacetime coordinates.

And a postulate is not unexplained, it is unproven. A statement that cannot be explained is gibberish, but right or wrong "matter tells spacetime how to curve" is not gibberish. 

 

> like the physical reason mass distorts spacetime.

And if tomorrow somebody found that X is the physical reason that mass exists then you would immediately ask what is the reason that X exists. As I keep saying there are only two possibilities, an iterated chain of questions either goes on forever or ends in a brute fact.  

That's a common view that iterated "why" questions must bottom out in something inexplicable.  But is that really so?Actually I have argued in other contexts that explanation can often be thought of as forming a virtuous circle, something like this



Reasonable people will just follow those arrows of implication backwards around from the domain of their question until they find a domain which contains an answer which satisfies them.  Unreasonable people may find themselves back where they started...in which case I suggest persistence.

Brent

 

> Consider the muon. Why does applying the LT cause its half-life to dilate?

The same exact reason relative velocity causes ANY clock to slow down, the speed of light is constant for all observers. And time is what a clock measures.  

On Thu, Jun 12, 2025 at 3:56 PM Brent Meeker <meeke...@gmail.com> wrote:

 > You're like Faraday

Brent, you can't be talking about Alan Grayson! If somebody told me I was like Michael Faraday I would take that as a huge compliment. But I've read about Michael Faraday and Alan Grayson is no Michael Faraday.

> You read worse than a Trumper.

I'm a little jealous, I thought I was the only one Grayson accused of being a Trumper because of a scientific disagreement. 

John K Clark    See what's on my new list at  Extropolis

ez1

 

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[Alan Grayson]

On Friday, June 13, 2025 at 6:02:57 AM UTC-6 John Clark wrote:

On Thu, Jun 12, 2025 at 7:33 PM Alan Grayson <agrays...@gmail.com> wrote:

 

> GR has many unexplained postulates,

Many? General Relativity only has 3 postulates:
1)The speed of light is constant for all observers.
2) Gravitational mass and inertial mass are equivalent.

3) Equations expressing physical laws should say the same thing regardless of what coordinate system is used to describe 4D spacetime, even accelerating or rotating ones. 

And bodies in free fall, move along geodesic paths; and matter / energy causes spacetime curvature. AG 

Or if you're willing to tolerate a little inaccuracy and wanted to say the same thing more poetically you could say it only has one postulate. "matter tells spacetime how to curve".

How does matter do that? AG

 

"Spacetime tells matter how to move" comes from the definition of spacetime.

From a definition we get motion? Any clue how that happens? AG

 

And the definition of "move" is a change in 4D spacetime coordinates.

And a postulate is not unexplained,

Hypothetically, a deeper theory of gravity might be able to establish a physical mechanism for some of the postulates of GR. Pushing gravity is an attempt to do just that. But as a conformist who gives undue support to current theories, this possibility is beyond your narrow conceptual framework. AG 

it is unproven. A statement that cannot be explained is gibberish, but right or wrong "matter tells spacetime how to curve" is not gibberish. 

It leaves much unanswered. AG 

 

> like the physical reason mass distorts spacetime.

And if tomorrow somebody found that X is the physical reason that mass exists then you would immediately ask what is the reason that X exists. As I keep saying there are only two possibilities, an iterated chain of questions either goes on forever or ends in a brute fact.  

 

> Consider the muon. Why does applying the LT cause its half-life to dilate?

The same exact reason relative velocity causes ANY clock to slow down, the speed of light is constant for all observers.

Firstly, you have no clue about the form of a muon's clock. Or how LT seems to select a clock no one can read. I mean the only clock which is read, is the clock in the muon's rest frame, which exhibits no time dilation. Who or what is reading the dilated clock? AG

 

And time is what a clock measures.  

So if there's no clock able to be defined, does this mean time ceases to exist? You can't define the form of a muon's clock, yet you speak glibly about time, as if you have clue what it is. AG 

On Thu, Jun 12, 2025 at 3:56 PM Brent Meeker <meeke...@gmail.com> wrote:

 > You're like Faraday

Brent, you can't be talking about Alan Grayson! If somebody told me I was like Michael Faraday I would take that as a huge compliment. But I've read about Michael Faraday and Alan Grayson is no Michael Faraday.

I wouldn't compare myself to anyone. I'm just a person who can see there are many questions you are unable to answer, but much worse, that you think the postulates of GR are the final answer to the mystery of gravity. AG  

[Alan Grayson]

On Friday, June 13, 2025 at 9:01:40 PM UTC-6 Alan Grayson wrote:

On Friday, June 13, 2025 at 6:02:57 AM UTC-6 John Clark wrote:

On Thu, Jun 12, 2025 at 7:33 PM Alan Grayson <agrays...@gmail.com> wrote:

 

> GR has many unexplained postulates,

Many? General Relativity only has 3 postulates:
1)The speed of light is constant for all observers.
2) Gravitational mass and inertial mass are equivalent.

3) Equations expressing physical laws should say the same thing regardless of what coordinate system is used to describe 4D spacetime, even accelerating or rotating ones. 

And bodies in free fall, move along geodesic paths; and matter / energy causes spacetime curvature. AG 

Or if you're willing to tolerate a little inaccuracy and wanted to say the same thing more poetically you could say it only has one postulate. "matter tells spacetime how to curve".

How does matter do that? AG

 

"Spacetime tells matter how to move" comes from the definition of spacetime.

From a definition we get motion? Any clue how that happens? AG

If a test particle is spatially at rest, and then let go, it moves. Why does it move? IMO, at the present time, we have no clue why it moves. AG 

[John Clark]

On Fri, Jun 13, 2025 at 11:01 PM Alan Grayson <agrays...@gmail.com> wrote:

>>> GR has many unexplained postulates,

>> Many? General Relativity only has 3 postulates:

1) The speed of light is constant for all observers.

2) Gravitational mass and inertial mass are equivalent.

3) Equations expressing physical laws should say the same thing regardless of what coordinate system is used to describe 4D spacetime, even accelerating or rotating ones. 

> And bodies in free fall, move along geodesic paths;

That fact is a logical consequence of the Equivalence Principle, which is the third postulate in the above. So no additional postulate is required. 

 

> and matter/energy causes spacetime curvature. AG 

The Equivalence Principle (postulate #3) says in effect that gravity is the curvature of 4D spacetime, and if gravitational mass and inertial mass are equivalent (postulate #2) then the logical conclusion is that matter causes spacetime to curve. So no additional postulate is required.

>> if you're willing to tolerate a little inaccuracy and wanted to say the same thing more poetically you could say it only has one postulate. "matter tells spacetime how to curve".

> How does matter do that? AG

The 4D shape of the resulting spacetime is determined by how the matter/energy is distributed, and its precise shape can be calculated with Einstein Field Equations, which uses 4D non-Euclidean tensor calculus. 

 

>> "Spacetime tells matter how to move" comes from the definition of spacetime.

> From a definition we get motion?

Obviously. If motion doesn't mean a change in spatial coordinates with respect to time then what does "motion" mean?  Newton could explain what gravity does (if things are not moving too fast and gravity is not too strong) but he admitted that he did not know what gravity was: 

  "I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses"

But Einstein knew, gravity is the curvature of 4D spacetime in non-Euclidean geometry. 

 

>>> Consider the muon. Why does applying the LT cause its half-life to dilate?

>>The same exact reason relative velocity causes ANY clock to slow down, the speed of light is constant for all observers.

> Firstly, you have no clue about the form of a muon's clock.

Our ancestors didn't know why the sun moved in the sky but that didn't prevent them from using the sun as a clock, and I don't know the exact mechanism the muon uses to keep time, but I don't need to know because I know for a fact that I can use muons to make a clock. And time is what a clock measures.   

 

>>And time is what a clock measures.  

> So if there's no clock able to be defined, does this mean time ceases to exist?

Yes exactly. If it was impossible to make a clock, if nothing occurred in a periodic manner, then the concept of time would be meaningless. That's why people say when the universe reaches thermal equilibrium (a.k.a. the heat death of the universe) nothing would be periodic and so time would come to an end.  

And do you have a better definition of time than "what a clock measures"? I don't. 

 

> You can't define the form of a muon's clock,

As I said I don't know what the muon's internal clock mechanism looks like, but I do know that whatever mechanism it uses it's accurate. And that's all I need to know. 

 

> you think the postulates of GR are the final answer to the mystery of gravity. AG  

Bullshit! Even Einstein didn't think that, and I doubt if a single living physicist thinks that either!

John K Clark    See what's on my new list at  Extropolis

8f/

[John Clark]

On Fri, Jun 13, 2025 at 11:09 PM Alan Grayson <agrays...@gmail.com> wrote:

> If a test particle is spatially at rest, and then let go, it moves. Why does it move? 

