a-cosmology-group/acg#153

Louis and Francois, These are very thought provoking ideas. Einstein’s article has also been discussed by Bloomer and Dunning-Davies, and black holes by Campbell and Carroll, as well as black hole universes by Browne (but without singularity!). Others had arrived at the same conclusion before Browne’s work. The problem of energy recycling through gravitation and radiation is addressed by Broberg through a concrete formulation of de Broglie’s vacuum thermostat.

The problem of energy recycling through gravitation and radiation is addressed by Broberg through a concrete formulation of de Broglie’s vacuum thermostat.

A friend of de Broglie is a friend of mine! This appears to be a fine pice of work which deserves a more thorough reading.

@Francois-Zinserling >> This causes the matter it pulls in to radiate the gravitational energy as intense light.

I cannot relate to this though. Where does this energy come from? Every object will radiate itself into nothing, or else how do you replenish the gravitational energy?

Take two masses separated by a large distance. Now let them fall on each other. Just before they collide they are down their self-generated gravitational potential (i.e. less gravitational energy) and have more kinetic energy. The total energy of the system is the same.

Now the masses collide, heat up to high temperatures and release a lot of light that escapes the central massive lump. A sphere of light carries the energy away from the collision site. The energy comes from the kinetic energy (which came from the potential gravitational energy of the initial system).

If the objects at the collision site are dense enough, gravity will be strong enough to further pull the parts of the massive lump together and convert more kinetic energy into light. As you describe, an “object will radiate itself into” no mass and the energy will all go to radiation. (And @Pierre314159 all this happens before reaching the unreachable $R_s$.) However, that object has to be dense enough for the gravitational forces to overcome the nuclear forces. Not every object will do that (although over time such an object will increase its density by attracting other matter it encounters in space). The entire mass may not be radiated in a finite time as relativistic effects slow down the process, but the radiation will spread over very large distances.

This causes the matter it pulls in to radiate the gravitational energy as intense light.

I get it now. I was picturing one object, undisturbed, radiating itself away into nothing. What you describe is effectively the Kevin Helmholtz mechanism? Not sure if it still applies to large-scale collisions, but the principle is the same.

@genotics . Two reviews from my side.

• Black Holes, Other Exotic Stars and Conventional Wisdom Three excellent sections: the Introduction, especially a surprising formulation of the Maxwell equations, with Euler derivatives $d/dt$ instead of the usual ones with $\partial/\partial t$. Furthermore the Black holes section and the Conclusion are worthwile reading. The rest of the paper about all sorts of Exotic Stars escapes me.
• Black Holes – Fact or Fiction? Unfortunately, the total energy stored in the gravitational force field as expressed in equation (3) has the wrong sign. It must be negative instead of positive, which makes the rest of the article questionable. Though there is exellent proze on page 154 that I would immediately copy & paste.

Thank you for a valuable post, Roy !

The last paragraph of your statement is correct

@Pierre314159

Pound and Rebka showed that clocks run slow, not that objects slow down…

Theorists assume the “black hole” already exists with a defined $R_s$, and calculate that it takes a finite time to reach $R_s$, as measured by the infalling clock. According to that, a clock dropped on a massive object should reach $R_s$ showing, say, ‘12-noon’. However, from our point of view, the Pound-Rebka redshift slows down the time we see on the clock, so if we look at it once a second, we see ‘11:59:59.0’, ‘11:59:59.5’, ‘11:59:59.75’, ‘11:59:59.875’, ‘11:59:59.9375’, etc… Even if we wait a long time the clock never reaches ‘12:00:00’ and appears to move by smaller distances $\delta x$ in a time interval $\Delta T$, so the velocity $\delta x/\Delta T$ becomes smaller and smaller with time. As a result we see the falling clock’s velocity slow down, but it never reaches zero.

even if that were valid, in-falling matter would come to a stop only when reaching $R_s$ which we postulated doesn’t physically exist.

