[Music] welcome to real physics the most fundamental
problem of gravity is solved. I know this sounds like an overstatement but in one respect
what I'm reporting today will give you a deeper understanding than the current theories of
Newton and even Einstein we have and nonetheless you might not even have heard of the problem.
so it's not of very practical use and will not help you weightlifting but it touches the very
fundamentals of our understanding of reality that is the origin of inertia and gravity. and
yes it's published in a 70-year-old paper so if you are really familiar with Newton's bucket
and its application applications and with Foucault pendulum you may skip to the times stamp given in
the description. But otherwise I would urge you to lean back and let me explain what the problem
is and let it sink in because we tend to suppress mentally problems until we have solved them. And
this is a deep one. Now all starts with Newton's postulate of absolute space and time and he said
okay let's start physics with here is time here is space and space is unaccelerated, it exists
in an absolute manner and he tries to prove this with his famous bucket experiment. He rotates a
bucket filled with water until friction transfers to the water and makes it a curved surface and
he says okay this way we know what rotation is and if you have a rotating frame you see the the
water surface level climbing up the walls and on the other hand if you have a flat surface you
know that you are in a unaccelerated rest frame without any forces. Sounds very simple but
(there was also Bishop Berkeley) now in 1883 Ernst Mach comes along with a very profound objection and
he says hold on wait a second I'm not convinced I don't believe absolute space that's a concept
that you cannot prove as a matter of principle . And there might be another explanation okay so
Mach says Newton's experiment with the rotating water vessel simply tells you that the relative
motion of the water with respect to the sides of the vessels creates no noticeable centrifugal
forces but that such forces are produced by the relative rotation with respect to the earth and
the other celestial objects no no one can say how the experiment would turn out if the walls of the
vessel increased in thickness and mass eventually reaching a thickness of several miles and he
thought of course even more what's his intention here is that the distant masses out there in in
the universe determine what is rest what is our absolute frame and that's very deep. You can
look at this in a couple of ways if you observe that the the surface of the water is curved
okay but what would if if you rotate the vessel but what would happen if the vessel is at rest and
you let the universe rotate outside and of course Newton's answer would be nothing would happen I
mean that surface would remain flat the distance masses don't have an influence on that because we
know what absolute space is okay and Mach says no I don't believe that I would rather believe that the
distant masses in the in the universe would create a similar force that makes the water surface
curve well I have discussed this recently in a real physics talk with Andre Assis and there
is also a very nice visualization of the Newton bucket with dialect the YouTube channel but
let's pinpoint the epistemological problem here: Whether you believe Mach or Newton never mind but
there is a problem Newton's bucket you can see it as a dynamical experiment that determines what
is absolute space and another dynamical experiment is Foucault's pendulum that tells you that the Earth
is rotating so you have these kind of dynamical experiments that determine the rest frames and
of course you also can look out to the universe and see what is not really rotating what is
at rest you look at galaxies and the distant quers and nowadays we have this very precise
measurements so here is the point you can see what is at rest and you can also feel with the
dynamic experiments what is at rest and these two frames nobody wonders very much about that these
two frames coincide there is the same that means we're not observing that the universe is rotating
okay but here's the problem there is no no reason for that in Newton's Theory Newton would say
okay that's just coincidence but as a physicist you don't want to believe in coincidences you
want an explanation and it's very irritating that there is no explanation in Newton's theory
for this coincidence of absolute frames and even more disconcertingly, even in Einstein's general
relativity there is no explanation even if Einstein took some ideas from Mach. But in in that
sense general relativity lacks explanatory power for this strange coincidence of inal frames now I
have mentioned the problem several times and there is also I mentioned also this nice paper by lint
Bell and cuts but let's say it's nothing compared to this real gem in the history of physics this
1953 paper of the British-Egyptian cosmologist Denise Sciama and he actually solves the problem
it's incredible but I myself didn't realize this for a long time now how I came to know Sciama's
paper I was pondering a long time ago about Mach's principle and how to possibly calculate
the gravitational constant and arrived with a very simple reasoning at the formula for the
gravitational Constant and immediately thought well somebody else must have thought about this and so
I looked up Sciama's paper and indeed there was the same formula and it's very very simple but very
intriguing it basically says um the potential the gravitational potential of the entire universe
you take the sum over all masses divided by the respective distance with a gravitational constant
equals c^2 so I read Sciama's paper but somehow I did not appreciate very much the way how he arrived at
this result and I did not really appreciate enough the details and overlooked completely that he had