If the particle is not moving relative to your hand and you let it go then it will NOT move, not unless you give it a push with your fingers, or you're in an accelerating spaceship, or you're in curved 4D spacetime (a.k.a. a gravitational field). 

  John K Clark    See what's on my new list at  Extropolis

fca

[Alan Grayson]

That's what I was assuming, that I'm in a gravitational field. It moves, but why? AG 

fca

[Alan Grayson]

I'm posing the question in the context of GR, 4D gravitational spacetime. AG 

fca

[Brent Meeker]

On 6/13/2025 8:01 PM, Alan Grayson wrote:

Firstly, you have no clue about the form of a muon's clock. Or how LT seems to select a clock no one can read. I mean the only clock which is read, is the clock in the muon's rest frame, which exhibits no time dilation. Who or what is reading the dilated clock? AG

We're reading the clock (dilated or not) by detecting when it decays.  In fact the "watched pot theorem" shows that if you measure the lack of decay on a short enough time scale, it won't decay.

But you've still not said what would satisfy you're demand to know the "form of a muon's clock"?  Would balance wheels and escapments satisfy you?  How do you think atomic clocks (the standard for the second) keep time?

Brent

[Alan Grayson]

On Saturday, June 14, 2025 at 6:07:46 PM UTC-6 Brent Meeker wrote:

On 6/13/2025 8:01 PM, Alan Grayson wrote:

Firstly, you have no clue about the form of a muon's clock. Or how LT seems to select a clock no one can read. I mean the only clock which is read, is the clock in the muon's rest frame, which exhibits no time dilation. Who or what is reading the dilated clock? AG

We're reading the clock (dilated or not) by detecting when it decays. 

How does observing a decay translate into reading a clock? AG

 

In fact the "watched pot theorem" shows that if you measure the lack of decay on a short enough time scale, it won't decay.

But you've still not said what would satisfy you're demand to know the "form of a muon's clock"?  Would balance wheels and escapments satisfy you?  How do you think atomic clocks (the standard for the second) keep time?

Atoms have structure and definite transition frequencies, so although I don't know exactly how Cesium 133 is used to define the standard second, it doesn't take a leap of faith to believe it's possible. OTOH, if a muon is anything like an electron except for its mass, it has no measurable structure and hence an unlikely candidate for having a clock. Moreover, since you're the one who believes the muon has a clock, the burden is yours to define what it is, or could be. AG

[Alan Grayson]

On Saturday, June 14, 2025 at 6:13:47 AM UTC-6 John Clark wrote:

On Fri, Jun 13, 2025 at 11:01 PM Alan Grayson <agrays...@gmail.com> wrote:

>>> GR has many unexplained postulates,

>> Many? General Relativity only has 3 postulates:

1) The speed of light is constant for all observers.

2) Gravitational mass and inertial mass are equivalent.

3) Equations expressing physical laws should say the same thing regardless of what coordinate system is used to describe 4D spacetime, even accelerating or rotating ones. 

> And bodies in free fall, move along geodesic paths;

That fact is a logical consequence of the Equivalence Principle, which is the third postulate in the above. So no additional postulate is required. 

Logical consequence? How so? AG 

 

> and matter/energy causes spacetime curvature. AG 

The Equivalence Principle (postulate #3) says in effect that gravity is the curvature of 4D spacetime, and if gravitational mass and inertial mass are equivalent (postulate #2) then the logical conclusion is that matter causes spacetime to curve. So no additional postulate is required.

See above comment. Can you prove your logical conclusion?  AG

>> if you're willing to tolerate a little inaccuracy and wanted to say the same thing more poetically you could say it only has one postulate. "matter tells spacetime how to curve".

> How does matter do that? AG

The 4D shape of the resulting spacetime is determined by how the matter/energy is distributed, and its precise shape can be calculated with Einstein Field Equations, which uses 4D non-Euclidean tensor calculus. 

What's obviously lacking is a physical mechanism to get to your conclusion. AG 

 

>> "Spacetime tells matter how to move" comes from the definition of spacetime.

> From a definition we get motion?

Obviously. If motion doesn't mean a change in spatial coordinates with respect to time then what does "motion" mean?  Newton could explain what gravity does (if things are not moving too fast and gravity is not too strong) but he admitted that he did not know what gravity was: 

  "I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses"

But Einstein knew, gravity is the curvature of 4D spacetime in non-Euclidean geometry. 

 

>>> Consider the muon. Why does applying the LT cause its half-life to dilate?

>>The same exact reason relative velocity causes ANY clock to slow down, the speed of light is constant for all observers.

You're missing the point; namely, that the clock in frame being observed does NOT slow down. In what frame is the clock you allege is slowing down?  AG 

> Firstly, you have no clue about the form of a muon's clock.

Our ancestors didn't know why the sun moved in the sky but that didn't prevent them from using the sun as a clock, and I don't know the exact mechanism the muon uses to keep time, but I don't need to know because I know for a fact that I can use muons to make a clock. And time is what a clock measures.   

What you claim you don't need to know, is what in fact you DO need to know, if your theory is to be complete. AG 

 

>>And time is what a clock measures.  

> So if there's no clock able to be defined, does this mean time ceases to exist?

Yes exactly. If it was impossible to make a clock, if nothing occurred in a periodic manner, then the concept of time would be meaningless.

A clock doesn't have to be periodic. It can be linear. It just needs to assign a unique real number to each event being  observed. AG

 

That's why people say when the universe reaches thermal equilibrium (a.k.a. the heat death of the universe) nothing would be periodic and so time would come to an end.  

And do you have a better definition of time than "what a clock measures"? I don't. 

Sure; time is caused by the existence of observed events. No events. No time. Nothing to do with clocks, AG 

 

> You can't define the form of a muon's clock,

As I said I don't know what the muon's internal clock mechanism looks like, but I do know that whatever mechanism it uses it's accurate. And that's all I need to know. 

 

> you think the postulates of GR are the final answer to the mystery of gravity. AG  

Bullshit! Even Einstein didn't think that, and I doubt if a single living physicist thinks that either!

Insofar as you defend the Gospel, and vehemently I might add, although at some level you don't think GR is the end of the road, but emotionally you do. AG 

[John Clark]

On Sat, Jun 14, 2025 at 11:20 PM Alan Grayson <agrays...@gmail.com> wrote:

On Saturday, June 14, 2025 at 6:07:46 PM UTC-6 Brent Meeker wrote:

> How do you think atomic clocks (the standard for the second) keep time?

On Sat, Jun 14, 2025 at 11:20 PM Alan Grayson <agrays...@gmail.com> wrote:

> Atoms have structure

But electrons have no structure, and the decay of an electron from a high energy orbit to a lower energy orbit is what an atomic clock uses to keep time, so they really should be called electron clocks. How does an electron know when it's time to emit a photon and move to a lower orbit? Nobody knows, but we don't need to know to make a clock out of an electron if it is near the nucleus of a cesium atom.

 

> and definite transition frequencies, 

And muons have a definite decay frequency.  

> Moreover, since you're the one who believes the muon has a clock, the burden is yours to define what it is, 

I've already defined what a clock is, it's a thing that measures time. And I have no obligation to explain how a muon clock works, I just need to demonstrate that it exists.  In a similar way our ancestors didn't know why a sundial could measure time, all they needed to know is that it did. 

>How does observing a decay translate into reading a clock? AG

Huh? We know from experiment that the mean lifetime of a muon at rest is 2.1969811 ± 0.0000022 microseconds, and you don't understand how it would be possible to use that fact to make a very accurate clock? 

 John K Clark    See what's on my new list at  Extropolis

7gu

[John Clark]

On Sat, Jun 14, 2025 at 11:42 PM Alan Grayson <agrays...@gmail.com> wrote:

>> General Relativity only has 3 postulates:
1) The speed of light is constant for all observers.
2) Gravitational mass and inertial mass are equivalent.

3) Equations expressing physical laws should say the same thing regardless of what coordinate system is used to describe 4D spacetime, even accelerating or rotating ones. 

> bodies in free fall, move along geodesic paths;

>> That fact is a logical consequence of the Equivalence Principle, which is the third postulate in the above. So no additional postulate is required. 

> Logical consequence? How so? AG 

The Equivalence Principle says an observer cannot distinguish between being in freefall near the surface of the Earth and being in intergalactic space far from any source of gravitation, if you release an object it will not move relative to your hand. If you are floating in intergalactic space then, because of the laws of geometry, that fact is represented by a straight line in flat Euclidean 4D spacetime. If you are falling to the Earth then, because of the laws of geometry, that fact is represented by a geodesic in curved non-Euclidean 4D spacetime. And Einstein's field equations can tell you precisely how much or how little spacetime needs to be curved.