To avoid using a $R_s$ that doesn’t exist, define $R_s^{ *}$ as the calculated Schwarzschild radius of the “black hole” once it has increased its mass by swallowing the clock we drop on it. The externally observed time to reach $R_s^{ *}$ is not finite, as described above.

Going beyond the simplistic models of “black hole” theorists and Einstein’s, things are actually worse. The argument made by Mersini-Houghton adds the unavoidable radiation loss emitted by the object falling in a large gravitational field when it collides with other objects as described above. The falling object loses kinetic energy to radiation and the integral of the time to reach $R_s^{ *}$ diverges. Since the time integral diverges for any $R_s^{ *}$, no “black hole” can be formed.

SgrA* is known to be an intense radio source (I thought nothing could escape black holes?)

The radio emission is from the “accretion disk”, far more distant from the center than $R_s^{ *}$.

Is this radio emission the “Intense light” gravitationally redshifted? Because if the frequency of this “intense light” is known, and the mass of the object is known, and that gravitational redshift holds, then the physical radius of the object could be inferred.

Of course it is redshifted but “the object” is the “accretion disk”. “Accretion disks” don’t generate sharp spectroscopic lines but broad radio spectra that depend on temperature and rotational velocity of the “accretion disk”. I am not familiar with the details of this calculation, but since the observed temperature depends on gravitational redshift $T(z) = T(0)/(1+z)$ there is a degeneracy on temperature and redshift which makes the calculated radius severely model dependent. The size of the accretion disk can also be calculated from the Doppler width of the spectrum, corrected for redshift, but again this is model dependent.

Note that since a tired-light effect contributes to redshift, every observation discussed above has to be re-interpreted 🤣

Correct reply, objects falling in lose kinetic energy to radiation, time it takes to fall in could contribute to redshift

The radio emission is from the “accretion disk”, far more distant from the center than $R^{*}_s$

Not according to this:

The radio source Sgr A✻ is coincident with the mass centroid to <1 mas (Plewa et al. 2015), and is itself very compact, with R (1.3 mm) < 18 µas ≈ 1.8 $R_S$

Correct

and is itself very compact, with R (1.3 mm) < 18 µas ≈ 1.8 $R_s$

That’s an artifact of the analysis procedure. The images generated to represent Sgr* and M87 are not pictures. They are made by assuming that a black hole exists in the first place…

@bgreenman

Correct reply, objects falling in lose kinetic energy to radiation, time it takes to fall in could contribute to redshift

Yes but, no but … If it loses kinetic energy in such a manner then it must be radiating (mostly) INTO the BH? So BH still gains all the energy.

I had prepared an elaborate reply to @RedshiftDrift earlier post, only to realise I was arguing in Newtonian terms, where $R_s$ is the point where escape velocity $V_e$ = $c$. In Schwarzschild and Einstein terms of course it is different, in that no photon can cross $R_s$, and since time dilation is closely related to $V_e$, the clocks at $R_s$ would stand still. It is curious that Newton and Einstein differ so greatly on this!

I would argue this only applies to a radial outward perspective, and the object must still fall inward, even though it can no longer be seen from outside. Inside it must be assimilated to the BorgBlackHole material. No electron degeneracy, not even neutron degeneracy. If not, all BH’s must appear at the same mass and grow no more.

There is also the possibility of causality violation. When the last tiny particle falls into the mass to create a BH with $R_s$ just above the surface of the object, an object falling in from the other side must immediately know $R_s$ has been formed. How? Speed of light is no longer valid inside, so how does the information get from one side of the sphere to the other?

