Energy isn't conserved in GR

[Alan Grayson]

But the question persists; when photons redden as the universe expands, where does the lost energy go? AG

[John Clark]

On Sun, Jun 1, 2025 at 3:16 AM Alan Grayson <agrays...@gmail.com> wrote:

> But the question persists; when photons redden as the universe expands, where does the lost energy go? AG

The energy doesn't go anywhere, it's just destroyed, energy is not conserved at the cosmic level. Noether's theorem says if there's a symmetry, then there's a corresponding conservation law (but the reverse does not necessarily hold, if there is a conservation law there may or may not be a corresponding symmetry). 

In the case of energy Noether says the corresponding symmetry is time, at the cosmic scale if energy is conserved then the universe should look the same from one time to another, but if the universe is expanding it doesn't look the same from one time to another, and if the universe is accelerating then time is even less symmetrical. So energy is not conserved globally, however it's still true that at the local level if things are at thermal equilibrium then the amount of energy entering a finite volume of space will equal the amount of energy leaving that volume.

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

7ma

 

[Brent Meeker]

That's not what Noether's theorem says.  Time symmetry means that if you put a time shift in the equations of evolution, then equations remain valid.  Not that the system state is static.  In your interpretation any process that conserved energy would leave the system unchanged and explosions wouldn't conserve energy.

Brent

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[John Clark]

On Sun, Jun 1, 2025 at 8:35 PM Brent Meeker <meeke...@gmail.com> wrote:

> That's not what Noether's theorem says.  Time symmetry means that if you put a time shift in the equations of evolution, then equations remain valid. 

 That's what I said! If there's a symmetry then there's a corresponding conservation law, equations remain valid because something has been conserved, and in the case of time it is energy. 

 

> In your interpretation any process that conserved energy would leave the system unchanged

And I also said that if all you know is that there is a conservation law then Noether's theorem can you tell you nothing. It only works one way. 

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

ugg

On 6/1/2025 4:38 AM, John Clark wrote:

On Sun, Jun 1, 2025 at 3:16 AM Alan Grayson <agrays...@gmail.com> wrote:

> But the question persists; when photons redden as the universe expands, where does the lost energy go? AG

The energy doesn't go anywhere, it's just destroyed, energy is not conserved at the cosmic level. Noether's theorem says if there's a symmetry, then there's a corresponding conservation law (but the reverse does not necessarily hold, if there is a conservation law there may or may not be a corresponding symmetry). 

In the case of energy Noether says the corresponding symmetry is time, at the cosmic scale if energy is conserved then the universe should look the same from one time to another, but if the universe is expanding it doesn't look the same from one time to another, and if the universe is accelerating then time is even less symmetrical. So energy is not conserved globally, however it's still true that at the local level if things are at thermal equilibrium then the amount of energy entering a finite volume of space will equal the amount of energy leaving that volume.

 

--

[Brent Meeker]

On 6/1/2025 6:26 PM, John Clark wrote:

On Sun, Jun 1, 2025 at 8:35 PM Brent Meeker <meeke...@gmail.com> wrote:

> That's not what Noether's theorem says.  Time symmetry means that if you put a time shift in the equations of evolution, then equations remain valid. 

 That's what I said! If there's a symmetry then there's a corresponding conservation law, equations remain valid because something has been conserved, and in the case of time it is energy.

What I was objecting to is you wrote, "... if energy is conserved then the universe should look the same from one time to another..." which is the converse of your (correct) statement below.  This is an interesting point.  Expansion of the universe is a failure of time symmetry that allows, but does not imply, failure of energy conservation.

Brent

 

> In your interpretation any process that conserved energy would leave the system unchanged

And I also said that if all you know is that there is a conservation law then Noether's theorem can you tell you nothing. It only works one way. 

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

ugg

On 6/1/2025 4:38 AM, John Clark wrote:

On Sun, Jun 1, 2025 at 3:16 AM Alan Grayson <agrays...@gmail.com> wrote:

> But the question persists; when photons redden as the universe expands, where does the lost energy go? AG

The energy doesn't go anywhere, it's just destroyed, energy is not conserved at the cosmic level. Noether's theorem says if there's a symmetry, then there's a corresponding conservation law (but the reverse does not necessarily hold, if there is a conservation law there may or may not be a corresponding symmetry). 

In the case of energy Noether says the corresponding symmetry is time, at the cosmic scale if energy is conserved then the universe should look the same from one time to another, but if the universe is expanding it doesn't look the same from one time to another, and if the universe is accelerating then time is even less symmetrical. So energy is not conserved globally, however it's still true that at the local level if things are at thermal equilibrium then the amount of energy entering a finite volume of space will equal the amount of energy leaving that volume.