>> The Equivalence Principle (postulate #3) says in effect that gravity is the curvature of 4D spacetime, and if gravitational mass and inertial mass are equivalent (postulate #2) then the logical conclusion is that matter causes spacetime to curve. So no additional postulate is required.

> See above comment. Can you prove your logical conclusion?  AG

The Equivalence Principle says gravity is the curvature of 4D spacetime, and if gravitational mass and inertial mass are equivalent but mass doesn't cause 4D spacetime to curve, then how in the world could gravitational mass and inertial mass be equivalent?!

>> do you have a better definition of time than "what a clock measures"? I don't. 

> Sure; time is caused by the existence of observed events. No events. No time. Nothing to do with clocks, AG 

An event is defined as a specific space in 4D spacetime and a specific TIME. So if you use time in a definition of time you get into an infinite regress. 

>> If it was impossible to make a clock, if nothing occurred in a periodic manner, then the concept of time would be meaningless.

> A clock doesn't have to be periodic. It can be linear. It just needs to assign a unique real number to each event being  observed. AG

So you think a clock could be made by making a list of the position of every particle in the universe with respect to time, but without a clock how do you know what time it is? And even if you could somehow manage to make such a list, how could you know which way to read it? We can tell which way the arrow time is pointing because tomorrow will have more entropy than today, but that would no longer be true when the universe has reached heat death and entropy has risen to a maximum. 

 

>> The 4D shape of the resulting spacetime is determined by how the matter/energy is distributed, and its precise shape can be calculated with Einstein Field Equations, which uses 4D non-Euclidean tensor calculus. 

> What's obviously lacking is a physical mechanism to get to your conclusion. AG 

My problem is I don't know what sort of explanation would satisfy you. Give me an example of a phenomenon, ANY phenomenon physical or otherwise, that you feel has a satisfactory explanation and doesn't generate additional questions that are very obvious. 

> Insofar as you defend the Gospel, and vehemently I might add, although at some level you don't think GR is the end of the road, but emotionally you do. AG 

Thanks for that very deep psychoanalysis Dr. Freud. 

John K Clark    See what's on my new list at  Extropolis

tsd

[Brent Meeker]

On 6/15/2025 3:15 AM, John Clark wrote:

On Sat, Jun 14, 2025 at 11:20 PM Alan Grayson <agrays...@gmail.com> wrote:

On Saturday, June 14, 2025 at 6:07:46 PM UTC-6 Brent Meeker wrote:

> How do you think atomic clocks (the standard for the second) keep time?

On Sat, Jun 14, 2025 at 11:20 PM Alan Grayson <agrays...@gmail.com> wrote:

> Atoms have structure

But electrons have no structure, and the decay of an electron from a high energy orbit to a lower energy orbit is what an atomic clock uses to keep time

No, the time keeping function is the frequency the photons absorb, not the decay or absorption rate.  The one used as a standard uses the cesium-133 transition between two specific energy levels that emit photons with frequency 9,192,631,770 Hz.  The atoms are excited at this frequency by a microwave emitter which is adjusted by a feedback loop to match this frequency.

, so they really should be called electron clocks. How does an electron know when it's time to emit a photon and move to a lower orbit? Nobody knows, but we don't need to know to make a clock out of an electron if it is near the nucleus of a cesium atom.

 

> and definite transition frequencies, 

And muons have a definite decay frequency. 

They decay at random with a certain average rate.

Brent

 

> Moreover, since you're the one who believes the muon has a clock, the burden is yours to define what it is, 

I've already defined what a clock is, it's a thing that measures time. And I have no obligation to explain how a muon clock works, I just need to demonstrate that it exists.  In a similar way our ancestors didn't know why a sundial could measure time, all they needed to know is that it did. 

>How does observing a decay translate into reading a clock? AG

Huh? We know from experiment that the mean lifetime of a muon at rest is 2.1969811 ± 0.0000022 microseconds, and you don't understand how it would be possible to use that fact to make a very accurate clock? 

 John K Clark    See what's on my new list at  Extropolis

7gu

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[Brent Meeker]

On 6/15/2025 4:48 AM, John Clark wrote:

On Sat, Jun 14, 2025 at 11:42 PM Alan Grayson <agrays...@gmail.com> wrote:

...

>> do you have a better definition of time than "what a clock measures"? I don't. 

> Sure; time is caused by the existence of observed events. No events. No time. Nothing to do with clocks, AG 

The events have to be time-like separated, i.e. "at the same place" in some reference frame.

An event is defined as a specific space in 4D spacetime and a specific TIME. So if you use time in a definition of time you get into an infinite regress. 

>> If it was impossible to make a clock, if nothing occurred in a periodic manner, then the concept of time would be meaningless.

> A clock doesn't have to be periodic. It can be linear. It just needs to assign a unique real number to each event being  observed. AG

So you think a clock could be made by making a list of the position of every particle in the universe with respect to time, 

I doubt AG thinks that.  But linear clocks are not unusual in thought experiments.  Gallileo showed that balls rolling down an inclined plane could be used as a clock.

but without a clock how do you know what time it is? And even if you could somehow manage to make such a list, how could you know which way to read it? We can tell which way the arrow time is pointing because tomorrow will have more entropy than today, but that would no longer be true when the universe has reached heat death and entropy has risen to a maximum. 

 

>> The 4D shape of the resulting spacetime is determined by how the matter/energy is distributed, and its precise shape can be calculated with Einstein Field Equations, which uses 4D non-Euclidean tensor calculus. 

> What's obviously lacking is a physical mechanism to get to your conclusion. AG 

My problem is I don't know what sort of explanation would satisfy you. Give me an example of a phenomenon, ANY phenomenon physical or otherwise, that you feel has a satisfactory explanation and doesn't generate additional questions that are very obvious. 

> Insofar as you defend the Gospel, and vehemently I might add, although at some level you don't think GR is the end of the road, but emotionally you do. AG 

You know very well since I've posted it repeatedly that GR isn't the "end of the road" because it is inconsistent with quantum mechanics and it predicts unphysical infinities in many cases.

Brent

[Alan Grayson]

That was written to Clark! You've done that before, attributing something posted to the wrong source. AG  

[Alan Grayson]

On Sunday, June 15, 2025 at 5:48:50 AM UTC-6 John Clark wrote:

On Sat, Jun 14, 2025 at 11:42 PM Alan Grayson <agrays...@gmail.com> wrote:

>> General Relativity only has 3 postulates:
1) The speed of light is constant for all observers.
2) Gravitational mass and inertial mass are equivalent.

3) Equations expressing physical laws should say the same thing regardless of what coordinate system is used to describe 4D spacetime, even accelerating or rotating ones. 

 

> bodies in free fall, move along geodesic paths;

>> That fact is a logical consequence of the Equivalence Principle, which is the third postulate in the above. So no additional postulate is required. 

I fail to see how the EP implies geodesic motion. If true, the proof must be exceedingly subtle. You're just asserting something you believe is true, as distinguished from actually proving it. AG 

> Logical consequence? How so? AG 

The Equivalence Principle says an observer cannot distinguish between being in freefall near the surface of the Earth and being in intergalactic space far from any source of gravitation, if you release an object it will not move relative to your hand. If you are floating in intergalactic space then, because of the laws of geometry, that fact is represented by a straight line in flat Euclidean 4D spacetime. If you are falling to the Earth then, because of the laws of geometry, that fact is represented by a geodesic in curved non-Euclidean 4D spacetime. And Einstein's field equations can tell you precisely how much or how little spacetime needs to be curved.

If we assume mass/energy somehow causes a distortion in spacetime gemetry, and we hold a test mass spatially at rest in a gravity field, the question "why does it move" when released, cannot be answered by an appeal to the "laws of geometry". You really have to be more specific to answer this question. When motion resumes, why does it take the path it does, a geodesic, and not some other path? AG 

>> The Equivalence Principle (postulate #3) says in effect that gravity is the curvature of 4D spacetime, and if gravitational mass and inertial mass are equivalent (postulate #2) then the logical conclusion is that matter causes spacetime to curve. So no additional postulate is required.

> See above comment. Can you prove your logical conclusion?  AG

The Equivalence Principle says gravity is the curvature of 4D spacetime, and if gravitational mass and inertial mass are equivalent but mass doesn't cause 4D spacetime to curve, then how in the world could gravitational mass and inertial mass be equivalent?!

>> do you have a better definition of time than "what a clock measures"? I don't. 

> Sure; time is caused by the existence of observed events. No events. No time. Nothing to do with clocks, AG 

An event is defined as a specific space in 4D spacetime and a specific TIME. So if you use time in a definition of time you get into an infinite regress. 