Right now we probably don’t know how information gets from one side of the sphere to another. Its necessary to test Newton,Einstein and other approaches to the problem to see what approach is either right or is a combination of approaches needed

@Francois-Zinserling,

I was arguing in Newtonian terms, where $R_s$ is the point where escape velocity $V_e=c$. In Schwarzschild and Einstein terms of course it is different

This is an interesting approach to the question of black holes. If, instead of the Newtonian formulation, SR is used for escape velocity, we get: $V_e=\sqrt{\frac{2GM}{r}-(\frac{GM}{rc})^2}=\frac{\sqrt{3}}{2}c$ (not $c$) at $r=R_s$. If, again, SR is used in the calculation of the kinetic energy, we obtain $E_k=\frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}-mc^2=mc^2$ at $v=V_e$. Which means that any mass $m$ that collides with $M$ at $R_s$ at escape velocity will need to shed off the equivalent of its mass in kinetic energy. Hence, no mass is added to the bigger mass $M$.

@Pierre314159 nice one. I was reading again about the photon sphere yesterday. I have not studied GR thoroughly so I might be caught talking rubbish now and then … :).

Agreed that kinetic energy can be $mc^2$ (I would argue it could be even more but let’s stay with your example) Shown another way from momentum P= $γmv$ and Energy = $Pc$ = $γmvc$ which equals $γmc^2$ at v=c. (Except γ is now infinite and this would be a problem). We can get around that though by stating that not $v=c$ but $γv=c$, meaning that in your case above, $γ=\frac{2}{\sqrt{3}}c$, because in the above example $v=\frac{\sqrt{3}}{2}c$ so the conclusion is that $γv=c$ I don’t think this is a maximum, because theoretically γ has no maximum, but $γv=c$ is certainly allowed.

Interesting further that Newton says you cannot escape a BH ($V_e=c$) but for SR it is less than c, $v=\frac{\sqrt{3}}{2}c$. My entire discussion of yesterday that I deleted reminded myself that ‘escape velocity’ means instantaneous velocity needed to ‘escape’ which means to reach infinity. Now I am even more confused as to why a photon may not cross the Schwarzschild radius! Were you possibly referring to escape from photon sphere in your equations above?

You also show $E_k=\frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}-mc^2=mc^2$ where $\frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}-mc^2$ can also be shown $E_k=mc^2*(γ-1)$ or $γmc^2-mc^2$

However the total energy of the object is $γmc^2$ = $E_k+mc^2$ = $2mc^2$ from your example. If $mc^2$ is radiated, where does the other $mc^2$ go?

However the total energy of the object is ${\gamma}mc^2=E_k+mc^2=2mc^2$ from your example. If $mc^2$ is radiated, where does the other $mc^2$ go?

That’s because the $v$ in $\gamma$ takes the value $\frac{\sqrt{3}}{2}c$, hence you get $2mc^2-mc^2=mc^2$

Two remarks on a remarkable post by @Pierre314159 .

1. The escape velocity according to Special Relativity is

$$ V_e=\sqrt{\frac{2GM}{r}-\left(\frac{GM}{rc}\right)^2}=\sqrt{\frac{2GM’}{r}} \quad \mbox{with} \quad M’ = M + \left[-\frac{GM^2}{2rc^2}\right] $$

The term between square brackets is recognized as the - Newtonian ! - negative mass of the Self Energy Field of the same body with radius $r$ and mass $M$.

2. Due to the SR formulation, the escape velocity $V_e$ cannot exceed the speed of light $c$ :

$$ c \gt V_e \quad \Longleftrightarrow \quad \frac{2GM}{r}-\left(\frac{GM}{rc}\right)^2 \lt c^2 $$

$$ r^2-2\frac{GM}{c^2}r+\left(\frac{GM}{c^2}\right)^2 \gt 0 $$

$$ \left(r-\frac{GM}{c^2}\right)^2 \gt 0 \quad \Longleftrightarrow \quad r \neq \frac{1}{2}\frac{2GM}{c^2} $$

It is concluded that the size of a (celestial) body cannot pass a radius less than one-half the Schwarzschild radius. Herewith the infamous Black Hole singularity is removed; by Special - no General - Relativity. I have the uneasy feeling that with SR and half the Schwarzschild radius we are running into the same problems as with GR and the “old” Schwarzschild radius.