 

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[John Clark]

On Mon, Jun 2, 2025 at 12:44 AM Brent Meeker <meeke...@gmail.com> wrote:

>>> That's not what Noether's theorem says.  Time symmetry means that if you put a time shift in the equations of evolution, then equations remain valid. 

 >>That's what I said! If there's a symmetry then there's a corresponding conservation law, equations remain valid because something has been conserved, and in the case of time it is energy.

>What I was objecting to is you wrote, "... if energy is conserved then the universe should look the same from one time to another..." which is the converse of your (correct) statement below.  This is an interesting point.  Expansion of the universe is a failure of time symmetry that allows, but does not imply, failure of energy conservation.

OK, we are in agreement.  

> And I also said that if all you know is that there is a conservation law then Noether's theorem can tell you nothing. It only works one way. 

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

iww 

[Alan Grayson]

On Sunday, June 1, 2025 at 5:38:51 AM UTC-6 John Clark wrote:

On Sun, Jun 1, 2025 at 3:16 AM Alan Grayson <agrays...@gmail.com> wrote:

> But the question persists; when photons redden as the universe expands, where does the lost energy go? AG

The energy doesn't go anywhere, it's just destroyed,

 Can't those photons being reddened as the universe expands, emit energy? How can the energy go nowhere? AG

[Alan Grayson]

On Sunday, June 1, 2025 at 5:38:51 AM UTC-6 John Clark wrote:

On Sun, Jun 1, 2025 at 3:16 AM Alan Grayson <agrays...@gmail.com> wrote:

> But the question persists; when photons redden as the universe expands, where does the lost energy go? AG

The energy doesn't go anywhere, it's just destroyed,

I don't get it. How can energy be destroyed? Destroyed by what? AG 

[John Clark]

On Wed, Jun 4, 2025 at 9:15 PM Alan Grayson <agrays...@gmail.com> wrote:

>>> But the question persists; when photons redden as the universe expands, where does the lost energy go? AG

>> The energy doesn't go anywhere, it's just destroyed,

> I don't get it. How can energy be destroyed? Destroyed by what? AG 

The short answer is energy is destroyed by the expansion of the universe because electromagnetic waves with long wavelengths have less energy than electromagnetic waves with short wavelengths. But there's something deeper going on.

 

It's a logical necessity that 2+2 be equal to 4, but there is no such logical necessity that energy be conserved. And if the energy was preserved I could ask "preserved by what?".  

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

303

[Alan Grayson]

On Thursday, June 5, 2025 at 5:09:45 AM UTC-6 John Clark wrote:

On Wed, Jun 4, 2025 at 9:15 PM Alan Grayson <agrays...@gmail.com> wrote:

>>> But the question persists; when photons redden as the universe expands, where does the lost energy go? AG

>> The energy doesn't go anywhere, it's just destroyed,

> I don't get it. How can energy be destroyed? Destroyed by what? AG 

The short answer is energy is destroyed by the expansion of the universe because electromagnetic waves with long wavelengths have less energy than electromagnetic waves with short wavelengths. But there's something deeper going on.

I see you want to be stupid. No one has ever shown that photons have spatial extent. The frequency is just a number that defines a photon's energy. Nothing to do with an extended wave. Just a number. The stretching of the wave as the universe expands is foolish explanation of the reddening. AG 

 

It's a logical necessity that 2+2 be equal to 4, but there is no such logical necessity that energy be conserved.

On the contrary, in classical mechanics one can show that the sum of kinetic and potential energy is constant. AG 

And if the energy was preserved I could ask "preserved by what?".  

Stupid question. Its sum is the same before and after interactions. There's no "thing" that preserves it. I was speaking loosely when I asked what destroys it, and you were so anxious to prove me mistaken, that you couldn't resist shooting off your mouth. This list isn't the place for speculation. Ultimately, you're a conformist who hates any type of speculation. AG  

[Brent Meeker]

On 6/4/2025 6:15 PM, Alan Grayson wrote:

On Sunday, June 1, 2025 at 5:38:51 AM UTC-6 John Clark wrote:

On Sun, Jun 1, 2025 at 3:16 AM Alan Grayson <agrays...@gmail.com> wrote:

> But the question persists; when photons redden as the universe expands, where does the lost energy go? AG

The energy doesn't go anywhere, it's just destroyed,

I don't get it. How can energy be destroyed? Destroyed by what? AG

Think of it this way.  You're floating in space.  Space is filled with randomly distributed tennis balls and they are all slowly receding away from one another.  So the further away they are, the faster they are receding from you. A mile away they are receding at 1mph.  Two miles away they are receding at 2mph.  Ten miles away they are receding from you at 10mph, etc.  This is uniform expansion of tennis ball distribution.  You take your tennis racket and hit a 130mph smash.  It goes flying off thru space, passing by the slowly moving tennis balls.  But at 100 miles the tennis balls are going 100mph and your ball is only going by them at 30mph.  At 125mi your ball is only passing the other balls at five mph.  So will it take your ball another hour to reach the balls going 130mph?  No it will never reach the balls going 130mph, it only asymptotically approaches them. 