I shouldn't have used the word "event" since it confused the issue. Earlier you wrote that time is what one reads on a clock, as if the existence of time depends on a clock. I was just trying to indicate that if, say, the universe had no mass and nothing was happening, then time wouldn't exist. The existence of time depends on things happening. Also, you've seen non-periodic clocks, say in the rollover from year 1999 to year 2000. It consisted of a set of numbers for year, month, day of year, and then hours, minutes, seconds elapsed in that day.  Such a clock could have continued its time keeping for as long as anyone wanted. AG

>> If it was impossible to make a clock, if nothing occurred in a periodic manner, then the concept of time would be meaningless.

To repeat; clocks do not have to be periodic, and this in no makes the concept of time meaningless. AG 

> A clock doesn't have to be periodic. It can be linear. It just needs to assign a unique real number to each event being  observed. AG

So you think a clock could be made by making a list of the position of every particle in the universe with respect to time, but without a clock how do you know what time it is? And even if you could somehow manage to make such a list, how could you know which way to read it? We can tell which way the arrow time is pointing because tomorrow will have more entropy than today, but that would no longer be true when the universe has reached heat death and entropy has risen to a maximum. 

 

>> The 4D shape of the resulting spacetime is determined by how the matter/energy is distributed, and its precise shape can be calculated with Einstein Field Equations, which uses 4D non-Euclidean tensor calculus. 

> What's obviously lacking is a physical mechanism to get to your conclusion. AG 

My problem is I don't know what sort of explanation would satisfy you.

A possible answer to my question might be the form of the equations of a geodesic path. I'm not sure, but space and time (here proper time) might be intertwinded in such a way that the spatial coordinates are forced to change because time continues to advance. In such case, the test particle would have move spatially, having been released in a gravity field. The movement itself would be geodesic since that's a postulate of GR. I don't see geodesic motion as following from the Equivalence Principle or the equivalence of inertial and gravitational mass. That is, IMO, your claim that geodesic motion follows from those facts is not convincing. AG

[John Clark]

On Sun, Jun 15, 2025 at 6:11 PM Brent Meeker <meeke...@gmail.com> wrote:

>> But electrons have no structure, and the decay of an electron from a high energy orbit to a lower energy orbit is what an atomic clock uses to keep time

 

> No, the time keeping function is the frequency the photons absorb, not the decay or absorption rate. 

That statement is at best confusing and at worst contradictory.  If an electron is capable of absorbing a photon that has a very specific frequency then it is also capable of emitting a photon that has that same very specific frequency. 

> The one used as a standard uses the cesium-133 transition between two specific energy levels that emit photons with frequency 9,192,631,770 Hz. 

That number is associated with the amount of energy an electron can have when it is very near a cesium 133 nucleus, and an electron has no internal structure as far as we know. When such an electron decays from a higher energy state to a lower one it emits a photon of light that has that frequency and the electron falls to a lower energy level. And such a low energy electron is equally capable of absorbing a photon with frequency 9,192,631,770 Hz and becoming a high energy electron. 

 John K Clark    See what's on my new list at  Extropolis

3s(

[John Clark]

On Sun, Jun 15, 2025 at 10:32 PM Alan Grayson <agrays...@gmail.com> wrote:

> I fail to see how the EP implies geodesic motion. If true, the proof must be exceedingly subtle.

I'll try one more time. If you are in freefall then you experience no gravity, so from your perspective your local spacetime is flat and things move in a path that is the shortest distance between two points, a Euclidean straight line. But from my perspective standing on the Earth's surface you are being affected by gravity and are moving through spacetime that is curved and non-Euclidean. The Equivalence Principle says both points of view are equally valid, but the only way that could be true is if I see you moving in a path that is the shortest distance between two points in 4D non-Euclidean space, and that is a geodesic.

> If we assume mass/energy somehow causes a distortion in spacetime gemetry, and we hold a test mass spatially at rest in a gravity field, the question "why does it move"

If you are holding an object and standing motionless on the Earth's surface then you and the object are still following a path through 4D non-Euclidean spacetime because both of you are still moving through time, but that path is NOT a geodesic because a force is being applied to the bottom of your feet. When you release the object its spacetime path suddenly changes to that of a geodesic while your path remains non-geodesic. And things on different spacetime paths is the definition of "movement".

>>My problem is I don't know what sort of explanation would satisfy you.

>A possible answer to my question might be the form of the equations of a geodesic path.

But that's what General Relativity's field equations do! They told Einstein what the geodesic would be in the curved non-Euclidean 4D spacetime 34 million miles from the sun, and it produced an orbit that was slightly different than the orbit Newton said it should have. 

 

> I'm not sure, but space and time (here proper time) might be intertwinded in such a way that the spatial coordinates are forced to change because time continues to advance.

But that's what a spacetime map is, it shows the relationship between space and time. If gravity is not involved then the map is flat and the relationship is simple; but if gravity is involved then that relationship changes and becomes more complicated because the map is curved, and the more gravity there is the more curvature there is.     

 John K Clark    See what's on my new list at  Extropolis

6hr

[Brent Meeker]

On 6/16/2025 3:51 AM, John Clark wrote:

On Sun, Jun 15, 2025 at 6:11 PM Brent Meeker <meeke...@gmail.com> wrote:

>> But electrons have no structure, and the decay of an electron from a high energy orbit to a lower energy orbit is what an atomic clock uses to keep time

 

> No, the time keeping function is the frequency the photons absorb, not the decay or absorption rate. 

That statement is at best confusing and at worst contradictory.  If an electron is capable of absorbing a photon that has a very specific frequency then it is also capable of emitting a photon that has that same very specific frequency. 

Right.  And a cesium clock uses a microwave oscillator which is tuned to be in resonance with the hyperfine transition. It is a corrective to you statement that it is the decay of electrons for one orbit to another that keeps time.  It is not their decay rate, which is what was discussed for muons, but the photons emitted is their decay that define the frequency.  In the context of muon decay as measure of time, it is your reference to decay electrons in an atom that is confusing at best.

Brent

[Alan Grayson]

On Monday, June 16, 2025 at 6:26:36 AM UTC-6 John Clark wrote:

On Sun, Jun 15, 2025 at 10:32 PM Alan Grayson <agrays...@gmail.com> wrote:

> I fail to see how the EP implies geodesic motion. If true, the proof must be exceedingly subtle.

I'll try one more time. If you are in freefall then you experience no gravity, so from your perspective your local spacetime is flat and things move in a path that is the shortest distance between two points, a Euclidean straight line. But from my perspective standing on the Earth's surface you are being affected by gravity and are moving through spacetime that is curved and non-Euclidean. The Equivalence Principle says both points of view are equally valid, but the only way that could be true is if I see you moving in a path that is the shortest distance between two points in 4D non-Euclidean space, and that is a geodesic.

Thank you. I have some questions about your "proof". First, why is the shortest distance between two point on a curved manifold a geodesic, and second, perhaps more important, how can your proof depend on a principle, the EP, which depends on an imprecise measuremen of tidal forces? AG 

> If we assume mass/energy somehow causes a distortion in spacetime gemetry, and we hold a test mass spatially at rest in a gravity field, the question "why does it move"

If you are holding an object and standing motionless on the Earth's surface then you and the object are still following a path through 4D non-Euclidean spacetime because both of you are still moving through time, but that path is NOT a geodesic because a force is being applied to the bottom of your feet. When you release the object its spacetime path suddenly changes to that of a geodesic while your path remains non-geodesic.

The logical necessity of that sudden change to a geodesic is not yet convincing. You claim it's related or caused by the EP, but the object suddenly shifting to that geodesic motion "knows" nothing about the EP and free fall in a gravity field. I prefer to reach that conclusion via a postulate, but I could be wrong. AG

And things on different spacetime paths is the definition of "movement".

As I wrote, and I think you agree, time doesn't exist because clocks do, but because there are things HAPPENING in the universe; for example, the motion of objects. The "movement" you describe above is caused by a gravitional mass in GR, so cannot be a vacuous universe within which time doesn't  exist. AG 

[Alan Grayson]

On Monday, June 16, 2025 at 6:26:36 AM UTC-6 John Clark wrote:

On Sun, Jun 15, 2025 at 10:32 PM Alan Grayson <agrays...@gmail.com> wrote:

> I fail to see how the EP implies geodesic motion. If true, the proof must be exceedingly subtle.

I'll try one more time. If you are in freefall then you experience no gravity, so from your perspective your local spacetime is flat and things move in a path that is the shortest distance between two points, a Euclidean straight line.