I think the only way to enhance our credibility is to not quote extremists

Thanks, bgreenman, I’m glad yo agree with me.

Thanks for pointing this out, I didn’t know who Austin Murphy was and only looked at that article found from a Google search. I replaced the reference with a link to Bouman’s talk where she explains the technique used to train the computer model with “familiar objects”.

Strangely, the merger didn’t take an infinite time because each “black hole’s” clock slows to a stop at the event horizon…🙃 Makes one wonder…

Makes me wonder too 😕 Two orbiting “black holes” is very close to the gravitating particles configuration in Einstein’s paper

Since you are on Quora @Pierre314159, you may find some specialist there who would know why the frequency of gravitational waves from “black hole” mergers increases rather than decreases as the “black holes” approach each other’s event horizon, where every frequency should be reduced.

(The usual answer is “Penrose already explained that”, without actually giving an explanation!)

The question has been asked on Quora numerous times, and never had a satisfactory answer, despite @bud’s insistent roasting of Mark Barton …

I ended up asking ChatGpt, and indeed got the straight answer no expert (not even Penrose) was willing to give: LIGO is a gravitational wave observatory, and unlike other electromagnetic-type of radiation, gravitational waves, while they do travel at the speed of light, are not subject to gravitational time dilation. There. Problem solved.

Here is a reference: https://osf.io/rha95/

@RedshiftDrift, what do you make of that?

@Pierre314159

... gravitational waves, while they do travel at the speed of light, are not subject to gravitational time dilation. There. Problem solved.

Ah Pierre, ChatGPT has been taught (or is simply regurgitating) the old college technique, if you can’t convince them with your logic, baffle them with bullshit. LIGO is PhD level bullshit; it gets piled higher and deeper at each iteration. I wrote a piece on the inconsistencies in the original detection paper shortly after it came out. That the gravitational waves are not time dilated is a dubious claim to begin with but its absurd in the context of a BH merger because according to standard BH theory the crossing of the two event horizons should never complete from our remote point of view. Since the crossing of the two event horizons cannot be observed, the claim that LIGO receives a complete GW signal of the total infall event that takes place after the event horizon crossing that hasn’t taken place yet from our point of view, breaks the BS meter as far as I’m concerned. But wait, there’s more…

Quite apart from the absurd BH BS, the basic premise of the LIGO project is itself ridiculous. According to LIGO their equipment, consisting of two classical interferometers with 4km arms can measure a variation in the separation between the two sets of mirrors of the two systems at the scale of $10^{-20}$ meters. That is 100 million times smaller than the scale of the atoms which comprise the system ($10^{-12}$ m) and the system is not super-cooled so those atoms are vibrating chaotically over an order of magnitude. Claiming you can measure a $10^{-20}$ signal with that equipment is like claiming that you can measure an atom with a micrometer.

Sabine Hossenfelder did a good Follow up piece on LIGO also.

In the abstract of the referenced paper

so the black hole will not respond to the change of the location of the celestial body. This will rule out the possibility of existence of binary black hole system…

I don’t understand that step in the reasoning. The author is talking about gravitational signals getting inside a “black hole”. This does not answer my question.

My question is only concerned with the gravitational waves outside the “black holes”.

Take two orbiting “black holes” and add an observer A in orbit at the same gravitational potential as the two “black holes”. Observer A shines a laser away from the center of mass of the system. An observer B (us), external to the system, sees the laser beam flash on every rotation like a lighthouse. This flash will be redshifted and the period decreased, so observer B concludes that the “black hole” pair orbits at a lower frequency. The gravitational wave must be synchronized with the optical wave since it also propagates at $c$.