When you hit the ball you gave it a big chunk of kinetic energy relative to you and the balls near you.  Now the ball is essentially stationary relative to the balls around it.  What happened to that kinetic energy?  Nothing...but it's relative.  So it still exists relative to you.  But in fact it also has the same kinetic energy relative to any other balls that are 130mi away in any direction. Every ball has that kinetic energy relative to other balls 130mi away.  So the kinetic energy is not really located just relative to you.  It's been absorbed into the overall expansion of tennis balls.

Brent

energy is not conserved at the cosmic level. Noether's theorem says if there's a symmetry, then there's a corresponding conservation law (but the reverse does not necessarily hold, if there is a conservation law there may or may not be a corresponding symmetry). 

In the case of energy Noether says the corresponding symmetry is time, at the cosmic scale if energy is conserved then the universe should look the same from one time to another, but if the universe is expanding it doesn't look the same from one time to another, and if the universe is accelerating then time is even less symmetrical. So energy is not conserved globally, however it's still true that at the local level if things are at thermal equilibrium then the amount of energy entering a finite volume of space will equal the amount of energy leaving that volume.

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

7ma

 

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[John Clark]

On Thu, Jun 5, 2025 at 1:35 PM Alan Grayson <agrays...@gmail.com> wrote:

 

> The frequency is just a number that defines a photon's energy. Nothing to do with an extended wave.

Nothing? Nothing at all? Not quite. There is a simple equation that shows the relationship between the frequency of light, its wavelength and its speed, its  c=λ⋅f. And because of that very simple relationship you can easily perform a fun experiment at home:

Measuring the speed of light with a microwave oven and a chocolate bar

If frequency and wavelength are just numbers and have no relationship with physical reality then I don't see how you could use them to calculate the speed of light which most certainly does have a relationship with physical reality.

 

>> It's a logical necessity that 2+2 be equal to 4, but there is no such logical necessity that energy be conserved.

> On the contrary, in classical mechanics one can show that the sum of kinetic and potential energy is constant. AG 

The conservation of energy is an empirical observation, it is not a logical necessity. That's why the ancient Greeks were able to figure out that there was no largest prime number but they were unable to figure out that energy was conserved, they were good theoreticians but lousy experimentalists.

>> And if the energy was preserved I could ask "preserved by what?".  

Stupid question. Its sum is the same before and after interactions.

It's easy for me to imagine a universe that had different laws of physics in which interactions did NOT conserve energy, but I find it impossible to imagine a universe in which 2+2 is equal to anything except 4, or one that had a largest prime number. 

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

ca2

[Alan Grayson]

On Thursday, June 5, 2025 at 2:53:01 PM UTC-6 John Clark wrote:

On Thu, Jun 5, 2025 at 1:35 PM Alan Grayson <agrays...@gmail.com> wrote:

 

> The frequency is just a number that defines a photon's energy. Nothing to do with an extended wave.

Nothing? Nothing at all? Not quite. There is a simple equation that shows the relationship between the frequency of light, its wavelength and its speed, its  c=λ⋅f. And because of that very simple relationship you can easily perform a fun experiment at home:

Measuring the speed of light with a microwave oven and a chocolate bar

If frequency and wavelength are just numbers and have no relationship with physical reality then I don't see how you could use them to calculate the speed of light which most certainly does have a relationship with physical reality.

Stop distorting my words, aka lying. I never claimed frequency and wavelength have no relation to physical reality. But as far as I know, it's never been shown that photons have spatial extention. If that's the case, then those parameters just allow us to calculate energy. AG  

>> It's a logical necessity that 2+2 be equal to 4, but there is no such logical necessity that energy be conserved.

> On the contrary, in classical mechanics one can show that the sum of kinetic and potential energy is constant. AG 

The conservation of energy is an empirical observation, it is not a logical necessity.

 

It is a logical necessity in Classical Mechanics, as well as being an empirical observation. AG 

That's why the ancient Greeks were able to figure out that there was no largest prime number but they were unable to figure out that energy was conserved, they were good theoreticians but lousy experimentalists.