 

Really? The astronauts in the SS are free-falling in the Earth's gravity field and their path is not  a  straight line. AG

[John Clark]

On Tue, Jun 17, 2025 at 12:19 AM Alan Grayson <agrays...@gmail.com> wrote:

>> If you are in freefall then you experience no gravity, so from your perspective your local spacetime is flat and things move in a path that is the shortest distance between two points, a Euclidean straight line. But from my perspective standing on the Earth's surface you are being affected by gravity and are moving through spacetime that is curved and non-Euclidean. The Equivalence Principle says both points of view are equally valid, but the only way that could be true is if I see you moving in a path that is the shortest distance between two points in 4D non-Euclidean space, and that is a geodesic.

> Thank you. I have some questions about your "proof". First, why is the shortest distance between two point on a curved manifold a geodesic,

Because my iMac says the definition of a geodesic is "the shortest possible line between two points on a sphere or other curved surface".

 

> and second, perhaps more important, how can your proof depend on a principle, the EP, which depends on an imprecise measuremen of tidal forces? AG 

The Equivalence Principle is about local space where tidal forces are too small to detect. For human sized objects tidal forces can be safely ignored unless they are close to a black hole or a neutron star, and molecules are so small tidal forces don't become important until after they have passed through a black hole's Event Horizon and are approaching the singularity at the center. Einstein certainly didn't ignore tidal forces, his field equations can tell you exactly how strong they will be and in which direction they will stretch and compress things.   

>> If you are holding an object and standing motionless on the Earth's surface then you and the object are still following a path through 4D non-Euclidean spacetime because both of you are still moving through time, but that path is NOT a geodesic because a force is being applied to the bottom of your feet. When you release the object its spacetime path suddenly changes to that of a geodesic while your path remains non-geodesic.

> The logical necessity of that sudden change to a geodesic is not yet convincing.

Why not? When you're holding the object both of you are on the same path through 4D non-Euclidean spacetime, but when you let go the force that the object felt suddenly stops, so just as suddenly it starts following the path of a geodesic. But you are still experiencing a force on the bottom of your feet so you, unlike the object, are still on a non-geodesic path. And objects that are not on the same geodesic path through 4D non-Euclidean spacetime are moving relative to each other.

> You claim it's related or caused by the EP, but the object suddenly shifting to that geodesic motion "knows" nothing about the EP and free fall in a gravity field.

When you were a kid playing with marbles did you wonder how the marble knew to move when you applied force to it with your finger even though the marble was never taught Newtonian physics?  

> As I wrote, and I think you agree, time doesn't exist because clocks do, but because there are things HAPPENING in the universe;

The word "happening" can't be defined without implicitly or explicitly employing the concept of time. A clock doesn't have to be based on a periodic phenomenon (although from an engineering point of view it makes construction much easier and results in a more elegant device) but it does have to be based on a phenomenon that is predictable. If the universe consisted of nothing but random white noise then building a clock would be impossible and time would become a meaningless word. Some people think that is the state our universe is heading for, but I think it's too early to make such a bold prediction because we don't even know what 95% of the universe is made of. Time will tell.

John K Clark    See what's on my new list at  Extropolis

.^!

[John Clark]

On Tue, Jun 17, 2025 at 3:09 AM Alan Grayson <agrays...@gmail.com> wrote:

If you are in freefall then you experience no gravity, so from your perspective your local spacetime is flat and things move in a path that is the shortest distance between two points, a Euclidean straight line.

 

Really? The astronauts in the SS are free-falling in the Earth's gravity field and their path is not  a  straight line. AG

No force is being applied to the space station but it is not following a Euclidean straight line because it is not in flat Euclidean space, it is in curved 4D non-Euclidean spacetime and is following a geodesic path. In curved 4D non-Euclidean spacetime the shortest path between any two points along the space station's orbit is the space station's orbit itself.

   John K Clark    See what's on my new list at  Extropolis

Ill

[Alan Grayson]

OK, but then your previous comment, to which I responded, is false. AG 

Ill

[Alan Grayson]

Earlier you wrote that free falling in a gravity is like falling, or moving along a straight line as in a flat Euclidean space, but the SS is free falling in a gravity field and traveling in a curved path around the Earth.  Can't you just acknowledge your error? AG

Ill

[John Clark]

On Tue, Jun 17, 2025 at 2:13 PM Alan Grayson <agrays...@gmail.com> wrote:

>>>No force is being applied to the space station but it is not following a Euclidean straight line because it is not in flat Euclidean space, it is in curved 4D non-Euclidean spacetime and is following a geodesic path. In curved 4D non-Euclidean spacetime the shortest path between any two points along the space station's orbit is the space station's orbit itself.

  

>> OK, but then your previous comment, to which I responded, is false. AG 

> Earlier you wrote that free falling in a gravity is like falling, or moving along a straight line as in a flat Euclidean space, but the SS is free falling in a gravity field and traveling in a curved path around the Earth.  Can't you just acknowledge your error?

 

I'm perfectly capable of making an error but I don't know what I said, or what you think I said, that you're referring to. But I do know that the Equivalence Principle says if you have no contact with anything that is not in your local space then you can't tell if you're in the gravitational field in curved non-Euclidean spacetime or if you're accelerating in a straight line in flat Euclidean space. Spacetime has to be non-Euclidean if time is involved because when it comes to defining a distance the Pythagorean Theorem must be modified, you need to throw in a minus into the equation, D^2=X^2+Y^2+Z^2 - (cT)^2.

And intuitively it sort of makes sense that when it comes to distance the spatial and temporal coordinates should have opposite signs because the larger the spatial distance between 2 points the harder it would be to travel between them, but the larger the time you had to make that journey the easier it would be. 

And the speed of light "c" is just a conversion factor between space and time.  

 John K Clark    See what's on my new list at  Extropolis

dd0

[Alan Grayson]

On Tuesday, June 17, 2025 at 1:27:51 PM UTC-6 John Clark wrote:

On Tue, Jun 17, 2025 at 2:13 PM Alan Grayson <agrays...@gmail.com> wrote:

>>>No force is being applied to the space station but it is not following a Euclidean straight line because it is not in flat Euclidean space, it is in curved 4D non-Euclidean spacetime and is following a geodesic path. In curved 4D non-Euclidean spacetime the shortest path between any two points along the space station's orbit is the space station's orbit itself.

  

>> OK, but then your previous comment, to which I responded, is false. AG 

> Earlier you wrote that free falling in a gravity is like falling, or moving along a straight line as in a flat Euclidean space, but the SS is free falling in a gravity field and traveling in a curved path around the Earth.  Can't you just acknowledge your error?

 

I'm perfectly capable of making an error but I don't know what I said, or what you think I said, that you're referring to.

You were very clear, two messages back, that a body in free fall will experience straight line motion as in a flat Euclidean space. We know this is false, and I gave the example of the SS orbiting the Earth. AG

But I do know that the Equivalence Principle says if you have no contact with anything that is not in your local space then you can't tell if you're in the gravitational field in curved non-Euclidean spacetime or if you're accelerating in a straight line in flat Euclidean space.

But with sufficiently sensitive instruments one can tell the difference. For this reason I don't like to base arguments on the EP. AG

 

Spacetime has to be non-Euclidean if time is involved because when it comes to defining a distance the Pythagorean Theorem must be modified, you need to throw in a minus into the equation, D^2=X^2+Y^2+Z^2 - (cT)^2.

This fall far short of an argument. The definition above is certainly non-Euclidean insofar as the Pythogorean theorem is violated, but how does this fact imply geodesic motion, specifically from an initial state of being spatially at rest? AG  

[John Clark]

On Wed, Jun 18, 2025 at 10:54 AM Alan Grayson <agrays...@gmail.com> wrote:

>>> Earlier you wrote that free falling in a gravity is like falling, or moving along a straight line as in a flat Euclidean space, but the SS is free falling in a gravity field and traveling in a curved path around the Earth.  Can't you just acknowledge your error?

 

>> I'm perfectly capable of making an error but I don't know what I said, or what you think I said, that you're referring to.

> You were very clear, two messages back, that a body in free fall will experience straight line motion as in a flat Euclidean space.

As I said before,  the Equivalence Principle says if you have no contact with anything that is not in your local space, a.k.a. you are at a point, then you have no way of telling if you are moving in a Euclidean straight line through flat space or if you are in a gravitational field moving along a geodesic in curved non-Euclidean spacetime.  

>and I gave the example of the SS orbiting the Earth. AG

And as I explained in another post that you evidently have not bothered to read: "No force is being applied to the space station but it is not following a Euclidean straight line because it is not in flat Euclidean space, it is in curved 4D non-Euclidean spacetime and is following a geodesic path. In curved 4D non-Euclidean spacetime the shortest path between any two points along the space station's orbit is the space station's orbit itself.