This synchronization between gravitational and optical waves shows that both are temporally slowed down. Time dilation appears for all orbiting masses, from the sun-mercury system (it takes longer to return to the aphelion, making the elliptical orbit precess forward @Pierre314159 😉), to orbiting “black holes”.

I have concerns about that paper. The author uses a moving ship but doesn’t seem to consider the Doppler effect nor SR time dilation in the moving ship. Where is this paper published, has it been reviewed by anyone? Has it been referred-to by anyone? It is predicted that gravity bends gravitational waves just like for light, which seems to contradict the paper.

This adds doubts to the “black hole” explanation of the gravitational wave signals.

I kinked on the same sentence you did from the abstract. How I understood it is: if gravitational waves were gravitationally redshifted, we couldn’t observe black hole mergers. We observe black hole mergers, therefore, gravitational waves are not gravitationally redshifted. I didn’t read further: that was enough for me.

I don’t know who OSF is, but certainly not peer reviewed. I was unsuccessful in finding other references, so this one or something similar is probably where ChatGPT got its info. However, I did ask Quora, in the hope of getting an answer by someone who knows better.

I think a decent answer would be: « Finally, they were not black holes, really, sorry. » but that would make those who measured the surface of event horizons look stupid, wouldn’t it?

if gravitational waves were gravitationally redshifted, we couldn’t observe black hole mergers. We observe black hole mergers, therefore…

I’m not convinced “we observe black hole mergers”. The LIGO and VIRGO interferometers are extremely sensitive devices that can detect all sorts of phenomena other than gravitational waves (GW) from “black holes” merger. High energy astronomical events release high energy particles which can strike the mirrors used in interferometers and produce mechanical resonances in the mirrors that look like a GW. LIGO and VIRGO use the same size mirrors, so they see “oscillations” that look the same.

I’m not against time dilation and my following post is certainly not an attempt at ‘time dilation does not exist’.

Black holes are predicted, even if you revert to Newtonian physics. By this I do not mean singularities. Call it dark stars then if you like. We observe bending of light around ‘invisible objects’, and LIGO has, in my opinion, displayed what I would expect from a ‘vibrating space’ when 2 very large masses circle and merge. All of these are observed. Galaxies have - in general - a supermassive object at the centre that, if it had been radiating like a star, it would have been very blue or UV or even up to X-Ray radiation. It would certainly outshine the stars in the centre of the galaxy. This is not observed. Radiation observed around galactic centres seem to be in the immediate surrounds of the BH, not from the centre.

Time dilation on the event horizon has not been observed, yet some of the posts above use a hypothetic time-dilation scenario to break all of the rest of science, including known science where observations closely matches theory. My opinion is we don’t understand time dilation (especially at the event horizon) and cannot use the ‘time stands still’ argument to break all of the rest.

@Francois-Zinserling, this is a very lucid summary of what has been said in this thread so far, thanks.

if it had been radiating like a star, it would have been very blue or UV or even up to X-Ray radiation

It most probably does, though, however, from our observational perspective, these UV or X-Rays (or gamma rays?) would be so much redshifted thanks to the object’s heavy gravitational potential, that we would perceive it as extra long wavelengths far down in the radio band. If we’d bother looking at the right frequency, I’ll bet my pay check that « outshining stars » is what we would see.

Time dilation on the event horizon has not been observed

…and a good reason for that is that event horizons themselves have never been observed (and they never will because they can’t exist, if you ask me). The part of science that needs to be « broken » is not the consequences of what happens at the event horizon, but rather the bit that predicts the existence in physical reality of event horizons.

if it had been radiating like a star, it would have been very blue or UV or even up to X-Ray radiation

Black hole theorists justify the lack of observed UV and X-rays caused by absorption in the dust of accretion disks - isn’t that convenient!

Accretion disks. And then we have the jets - another artist impression, of course:

From Wikipedia Astrophysical jet: >The formation and powering of astrophysical jets are highly complex phenomena >Mechanisms behind the composition of jets remain uncertain

Isn’t it easier to say that we understand nothing of it ??