There were some good experimentalists in ancient Greece, such as the fellow who made a decent measurement of the circumference of the Earth. Can't recall his name. AG 

>> And if the energy was preserved I could ask "preserved by what?".  

Stupid question. Its sum is the same before and after interactions.

It's easy for me to imagine a universe that had different laws of physics in which interactions did NOT conserve energy, but I find it impossible to imagine a universe in which 2+2 is equal to anything except 4, or one that had a largest prime number. 

If your intuition is so good, how about explaining what the LT is predicting wrt time dilation; that is, which imaginary clock is being dilated, surely not the one in the muon's frame, assuming such a clock exists. AG 

[Brent Meeker]

On 6/5/2025 6:57 PM, Alan Grayson wrote:

On Thursday, June 5, 2025 at 2:53:01 PM UTC-6 John Clark wrote:

On Thu, Jun 5, 2025 at 1:35 PM Alan Grayson <agrays...@gmail.com> wrote:

 

> The frequency is just a number that defines a photon's energy. Nothing to do with an extended wave.

Nothing? Nothing at all? Not quite. There is a simple equation that shows the relationship between the frequency of light, its wavelength and its speed, its  c=λ⋅f. And because of that very simple relationship you can easily perform a fun experiment at home:

Measuring the speed of light with a microwave oven and a chocolate bar

If frequency and wavelength are just numbers and have no relationship with physical reality then I don't see how you could use them to calculate the speed of light which most certainly does have a relationship with physical reality.

 

As far as I know, it's never been shown that photons have spatial extent. So, the frequency and wavelength are just numbers that allow us to calculate a photon's energy. AG

You're directly measuring the wavelength.  The speed of light is just a conversion constant.  So you're inferring the frequency of the microwave.

Brent

[Alan Grayson]

Then the photon has extention in space? Is this your claim? AG

[Brent Meeker]

No.

Brent

[Alan Grayson]

So we're in agreement, and therefore the frequency and wavelength of a photon do not correspond to any extention in space as those parameters usually do. AG 

[John Clark]

On Thu, Jun 5, 2025 at 10:15 PM Alan Grayson <agrays...@gmail.com> wrote:

> Stop distorting my words, aka lying. I never claimed frequency and wavelength have no relation to physical reality. But as far as I know, it's never been shown that photons have spatial extention.

 

It's never been shown that photons have spatial extent, but it has been shown that the wavelength of light has spatial extent. But if light is composed of photons, which are particles, then how can they have a wavelength? Physicists have been asking themselves that question for the last 120 years, and there is still no consensus on what the correct answer is, and I think it unlikely that you are going to come up with one today.

>>>> It's a logical necessity that 2+2 be equal to 4, but there is no such logical necessity that energy be conserved.

>>> On the contrary, in classical mechanics one can show that the sum of kinetic and potential energy is constant. AG 

>> The conservation of energy is an empirical observation, it is not a logical necessity.

 

> It is a logical necessity in Classical Mechanics, as well as being an empirical observation. AG 

No it is not. In the 1640s Descartes proposed that mv, what we now call momentum, was conserved but Leibniz disagreed, about the same time he proposed that it was mv^2, a.k.a. energy, that was conserved. It turned out that both men were correct but that fact was not made apparent for another 200 years. It was easy to demonstrate that momentum was conserved, you can do that with a simple pool table, but for a long time it seemed that Leibniz must be wrong because their experiments indicated energy was not conserved. Their confusion stems from the fact that nobody understood the concept of heat, much less entropy. The law of conservation of energy wasn't universally accepted by physicists until the mid to late 19th century with the rise of greatly improved experimental techniques and the arrival of the new science of thermodynamics.  

 >> the ancient Greeks were able to figure out that there was no largest prime number but they were unable to figure out that energy was conserved, they were good theoreticians but lousy experimentalists.

> There were some good experimentalists in ancient Greece, such as the fellow who made a decent measurement of the circumference of the Earth. Can't recall his name. AG 

Eratosthenes, he was of Greek heritage but did his work in Alexandria Egypt not Athens, and he lived several hundred years after the time of Socrates and Plato. He was a good experimentalist but that was a very rare attribute for an ancient Greek to have.

> If your intuition is so good, how about explaining what the LT is predicting wrt time dilation; that is, which imaginary clock is being dilated, surely not the one in the muon's frame, assuming such a clock exists. AG 

I don't know what that means or what you're asking. 

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

vfv

[Alan Grayson]

On Friday, June 6, 2025 at 5:47:01 AM UTC-6 John Clark wrote:

On Thu, Jun 5, 2025 at 10:15 PM Alan Grayson <agrays...@gmail.com> wrote:

> Stop distorting my words, aka lying. I never claimed frequency and wavelength have no relation to physical reality. But as far as I know, it's never been shown that photons have spatial extention.