>> But I do know that the Equivalence Principle says if you have no contact with anything that is not in your local space then you can't tell if you're in the gravitational field in curved non-Euclidean spacetime or if you're accelerating in a straight line in flat Euclidean space.

> But with sufficiently sensitive instruments one can tell the difference.

The sensitivity of the instrument is not the issue, no matter how sensitive it is if you pick a small enough region of space it will not be able to tell the difference, or alternately if the gravitational field producing object is sufficiently large. In both cases the limit of the difference is zero. Or are you implying that when he proposed the Equivalence Principle Albert Einstein, the greatest physicist in 300 years, was ignorant that a phenomenon called "tidal effects" existed?! 

>>Spacetime has to be non-Euclidean if time is involved because when it comes to defining a distance the Pythagorean Theorem must be modified, you need to throw in a minus into the equation, D^2=X^2+Y^2+Z^2 - (cT)^2.

> This fall far short of an argument. The definition above is certainly non-Euclidean insofar as the Pythogorean theorem is violated, but how does this fact imply geodesic motion, specifically from an initial state of being spatially at rest? AG 

I'm not sure what you mean because we're talking about relativity so I have to ask "spatially at resf" relative to what? I will say that if you're standing on the Earth's surface then you can NOT be in an initial state 

[Alan Grayson]

On Wednesday, June 18, 2025 at 10:55:53 AM UTC-6 John Clark wrote:

On Wed, Jun 18, 2025 at 10:54 AM Alan Grayson <agrays...@gmail.com> wrote:

>>> Earlier you wrote that free falling in a gravity is like falling, or moving along a straight line as in a flat Euclidean space, but the SS is free falling in a gravity field and traveling in a curved path around the Earth.  Can't you just acknowledge your error?

 

>> I'm perfectly capable of making an error but I don't know what I said, or what you think I said, that you're referring to.

> You were very clear, two messages back, that a body in free fall will experience straight line motion as in a flat Euclidean space.

As I said before,  the Equivalence Principle says if you have no contact with anything that is not in your local space, a.k.a. you are at a point, then you have no way of telling if you are moving in a Euclidean straight line through flat space or if you are in a gravitational field moving along a geodesic in curved non-Euclidean spacetime.  

>and I gave the example of the SS orbiting the Earth. AG

And as I explained in another post that you evidently have not bothered to read:

Evidently?  I indeed read it and I pointed out your error, which you completely forgot and correctly below. AG

 

"No force is being applied to the space station but it is not following a Euclidean straight line because it is not in flat Euclidean space, it is in curved 4D non-Euclidean spacetime and is following a geodesic path. In curved 4D non-Euclidean spacetime the shortest path between any two points along the space station's orbit is the space station's orbit itself.

>> But I do know that the Equivalence Principle says if you have no contact with anything that is not in your local space then you can't tell if you're in the gravitational field in curved non-Euclidean spacetime or if you're accelerating in a straight line in flat Euclidean space.

> But with sufficiently sensitive instruments one can tell the difference.

The sensitivity of the instrument is not the issue, no matter how sensitive it is if you pick a small enough region of space it will not be able to tell the difference,

Indeed, it IS the issue. The enclosed observer must drop two test masses and determine any tendency for them to converge. So if the region is small enough, and the measurements sufficiently approximate, tidal forces, if they exist, won't be detected. AG  

or alternately if the gravitational field producing object is sufficiently large. In both cases the limit of the difference is zero. Or are you implying that when he proposed the Equivalence Principle Albert Einstein, the greatest physicist in 300 years, was ignorant that a phenomenon called "tidal effects" existed?! 

No, but what I am stating as FACT, that what's called a PRINCIPLE, is an APPROXIMATION. This is Einstein's error; mistaking an approximation for a principle. AG

>>Spacetime has to be non-Euclidean if time is involved because when it comes to defining a distance the Pythagorean Theorem must be modified, you need to throw in a minus into the equation, D^2=X^2+Y^2+Z^2 - (cT)^2.

> This fall far short of an argument. The definition above is certainly non-Euclidean insofar as the Pythogorean theorem is violated, but how does this fact imply geodesic motion, specifically from an initial state of being spatially at rest? AG 

I'm not sure what you mean because we're talking about relativity so I have to ask "spatially at resf" relative to what?

Spatially at rest means spatially coordinates are not changing, as you are now, sitting on your butt! So, if an object which is falling toward the Sun is restrained by an external force and then let go, why does it move according to GR, why is that path geodesic? AG

I will say that if you're standing on the Earth's surface then you can NOT be in an initial state  

For simplicity, imagine standing on a non-rotating Earth as the initial condition. AG

[John Clark]

On Thu, Jun 19, 2025 at 1:47 AM Alan Grayson <agrays...@gmail.com> wrote:

>>> I gave the example of the SS orbiting the Earth. AG

>> And as I explained in another post that you evidently have not bothered to read:

> Evidently?  I indeed read it and I pointed out your error, which you completely forgot and correctly below. AG

Where is the error in the below?  You know of course that in flat 3D Euclidean space a straight line is a geodesic. Don't you? 

"No force is being applied to the space station but it is not following a Euclidean straight line because it is not in flat Euclidean space, it is in curved 4D non-Euclidean spacetime and is following a geodesic path. In curved 4D non-Euclidean spacetime the shortest path between any two points along the space station's orbit is the space station's orbit itself."

>> The sensitivity of the instrument is not the issue, no matter how sensitive it is if you pick a small enough region of space it will not be able to tell the difference,

> Indeed, it IS the issue. The enclosed observer must drop two test masses and determine any tendency for them to converge. So if the region is small enough, and the measurements sufficiently approximate, tidal forces, if they exist, won't be detected. AG 

There is a limit on the precision that any real instrument can have because it will always produce an error, let's call it Ω, that is greater than zero. So no matter how small Ω is, I can always produce a finite region of space in which your instrument cannot detect a difference between gravitational mass and inertial mass. And regardless of how large a volume of space you're interested in, provided it's not infinite, I can produce a large but finite sphere of matter that produces a gravitational field that your instrument cannot distinguish from acceleration. 

And if in your thought experiment you want to conjure up an instrument that has infinite precision even though that would be unphysical then, if you're playing fair, you should allow me to conjure up a sphere made of matter that is of infinite size even though that is unphysical.

 

> This is Einstein's error;

When somebody on the Internet claims to have found an error that Einstein made that nobody had noticed before my built-in bullshit detector goes off.  It goes off a lot. My bullshit detector may not be perfect but it has served me pretty damn well over the years. 

 

> mistaking an approximation for a principle. AG

The second law of thermodynamics is an approximation, but not only is it a superb approximation it is also the most important principle in physics.  

>  if an object which is falling toward the Sun is restrained by an external force and then let go, why does it move according to GR

The external force is provided to the object by your fingers, when you let go that external force suddenly stops and then just as suddenly the object starts following a geodesic path to the ground (not the sun) and then the force of the ground switches the object back to following a non-geodesic one which is the reason why it doesn't continue on to the center of the Earth. But during all of this you have continued to experience a force through the bottom of your feet. So you never stopped following a non-geodesic path and that's why the object is now on the ground and not still between your fingers.

> why is that path geodesic? AG

Both Newton and Einstein would give the same answer to that question. General Relativity and Newtonian Physics have one thing in common; they both say objects that are not experiencing a force always follow a path that is the shortest distance between two points, the only difference is in Newtonian physics were talking about flat 3-D Euclidean space (in which the geodesic is a Euclidean straight line with all the properties you were taught in high school) but in Einsteinian physics we're talking about curved 4D non-Euclidean spacetime where the geodesic is NOT a Euclidean straight line.

>> I will say that if you're standing on the Earth's surface then you can NOT be in an initial state  

> For simplicity, imagine standing on a non-rotating Earth as the initial condition. AG

That won't help, you would still be following a non-geodesic path because a force is still being applied to the bottom of your feet. That's why even if its rotation stopped you would still not fall to the center of the Earth. 

John K Clark    See what's on my new list at  Extropolis

gaa

[Alan Grayson]

On Thursday, June 19, 2025 at 5:38:47 AM UTC-6 John Clark wrote:

On Thu, Jun 19, 2025 at 1:47 AM Alan Grayson <agrays...@gmail.com> wrote:

>>> I gave the example of the SS orbiting the Earth. AG

>> And as I explained in another post that you evidently have not bothered to read:

> Evidently?  I indeed read it and I pointed out your error, which you completely forgot and correctly below. AG

Where is the error in the below?  

This is getting retarded. What you have below is correct. What you wrote a few messages ago was in error. Your error was your claim that free fall motion is like moving along a straight line in flat space. I suppose, loosely speaking I could agree. AG

 

You know of course that in flat 3D Euclidean space a straight line is a geodesic. Don't you? 