From the Kerr paper:

There are many reasons why I never believed that Penrose proved that black holes must be singular, e.g.

1. There are no trapped surfaces inside the inner horizon.
2. It is not good enough to show that there is a FALL that is normal to the original trapped surface.
3. It is very much a ”do it yourself” paper where the reader is supposed to prove the more difficult parts. Some of these may not even be true.

(My highlight.)

Why do so many believe that the star inside must become singular at this moment? Faith, not science! Sixty years without a proof, but they believe!

This could be said about the Big Bang as well, ninety years without a proof of expansion, but cosmologists believe.

Related: comment & replies in discussions 144 and 129 .

So a mathematician has disproven a mathematicians proof that singularities must exist! Physical reality heaves a sigh of relief.

There remains the one-way trap door event horizon(s) of course. This is like proving the Big Bang didn’t have a singularity. In both cases the fundamental problem remains - the models are not physically realistic even without the singularities. Even though General Relativity is usually blamed for this mess, it is actually the failure to properly implement GR that is at fault.

Taking proper account of GR, the FLRW model is an oxymoronic exercise since GR does not have a universal frame but FLRW “solves” the GR equations for a universal metric. The result of that misbegotten effort speaks for itself. As Louis points out cosmologists believe in a universal expansion without benefit of proof or evidence. You can’t have an expanding universe if you don’t have a universe at all. In GR there is no universal frame and therefore no universal entity capable of expanding.

According to GR the speed of light varies with position in a gravitational field and that is an observed fact. As the field strength increases all physical processes slow down, including the SOL. Since $\frac{E}{m}=c^2$ gravitational collapse will be self-limiting as the collapsing body will of necessity begin converting mass to electromagnetic radiation, counteracting the collapse. Neither the Schwarzschild nor Kerr models take account of the GR stipulated varying SOL - they do not accurately represent the physics of the situation. The use of GR as intended proves the expression BB+BH=BS.

Can someone understand this nonsense? https://youtu.be/HRir6-9tsJs

Yes. Kerr and Penrose fighting for who pisses farthest.

Can someone understand this nonsense?

I do not agree with @RedshiftDrift . On the contrary: the video reveals some interesting issues. Jump to 9:30 and read/listen:

To illustrate this crudely: the affine parameter could be an exponential of coordinate time. This function is bounded from below even though time can go from minus to plus infinity. So, that limit of the affine parameter doesn’t mean that time itself has come to a halt, argues Roy Kerr. He also argues that this invalidates any arguments about the inevitability of singularities due to coordinate system dead ends.

Is it so simple? Roger Penrose doesn’t know what “proper time” is, so he takes any “affine parameter” and thinks he can get away with it Jumping on my hobby horse, I think that the mistake is indeed purely mathematical, just a matter of improper interpretation of an affine parameter. Let’s start with the well known approximation of an exponential function.

$$ \lim_{n\to\infty}\left(1+\frac{x}{n}\right)^n = e^x \quad \mbox{with} \quad x = H_0t $$

Replace the expression on the left by approximation for finite $n$ and replace variable $t$ there by another timescale $\tau$ in order to maintain equality.

$$ \left(1+\frac{H_0\tau}{n}\right)^n = e^{H_0t} \quad \Longleftrightarrow \quad 1+\frac{H_0\tau}{n} = e^{H_0/n.t} $$

Now replace $n/H_0$ by an timelap named Age, giving at last

$$ A = n/H_0 \quad \Longrightarrow \quad 1+\tau/A = e^{t/A} $$

Something weird has happened. Just like in the video, time on the right hand side can go from minus to plus infinity. But on the left hand side we have, for $t\to -\infty$

$$ 1+\tau/A = e^{-\infty} = 0 \quad \Longrightarrow \quad \tau = -A $$

This means that, in the past, the other affine parameter [ .. ] has come to a halt. One timescale ($t$) is not the other ($\tau$). I’m not making this up. Put $\lambda=1/A$ in $a(t)=e^{\lambda t}$ below.