 

It's never been shown that photons have spatial extent, but it has been shown that the wavelength of light has spatial extent.

The concept of wavelength has units of length by definition. But if a photon has no spatial extent, the concept of wavelength cannot be physically applied to it. That's why I claim the wavelength and frequency of photons are just parameters used to calculate energy, and nothing more. AG

 

But if light is composed of photons, which are particles, then how can they have a wavelength? Physicists have been asking themselves that question for the last 120 years, and there is still no consensus on what the correct answer is, and I think it unlikely that you are going to come up with one today.

>>>> It's a logical necessity that 2+2 be equal to 4, but there is no such logical necessity that energy be conserved.

>>> On the contrary, in classical mechanics one can show that the sum of kinetic and potential energy is constant. AG 

>> The conservation of energy is an empirical observation, it is not a logical necessity.

 

> It is a logical necessity in Classical Mechanics, as well as being an empirical observation. AG 

No it is not.

In CM it can be shown that the sum of kinetic and potential energy is unchanged. The proof isn't difficult. AG

 

In the 1640s Descartes proposed that mv, what we now call momentum, was conserved but Leibniz disagreed, about the same time he proposed that it was mv^2, a.k.a. energy, that was conserved. It turned out that both men were correct but that fact was not made apparent for another 200 years. It was easy to demonstrate that momentum was conserved, you can do that with a simple pool table, but for a long time it seemed that Leibniz must be wrong because their experiments indicated energy was not conserved. Their confusion stems from the fact that nobody understood the concept of heat, much less entropy. The law of conservation of energy wasn't universally accepted by physicists until the mid to late 19th century with the rise of greatly improved experimental techniques and the arrival of the new science of thermodynamics.  

 >> the ancient Greeks were able to figure out that there was no largest prime number but they were unable to figure out that energy was conserved, they were good theoreticians but lousy experimentalists.

> There were some good experimentalists in ancient Greece, such as the fellow who made a decent measurement of the circumference of the Earth. Can't recall his name. AG 

Eratosthenes, he was of Greek heritage but did his work in Alexandria Egypt not Athens, and he lived several hundred years after the time of Socrates and Plato. He was a good experimentalist but that was a very rare attribute for an ancient Greek to have.

> If your intuition is so good, how about explaining what the LT is predicting wrt time dilation; that is, which imaginary clock is being dilated, surely not the one in the muon's frame, assuming such a clock exists. AG 

I don't know what that means or what you're asking. 

I'm asking you to identify the clock which is dilated when applying the LT. For example, even if we assume the muon has a clock, in the muon's frame its clock isn't dilated. So what clock is dilated as predicted by the LT? AG 

[John Clark]

On Fri, Jun 6, 2025 at 9:09 AM Alan Grayson <agrays...@gmail.com> wrote:

> In CM it can be shown that the sum of kinetic and potential energy is unchanged. The proof isn't difficult. AGIn CM it can be shown that the sum of kinetic and potential energy is unchanged. The proof isn't diffiultAG

BULLSHIT!  The conservation of energy is not a statement about pure mathematics or logic, it is a statement about the physical world, so it's not surprising that historically its derivation has come from observation and experimentation. Nobody has ever been able to derive the conservation of energy from logic alone, and I very much doubt anybody ever will. In fact nobody has ever been able to derive ANY physical law from mathematics alone, unless you want to say that it's a physical law that 2 rocks plus another 2 rocks is equal to 4 rocks.  

> I'm asking you to identify the clock which is dilated when applying the LT.

It's the clock that is moving relative to the observer.  

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

qoo

[Alan Grayson]

On Friday, June 6, 2025 at 7:37:25 AM UTC-6 John Clark wrote:

On Fri, Jun 6, 2025 at 9:09 AM Alan Grayson <agrays...@gmail.com> wrote:

> In CM it can be shown that the sum of kinetic and potential energy is unchanged. The proof isn't difficult. AGIn CM it can be shown that the sum of kinetic and potential energy is unchanged. The proof isn't diffiultAG

BULLSHIT!  The conservation of energy is not a statement about pure mathematics or logic, it is a statement about the physical world, so it's not surprising that historically its derivation has come from observation and experimentation. Nobody has ever been able to derive the conservation of energy from logic alone, and I very much doubt anybody ever will. In fact nobody has ever been able to derive ANY physical law from mathematics alone, unless you want to say that it's a physical law that 2 rocks plus another 2 rocks is equal to 4 rocks.  

You're mistaken. Look it up. AG

> I'm asking you to identify the clock which is dilated when applying the LT.

It's the clock that is moving relative to the observer.  