"No force is being applied to the space station but it is not following a Euclidean straight line because it is not in flat Euclidean space, it is in curved 4D non-Euclidean spacetime and is following a geodesic path. In curved 4D non-Euclidean spacetime the shortest path between any two points along the space station's orbit is the space station's orbit itself."

>> The sensitivity of the instrument is not the issue, no matter how sensitive it is if you pick a small enough region of space it will not be able to tell the difference,

> Indeed, it IS the issue. The enclosed observer must drop two test masses and determine any tendency for them to converge. So if the region is small enough, and the measurements sufficiently approximate, tidal forces, if they exist, won't be detected. AG 

There is a limit on the precision that any real instrument can have because it will always produce an error, let's call it Ω, that is greater than zero. So no matter how small Ω is, I can always produce a finite region of space in which your instrument cannot detect a difference between gravitational mass and inertial mass. 

If a man is 6 ft tall, and you put him into an elevator of volume 1 cubic inch, will he be able to measure the convergence of two test particles he drops??? Sure, you can't always show the gravity and acceleration are equivalent, because they are not. AG

 

And regardless of how large a volume of space you're interested in, provided it's not infinite, I can produce a large but finite sphere of matter that produces a gravitational field that your instrument cannot distinguish from acceleration. 

And if in your thought experiment you want to conjure up an instrument that has infinite precision even though that would be unphysical then, if you're playing fair, you should allow me to conjure up a sphere made of matter that is of infinite size even though that is unphysical.

 

> This is Einstein's error;

When somebody on the Internet claims to have found an error that Einstein made that nobody had noticed before my built-in bullshit detector goes off.  It goes off a lot. My bullshit detector may not be perfect but it has served me pretty damn well over the years. 

I have no idea, nor do I care if anyone else has claimed that the EP is just an approximation, not truly a principle. AG 

 

> mistaking an approximation for a principle. AG

The second law of thermodynamics is an approximation, but not only is it a superb approximation it is also the most important principle in physics.  

It's not an approximation IMO, whereas the EP is. The latter appears to be true in some cases, and not in others, depening on the space allowed for the experiment and the accuracy of the measuring device. AG 

>  if an object which is falling toward the Sun is restrained by an external force and then let go, why does it move according to GR

The external force is provided to the object by your fingers, when you let go that external force suddenly stops and then just as suddenly the object starts following a geodesic path to the ground (not the sun) and then the force of the ground switches the object back to following a non-geodesic one which is the reason why it doesn't continue on to the center of the Earth. But during all of this you have continued to experience a force through the bottom of your feet. So you never stopped following a non-geodesic path and that's why the object is now on the ground and not still between your fingers.

> why is that path geodesic? AG

Both Newton and Einstein would give the same answer to that question. General Relativity and Newtonian Physics have one thing in common; they both say objects that are not experiencing a force always follow a path that is the shortest distance between two points, the only difference is in Newtonian physics were talking about flat 3-D Euclidean space (in which the geodesic is a Euclidean straight line with all the properties you were taught in high school) but in Einsteinian physics we're talking about curved 4D non-Euclidean spacetime where the geodesic is NOT a Euclidean straight line.

Is that a postulate of GR? In GR, why does the test particle move when it is released from an external force while in a gravitational field, and take a geodesic path? You keep claiming the path is geodesic in GR, but can't say why. AG 

>> I will say that if you're standing on the Earth's surface then you can NOT be in an initial state  

> For simplicity, imagine standing on a non-rotating Earth as the initial condition. AG

That won't help, you would still be following a non-geodesic path because a force is still being applied to the bottom of your feet.

Sorry, but lately you seem a bit retarded. I know the path is non-geodesic in that case. Nowwhere did I deny that. I was answering your question of what "spatially at rest" means. I figured if the Earth is rotating, you could claim a person standing on the Earth would have his spatial coordinates change. AG

[John Clark]

On Thu, Jun 19, 2025 at 10:07 AM Alan Grayson <agrays...@gmail.com> wrote:

>>>>> I gave the example of the SS orbiting the Earth. AG

>>>> And as I explained in another post that you evidently have not bothered to read:

>>> Evidently?  I indeed read it and I pointed out your error, which you completely forgot and correctly below. AG

>> Where is the error in the below?  

> This is getting retarded. What you have below is correct. What you wrote a few messages ago was in error. Your error was your claim that free fall motion is like moving along a straight line in flat space. I suppose, loosely speaking I could agree. AG

 A free fall through 4D non-Euclidean curved spacetime IS like moving in a Euclidean straight line through flat 3-D space in that an observer couldn't tell the difference because gravitational mass and inertial mass are equivalent.  

>> There is a limit on the precision that any real instrument can have because it will always produce an error, let's call it Ω, that is greater than zero. So no matter how small Ω is, I can always produce a finite region of space in which your instrument cannot detect a difference between gravitational mass and inertial mass. 

> If a man is 6 ft tall, and you put him into an elevator of volume 1 cubic inch, will he be able to measure the convergence of two test particles he drops???

Well, I do agree with one thing you said, "this is getting retarded". I was getting tired of your strawman equivalence principle, so I asked Claude to give me the full definition and this is what he said: 

"The full, rigorous equivalence principle has several forms, but the most precise is the Einstein Equivalence Principle, which states:

1. Weak Equivalence Principle: All objects fall at the same rate in a gravitational field (regardless of their composition)
2. Local Position Invariance: The outcome of any local non-gravitational experiment is independent of where and when it's performed
3. Local Lorentz Invariance: The outcome of any local non-gravitational experiment is independent of the velocity of the (freely falling) reference frame

The key word here is LOCAL. The equivalence principle was never meant to apply globally - it specifically applies to small enough regions of spacetime where tidal effects become negligible.

Einstein himself was well aware of tidal effects. He knew that if you made your "elevator" big enough, you'd eventually detect the slight differences in gravitational field strength and direction across the elevator. That's exactly why the principle is formulated as a local statement.

Think of it this way: in any small enough neighborhood of spacetime, you can always find a coordinate system where gravity "disappears" locally. But "small enough" means small enough that tidal effects don't matter for whatever experiment you're doing."

>> The second law of thermodynamics is an approximation, but not only is it a superb approximation it is also the most important principle in physics.  

> It's not an approximation IMO,

Then your opinion is dead wrong because the second law of thermodynamics is an approximation , and there is no doubt about it.  

>>>>The external force is provided to the object by your fingers, when you let go that external force suddenly stops and then just as suddenly the object starts following a geodesic path to the ground (not the sun) and then the force of the ground switches the object back to following a non-geodesic one which is the reason why it doesn't continue on to the center of the Earth. But during all of this you have continued to experience a force through the bottom of your feet. So you never stopped following a non-geodesic path and that's why the object is now on the ground and not still between your fingers.

>>> why is that path geodesic? AG

>> Both Newton and Einstein would give the same answer to that question. General Relativity and Newtonian Physics have one thing in common; they both say objects that are not experiencing a force always follow a path that is the shortest distance between two points, the only difference is in Newtonian physics were talking about flat 3-D Euclidean space (in which the geodesic is a Euclidean straight line with all the properties you were taught in high school) but in Einsteinian physics we're talking about curved 4D non-Euclidean spacetime where the geodesic is NOT a Euclidean straight line.

> Is that a postulate of GR?

It's a postulate of both General Relativity and of Newtonian physics that things that are not acted upon by a force move in a geodesic, a straight line is just the particular geodesic you get in flat Euclidean space. 

 

> In GR, why does the test particle move when it is released from an external force while in a gravitational field, and take a geodesic path?

You've asked that question before and I've answered that question before. I'm not going to give a new answer until you ask a new question.  

> You keep claiming the path is geodesic in GR, but can't say why. AG

It's the same reason the path is a geodesic in Newtonian Physics for any object that is not being acted upon by a force.    

> lately you seem a bit retarded.

That's two "retarded" in one post. It's always the same with you, whenever a new topic comes up you start by asking questions that are friendly and sometimes even interesting, but then after just a few exchanges you get personal, things get really nasty, and the conversation degenerates into an insult contest.   

 John K Clark    See what's on my new list at  Extropolis

urn

[Alan Grayson]

On Thursday, June 19, 2025 at 9:45:07 AM UTC-6 John Clark wrote:

On Thu, Jun 19, 2025 at 10:07 AM Alan Grayson <agrays...@gmail.com> wrote:

>>>>> I gave the example of the SS orbiting the Earth. AG

>>>> And as I explained in another post that you evidently have not bothered to read:

>>> Evidently?  I indeed read it and I pointed out your error, which you completely forgot and correctly below. AG

>> Where is the error in the below?  