Their error is to fit a mathematical function to a physical quantity without any concern for the physical meaning of all this (for which there is none).

the physical meaning of all this (for which there is none).

I wouldn’t go this far with that “none”, but it is for sure that any physical meaning is missing too much of the time. An example is given in a thread 198 reply where @mikehelland says the following. >Minkowski time isn’t a real thing, it’s what you’d have, hypothetically, without time dilation.

Isn’t a real thing ? Dismissed, I would say ! With the Variable Mass Theory we have, on the contrary (in Mike’s notation)

$$ \frac{m}{m_0} = e^{H_0t} \quad \mbox{and} \quad \frac{d\tau}{dt}=\sqrt{\frac{m}{m_0}}=e^{H_0/2.t} $$

With some calculus it follows that Mike’s “Minkowsi time” $\tau$ is our “Orbital time”, which definitely has a physical meaning.

$$ 1+\tau/A = e^{t/A} \quad \mbox{with} \quad A=\frac{2}{H_0} $$

Orbital time $\tau$ is the governing timescale in (Newtonian) gravity. Atomic time $t$ is for all the rest, as far as I know. Mind the factor $2$ in the relationship between Hubble parameter $H_0$ and Age $A$. Quite in general, the relationship between Hubble parameter and Age has become quite loose in the latest version of our theory. The same can be said about the relationship between Hubble parameter and (gravitational constant times) mass density (here and now). Independent of any further cosmological models it is claimed that there are proportionalities and that’s it, namely

$$ H_0 \sim 1/A \quad \mbox{and} \quad H_0^2 \sim G\rho_0 $$

Update.

Let’s take a look at Wikipedia’s Leap second and quote: >A leap second is a one-second adjustment that is occasionally applied to Coordinated Universal Time (UTC), to accommodate the difference between precise time (International Atomic Time (TAI), as measured by atomic clocks) and imprecise observed solar time [ .. ] The leap second was introduced in 1972 and since then 27 leap seconds have been added to UTC. [ .. ] In 1972 [ .. ] the UTC clock was already 10 seconds behind TAI [ .. ] so the difference is 10 + 27 = 37 seconds.

Remember the latter value. In Wikipedia’s Wikipedia’s page about $\Delta T$ (timekeeping) we read, on the other hand: >The value of $\Delta T$ for the start of 1902 was approximately zero; for 2002 it was about 64 seconds. [ .. ] Since early 2017, the length of the day has happened to be very close to the conventional value, and $\Delta T$ has remained within half a second of 69 seconds.

Don’t know what other people think about all this, but I find it a mess.

Nevertheless there maybe empirical evidence, especially meant for those who do not believe in Variable Mass. Most of us may think that there is NO difference between orbital time $\tau$ - with an age of the earth $A$ - and enduring atomic time $t$, because time is time with an atomic clock, isn’t it? Let mathematics come in and help to decide.

$$ 1+\tau/A=e^{t/A} \quad \Longleftrightarrow \quad t/A = \ln(1+\tau/A) $$

Because the exponent is the inverse of the logarithm. Taylor series expansion of $\ln(1+x)$ gives

$$ t/A = \ln(1+\tau/A) \approx \tau/A-\frac{(\tau/A)^2}{2} \quad \Longrightarrow \quad \tau-t \approx \frac{\tau^2}{2A} $$

In words: atomic clocks shall always been running ahead of orbital clocks with a difference of $\tau^2/(2A)$ . Let’s calculate and see what happens.

year := 31556926; # seconds
Age := 4.54*10^9*year;
period := (2002-1902)*year;
leaps := period^2/(2*Age);

                         leaps := 34.75432380

That is close to the above 37 seconds. Coincidence? I don’t know.