In the case of a muon, you must be referring to the muon's clock, moving relative to the Earth-bound observer. Now you know that that clock isn't dilated. So which clock is? AG 

[John Clark]

On Fri, Jun 6, 2025 at 9:51 AM Alan Grayson <agrays...@gmail.com> wrote:

>>> In CM it can be shown that the sum of kinetic and potential energy is unchanged. The proof isn't difficult. AGIn CM it can be shown that the sum of kinetic and potential energy is unchanged. The proof isn't diffiultAG

>> BULLSHIT!  The conservation of energy is not a statement about pure mathematics or logic, it is a statement about the physical world, so it's not surprising that historically its derivation has come from observation and experimentation. Nobody has ever been able to derive the conservation of energy from logic alone, and I very much doubt anybody ever will. In fact nobody has ever been able to derive ANY physical law from mathematics alone, unless you want to say that it's a physical law that 2 rocks plus another 2 rocks is equal to 4 rocks.  

>You're mistaken.

BULLSHIT!

 > Look it up. AG

I can't, it doesn't exist.

 

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

ude

\

[Alan Grayson]

Try this, by Feynman, https://ocw.mit.edu/courses/8-01sc-classical-mechanics-fall-2016/mit8_01scs22_chapter14.pdf

AG

[Brent Meeker]

The answer is both.  According to the muon's own clock, i.e. it's decay rate, the observers clocks run slow.  That's why they measure so little time for the muon's flight from the upper atmosphere.  According to the observers the muon's clock runs slow, that's why it penetrates down so far before decaying.



 David H. Frisch and Smith (1963), 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).

Brent

[Brent Meeker]

I didn't say that, I said they wasn't what I was claiming above your query.  Obviously wavelength is an extension in space and frequency is the inverse of a time period.  Physically these exhibited by things like the chocolate bar in the microwave and more commonly by the design of antennae and resonators.

As for lateral extension, normal to the direction of propagation, I think that's quantum, i.e. a probabilistic distribution that depend of the emitter.

Brent

[Alan Grayson]

If I understand basic English, you agreed that there's no evidence that photons have spatial extention. Antennae work because of the ensemble property of photons. As for Relativity and half-lives, it's easy to speak as if one knows, but the core question remains unanswered.  If an external observer uses the LT to predict a dilation of the half-life of a muon, how is that result physically possible if the muon's clock in its own frame remains unchanged? AG

[Alan Grayson]

If you look, you'll see that Feynman shows that in classical mechanics, energy is conserved on a closed loop. He proves many other things about energy conservation in that link. AG 

[Brent Meeker]

On 6/6/2025 10:49 PM, Alan Grayson wrote:

On Friday, June 6, 2025 at 6:52:51 PM UTC-6 Brent Meeker wrote:

On 6/6/2025 1:37 AM, Alan Grayson wrote:

On Thursday, June 5, 2025 at 11:19:09 PM UTC-6 Brent Meeker wrote:

On 6/5/2025 8:37 PM, Alan Grayson wrote:

On Thursday, June 5, 2025 at 9:17:34 PM UTC-6 Brent Meeker wrote:

On 6/5/2025 6:57 PM, Alan Grayson wrote:

On Thursday, June 5, 2025 at 2:53:01 PM UTC-6 John Clark wrote:

On Thu, Jun 5, 2025 at 1:35 PM Alan Grayson <agrays...@gmail.com> wrote:

 

> The frequency is just a number that defines a photon's energy. Nothing to do with an extended wave.

Nothing? Nothing at all? Not quite. There is a simple equation that shows the relationship between the frequency of light, its wavelength and its speed, its  c=λ⋅f. And because of that very simple relationship you can easily perform a fun experiment at home:

Measuring the speed of light with a microwave oven and a chocolate bar

If frequency and wavelength are just numbers and have no relationship with physical reality then I don't see how you could use them to calculate the speed of light which most certainly does have a relationship with physical reality.

 

As far as I know, it's never been shown that photons have spatial extent. So, the frequency and wavelength are just numbers that allow us to calculate a photon's energy. AG

You're directly measuring the wavelength.  The speed of light is just a conversion constant.  So you're inferring the frequency of the microwave.

Brent

Then the photon has extention in space? Is this your claim? AG

No.

Brent

So we're in agreement, and therefore the frequency and wavelength of a photon do not correspond to any extention in space as those parameters usually do. AG

I didn't say that, I said they wasn't what I was claiming above your query.  Obviously wavelength is an extension in space and frequency is the inverse of a time period.  Physically these exhibited by things like the chocolate bar in the microwave and more commonly by the design of antennae and resonators.