> This is getting retarded. What you have below is correct. What you wrote a few messages ago was in error. Your error was your claim that free fall motion is like moving along a straight line in flat space. I suppose, loosely speaking I could agree. AG

 A free fall through 4D non-Euclidean curved spacetime IS like moving in a Euclidean straight line through flat 3-D space in that an observer couldn't tell the difference because gravitational mass and inertial mass are equivalent.  

>> There is a limit on the precision that any real instrument can have because it will always produce an error, let's call it Ω, that is greater than zero. So no matter how small Ω is, I can always produce a finite region of space in which your instrument cannot detect a difference between gravitational mass and inertial mass. 

What has the latter fact to do with whether tidal forces can be determined; that is, that gravitation and acceleration are indistinguishable? Earlier you seemed to think this was key, but if true the argument is subtle, and merely saying it's so, is insufficient as a argument. AG 

> If a man is 6 ft tall, and you put him into an elevator of volume 1 cubic inch, will he be able to measure the convergence of two test particles he drops???

Well, I do agree with one thing you said, "this is getting retarded". I was getting tired of your strawman equivalence principle, 

 

An example of your abuse. AG

 

so I asked Claude to give me the full definition and this is what he said: 

"The full, rigorous equivalence principle has several forms, but the most precise is the Einstein Equivalence Principle, which states:

1. Weak Equivalence Principle: All objects fall at the same rate in a gravitational field (regardless of their composition)
2. Local Position Invariance: The outcome of any local non-gravitational experiment is independent of where and when it's performed
3. Local Lorentz Invariance: The outcome of any local non-gravitational experiment is independent of the velocity of the (freely falling) reference frame

The key word here is LOCAL. The equivalence principle was never meant to apply globally - it specifically applies to small enough regions of spacetime where tidal effects become negligible.

Einstein himself was well aware of tidal effects. He knew that if you made your "elevator" big enough, you'd eventually detect the slight differences in gravitational field strength and direction across the elevator. That's exactly why the principle is formulated as a local statement.

Think of it this way: in any small enough neighborhood of spacetime, you can always find a coordinate system where gravity "disappears" locally. But "small enough" means small enough that tidal effects don't matter for whatever experiment you're doing."

I agree. "Local" resolves this issue. AG 

>> The second law of thermodynamics is an approximation, but not only is it a superb approximation it is also the most important principle in physics.  

> It's not an approximation IMO,

Then your opinion is dead wrong because the second law of thermodynamics is an approximation , and there is no doubt about it.  

If I recall correctly, the Second Law states that the entropy of closed system never decreases. Where is the approximation or a counter example? AG 

>>>>The external force is provided to the object by your fingers, when you let go that external force suddenly stops and then just as suddenly the object starts following a geodesic path to the ground (not the sun) and then the force of the ground switches the object back to following a non-geodesic one which is the reason why it doesn't continue on to the center of the Earth. But during all of this you have continued to experience a force through the bottom of your feet. So you never stopped following a non-geodesic path and that's why the object is now on the ground and not still between your fingers.

>>> why is that path geodesic? AG

>> Both Newton and Einstein would give the same answer to that question. General Relativity and Newtonian Physics have one thing in common; they both say objects that are not experiencing a force always follow a path that is the shortest distance between two points, the only difference is in Newtonian physics were talking about flat 3-D Euclidean space (in which the geodesic is a Euclidean straight line with all the properties you were taught in high school) but in Einsteinian physics we're talking about curved 4D non-Euclidean spacetime where the geodesic is NOT a Euclidean straight line.

> Is that a postulate of GR?

It's a postulate of both General Relativity and of Newtonian physics that things that are not acted upon by a force move in a geodesic, a straight line is just the particular geodesic you get in flat Euclidean space. 

Earlier, I'm pretty sure you denied it was a postulate. More important from my pov, is why it moves from being spatially at rest if there are no forces acting in GR. AG 

 

> In GR, why does the test particle move when it is released from an external force while in a gravitational field, and take a geodesic path?

You've asked that question before and I've answered that question before. I'm not going to give a new answer until you ask a new question.  

> You keep claiming the path is geodesic in GR, but can't say why. AG

It's the same reason the path is a geodesic in Newtonian Physics for any object that is not being acted upon by a force.    

> lately you seem a bit retarded.

That's two "retarded" in one post. It's always the same with you, whenever a new topic comes up you start by asking questions that are friendly and sometimes even interesting, but then after just a few exchanges you get personal, things get really nasty, and the conversation degenerates into an insult contest.  

You're the one who starts the abuse but are unaware of it. AG 

[John Clark]

On Thu, Jun 19, 2025 at 4:16 PM Alan Grayson <agrays...@gmail.com> wrote:

>> There is a limit on the precision that any real instrument can have because it will always produce an error, let's call it Ω, that is greater than zero. So no matter how small Ω is, I can always produce a finite region of space in which your instrument cannot detect a difference between gravitational mass and inertial mass. 

> What has the latter fact to do with whether tidal forces can be determined; that is, that gravitation and acceleration are indistinguishable?

If the volume of space is so small or the gravity producing object is so large that tidal forces are negligible then gravitational mass and inertial mass are indistinguishable. And if standing on the surface of the Earth and accelerating in a rocket in intergalactic space is indistinguishable then the  Equivalence Principle is true.

 

> Earlier you seemed to think this was key,

It is.  

 

> but if true the argument is subtle,

I think the argument is obvious.  

 >> I was getting tired of your strawman equivalence principle, 

 

> An example of your abuse. AG

Abuse? Saying somebody is giving a strawman argument is not equivalent to saying that somebody is retarded. Twice. In the same post. Especially when it really is a strawman argument.   

>> so I asked Claude to give me the full definition and this is what he said: 

"The full, rigorous equivalence principle has several forms, but the most precise is the Einstein Equivalence Principle, which states:

1. Weak Equivalence Principle: All objects fall at the same rate in a gravitational field (regardless of their composition)
2. Local Position Invariance: The outcome of any local non-gravitational experiment is independent of where and when it's performed
3. Local Lorentz Invariance: The outcome of any local non-gravitational experiment is independent of the velocity of the (freely falling) reference frame

The key word here is LOCAL. The equivalence principle was never meant to apply globally - it specifically applies to small enough regions of spacetime where tidal effects become negligible.

Einstein himself was well aware of tidal effects. He knew that if you made your "elevator" big enough, you'd eventually detect the slight differences in gravitational field strength and direction across the elevator. That's exactly why the principle is formulated as a local statement.

Think of it this way: in any small enough neighborhood of spacetime, you can always find a coordinate system where gravity "disappears" locally. But "small enough" means small enough that tidal effects don't matter for whatever experiment you're doing."

>I agree. "Local" resolves this issue. AG 

Then what on earth are we arguing about?! I've been using that word constantly.  

> If I recall correctly, the Second Law states that the entropy of closed system never decreases.

The word "never" in that statement of the second law is itself an approximation of the formal definition of the second law, to be precise it should have said "almost never". There are an astronomical number of different ways an egg can be broken, but there is only one way an egg can be unbroken, so statistically it's astronomically more likely you will see an egg being broken rather than see a broken egg becoming unbroken. That's why when you look at a movie that is being run backwards, actions look ridiculous, but the actions don't look like random white noise because they are still following the laws of both Newtonian and Einsteinian physics. 

If you want to understand where the arrow of time comes from you've got to understand the science of thermodynamics, and the foundations of that science is in logic and the mathematical properties of probability. That's why I can imagine a universe in which the law of the conservation of mass/energy is untrue, or quantum mechanics or relativity is untrue; but I can no more imagine a universe in which the second law is untrue than I can imagine a universe in which 2+2=5.   

>> It's a postulate of both General Relativity and of Newtonian physics that things that are not acted upon by a force move in a geodesic, a straight line is just the particular geodesic you get in flat Euclidean space. 

> Earlier, I'm pretty sure you denied it was a postulate.

I'm pretty sure I said it's because the Principle Of Least Action is true, and the best I could do to explain why the Principle Of Least Action is true is just to say that nature wants to be lazy and I don't know why nature wants to be lazy. I'm also pretty sure I said that every iterated sequence of how or why questions either goes on forever or terminates in a brute fact.  

  John K Clark    See what's on my new list at  Extropolis

aps

[Brent Meeker]

On 6/20/2025 4:31 AM, John Clark wrote:

If the volume of space is so small or the gravity producing object is so large that tidal forces are negligible then gravitational mass and inertial mass are indistinguishable.

Suppose those conditions are NOT met.  What then do you mean by being able to "distinguish" (have different values?) gravitational and inertial mass?

Brent