As for lateral extension, normal to the direction of propagation, I think that's quantum, i.e. a probabilistic distribution that depend of the emitter.

Brent

If I understand basic English, you agreed that there's no evidence that photons have spatial extention. Antennae work because of the ensemble property of photons.

But they are scaled to wavelength.  And it's the wavelength that determines the standing waves in you microwave and makes the chocolate bar test work.

As for Relativity and half-lives, it's easy to speak as if one knows, but the core question remains unanswered.  If an external observer uses the LT to predict a dilation of the half-life of a muon, how is that result physically possible if the muon's clock in its own frame remains unchanged? AG

Because two clocks moving relative to one another don't agree on the direction of "future" in spacetime.

Brent

[John Clark]

On Sat, Jun 7, 2025 at 1:52 AM Alan Grayson <agrays...@gmail.com> wrote:

>> The conservation of energy is not a statement about pure mathematics or logic, it is a statement about the physical world, so it's not surprising that historically its derivation has come from observation and experimentation. Nobody has ever been able to derive the conservation of energy from logic alone, and I very much doubt anybody ever will. In fact nobody has ever been able to derive ANY physical law from mathematics alone, unless you want to say that it's a physical law that 2 rocks plus another 2 rocks is equal to 4 rocks.  

> You're mistaken. Try this, by Feynman, https://ocw.mit.edu/courses/8-01sc-classical-mechanics-fall-2016/mit8_01scs22_chapter14.pdf

If you look, you'll see that Feynman shows that in classical mechanics, energy is conserved on a closed loop. He proves many other things about energy conservation in that link.

NO!  Feynman proved IF you assume that a system obeys the Principle Of Least Action AND you assume that the system has Time-translation invariance THEN, because of Noether's theorem, the system must obey the law of Conservation Of Energy. But both the Principle Of Least Action and Time-Translation Invariance are observations, NOT logical necessities. I can imagine a universe with different physics in which neither the Principle Of Least Action nor Time Translation Invariance are true, but I can't imagine a universe that contained a largest prime number. 

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

753

[Alan Grayson]

Where in Feynman's argument does he assume the Principle of Least Action and Time-translation invariance to conclude Conservation of Energy around a closed loop? AG 

[John Clark]

On Sat, Jun 7, 2025 at 8:10 AM Alan Grayson <agrays...@gmail.com> wrote:

> Where in Feynman's argument does he assume the Principle of Least Action and Time-translation invariance to conclude Conservation of Energy around a closed loop? AG 

Where? I don't understand the question. Feynman showed that IF you can formulate classical mechanics using the Principle of Least Action, AND IF the system has time-translation symmetry, THEN Noether tells us that the conservation of energy is a logical necessity. 

BUT can we successfully formulate classical mechanics using the Principle of Least Action? Only experimentation can answer that question. And does our universe have time-translation symmetry? Only observation can answer that question.

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

ooa

[Alan Grayson]

I see you haven't looked at the link I posted. CM can be derived by several methods, such as applying Hamilton's or Lagrange's as the starting point. So what Feynman did is irrelevant to the issue I've raised; whether Conservation of Energy on a closed loop can be derived independent of the principles you cite. AG 

[John Clark]

On Sat, Jun 7, 2025 at 3:00 PM Alan Grayson <agrays...@gmail.com> wrote:

> I see you haven't looked at the link I posted.

 

That is incorrect.  

> CM can be derived by several methods, such as applying Hamilton's or Lagrange's as the starting point. 

But if you were starting from first principles and had absolutely no knowledge that came from experimentation or observation then you would have no reason to think Hamilton's or Lagrange had anything relevant to say about classical mechanics. Hamilton's and Lagrange's methods are reformulations of classical mechanics, NOT derivations of it. They're different mathematical ways of expressing the exact same physical content that was originally found through observation and experimentation. And their reformulations were discovered centuries after Newton discovered his way of doing things. The methods of Hamilton's and Lagrange, and Newton's too, are powerful because they encode our empirical knowledge of how the world works, NOT because they can generate fundamental physical knowledge from pure mathematics alone.

> So what Feynman did is irrelevant to the issue I've raised;

Then why the hell did you mention Feynman and give a link to what he said?! 

 > whether Conservation of Energy on a closed loop can be derived independent of the principles you cite. AG 

I see that you don't understand what a closed loop means in classical mechanics, Energy conservation doesn't demand a closed loop.  

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

ez6

[Alan Grayson]

On Saturday, June 7, 2025 at 1:34:14 PM UTC-6 John Clark wrote:

On Sat, Jun 7, 2025 at 3:00 PM Alan Grayson <agrays...@gmail.com> wrote:

> I see you haven't looked at the link I posted.

 

That is incorrect.  

> CM can be derived by several methods, such as applying Hamilton's or Lagrange's as the starting point. 

But if you were starting from first principles and had absolutely no knowledge that came from experimentation or observation then you would have no reason to think Hamilton's or Lagrange had anything relevant to say about classical mechanics. Hamilton's and Lagrange's methods are reformulations of classical mechanics, NOT derivations of it. They're different mathematical ways of expressing the exact same physical content that was originally found through observation and experimentation. And their reformulations were discovered centuries after Newton discovered his way of doing things. The methods of Hamilton's and Lagrange, and Newton's too, are powerful because they encode our empirical knowledge of how the world works, NOT because they can generate fundamental physical knowledge from pure mathematics alone.

IMO, the discovery of Inertia was not realized via empiricism. It's what you get when you forget about empiricism. AG  

> So what Feynman did is irrelevant to the issue I've raised;

Then why the hell did you mention Feynman and give a link to what he said?! 

It's a long post, Somewhere he shows that energy is conserved along a closed loop. That was the point of the link. AG 

 > whether Conservation of Energy on a closed loop can be derived independent of the principles you cite. AG 

I see that you don't understand what a closed loop means in classical mechanics, Energy conservation doesn't demand a closed loop.  

I see you read badly, a failing of convenience. I never alleged it did. I was just making the case that in one instance at least, conservation of energy is a logical conclusion of CM. AG 

[Brent Meeker]

Lagrange (1736-1813) was born nine years after Newton (1642-1727) died.  They weren't centuries apart.  Hamilton was the next generation (1805-1865) just overlapping Lagrange.

Brent

[Alan Grayson]

That's what CLARK wrote! Why don't you comment on a substantive matter, such as can conservation of energy on a closed path be established without the principles Clark alleges, such as Least Action? AG 

[John Clark]

On Sun, Jun 8, 2025 at 12:45 AM Brent Meeker <meeke...@gmail.com> wrote:

> Lagrange (1736-1813) was born nine years after Newton (1642-1727) died.  They weren't centuries apart.  Hamilton was the next generation (1805-1865) just overlapping Lagrange.

 

I stand corrected. 

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

5gg

 

[John Clark]

On Sun, Jun 8, 2025 at 2:04 AM Alan Grayson <agrays...@gmail.com> wrote:

On Saturday, June 7, 2025 at 10:45:36 PM UTC-6 Brent Meeker wrote:

Lagrange (1736-1813) was born nine years after Newton (1642-1727) died.  They weren't centuries apart.  Hamilton was the next generation (1805-1865) just overlapping Lagrange.

On 6/7/2025 3:46 PM, Alan Grayson wrote:

> That's what CLARK wrote! Why don't you comment on a substantive matter, such as can conservation of energy on a closed path be established without the principles Clark alleges, such as Least Action? AG 

I wonder if there is a universe where Alan Grayson is able to admit that he was wrong. I'm sure that if Everett is right then there must be a lot of very strange things in some of his Many Worlds, but I'm not sure any of them contain anything as unusual as that.

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

bcx

[Alan Grayson]

On Sunday, June 8, 2025 at 4:28:57 AM UTC-6 John Clark wrote:

On Sun, Jun 8, 2025 at 2:04 AM Alan Grayson <agrays...@gmail.com> wrote:

On Saturday, June 7, 2025 at 10:45:36 PM UTC-6 Brent Meeker wrote:

Lagrange (1736-1813) was born nine years after Newton (1642-1727) died.  They weren't centuries apart.  Hamilton was the next generation (1805-1865) just overlapping Lagrange.

On 6/7/2025 3:46 PM, Alan Grayson wrote:

> That's what CLARK wrote! Why don't you comment on a substantive matter, such as can conservation of energy on a closed path be established without the principles Clark alleges, such as Least Action? AG 

I wonder if there is a universe where Alan Grayson is able to admit that he was wrong.

And I wonder if you'll ever be able, really able, to read English well, and then hopefully you'll have your answer. AG

[Brent Meeker]

Because there is so much slop in in the question.  First, what does "a closed path" mean.  If it means in the state space of an isolated system then it is trivially true that energy is conserved.  And then J.C. refers to a system that obeys a least action principle.  I think that's equivalent to a system without a dissipative term, like friction, so that would be sufficient.  But applying a least action principle means knowing two points in state space.  Noether's proved her theorem for a system defined by a Lagrangian which applies to both a least action and also to a problem in terms of initial state.  Then it is sufficient that the Lagrangian be time-translation invariant in order for a conserved energy exist.

And that's why I didn't comment, because I hate to have to explain the question before answering it.

Brent