solved the other important problem so let's have a look at Sciama's original paper we have it here so
what Sciama does basically he defines a potential that is mass divided by distance and note here
is there is still no gravitational constant here uh you can phrase this as an integral it's the
same thing as the sum over masses divided by the relative distance you can also phrase it as the
density divided by the distance and integrate over the volume so this would be just kilogram
over meters what he calls potential and then he develops an analogy with the electric and magnetic
field and says okay let's assume that there is a vector potential and there is then you can
derive certain forces from this Vector potential but at the time somehow it did not convince
me it seemed to me like he was trying to set up some strange analogy with electrodynamics
and tried to unify maybe electrodynamics and I was convinced no it's not possible and that
I still think it's not possible unless I'm really mistaken but uh what's interesting here
I mean it it's useful if you're familiar with the formalism in Electrodynamics just look at or
just remind you that the electric field can be computed from the gradient of a potential and then you add the
time derivative of the vector potential and the magnetic field can be derived by the curl of that
Vector potential so but as I as I said I failed to recognize the significance of all this and even
if I had mentioned the problem let's say I didn't understand properly the paper unless recently
a guy from Bristol approached me saying that he was doing a PhD on Sciama's thesis and and I said okay
interesting send your papers and I had a look at the papers and still I didn't realize unless
my friend and collaborator Yan Preuss who is a co-author of that paper on Mach's principle he
said to me you got to look at this this is really interesting and now if eventually we had a look
at Fay's paper which is very didactical and I will show you some uh this is still unpublished
I hope he will publish it soon but it's it's very didactical now as I said he recounts what's
in Sciama's paper and then he has this section a rotating homogeneous universe and now just
again repeating this would still be just the Mass over distance with the unit kilogram over
meters this integral over the density and now what he does is this is the zeroth component of
this Vector potential and he adds a term which accounts for the relativistic invariance that what
makes the the four potential Lorentz invariant so in a way it's a technicality but you recognize here
Omega square, Omega is the rotational velocity Omega square R square would be the usual V square the
speed and v^2 over c^2 is a well-known expression in special relativity and then he writes down
the potential of a rotating Universe I should have mentioned that the other three components
are just the same potential times the velocity divided by the uh speed of light and that's the
same definition used by Fay in his section of rotating universe and now he applies this to the
problem of a rotating frame for example the first component would be the Velocity in two direction
the second component would be minus the Velocity in One Direction and the zero in the third
Direction and then you have this potential and now you try to derive these analogous quantities
to the electric and magnetic field and you have the gradient of the zeroth component and you
have the time derivative of the rest of the three components this is the vector here and
now the time derivative of this three components which is basically the time derivative
of the Velocity that means is the acceleration so you have one side of the equation the acceleration
and then the other side something very interesting happens you have due to this uh gradient you have
not omega square but you have just an R Vector here if you take the gradient and that means you have
omega r/ c^2 that is your centrifugal force! Here it is, once you are in a rotating Universe
a little bit off-center you automatically get from this potential the yeah what's called the
inertial force caused by the rotational motion the centrifugal force that's a fantastic result
and well Sciama phrases it you can imagine now that you are on the earth at rest and Foucault's
pendulum is pulled around by the rotating Universe now we have introduced this Machian version and put
it into a real formula into a real theory that indeed realizes Mach's suggestion that the distant
masses in the universe would be responsible for inertia and if we could perform that thought
experiment let the universe rotate around us indeed it would curve the water surface in the
bucket and would also influence Foucault's pendulum as we know and now another technicality is that you
get the Coriolis Force if you apply this curl to the vector potential you get the Coriolis force
here but I haven't mentioned the big one! The big one is the next section here and Fay considers
not a homogeneous rotating universe but a Universe At rest but with a mass at the center and that
means a inhomogeneity and where's the section yeah here we are so uh this usual potential you
would add that little potential say from the Sun or from the earth and now you do the very same
calculation okay it's the very same formulas you apply the gradient to the 0th component this
one 1/ c um time derivative of the spatial three components gives you time derivative of the
Velocity which is again acceleration so here we have nothing else but the acceleration in this
term and now but you if you have the homogeneous universe and you have just one mass at the center
and you take the gradient since it's homogeneous everywhere all this vanishes and you have just
this local component which is m / R^2 you see the inverse Square law popping out here but on
the other side of the equation you have still the contribution of the entire universe here
the potential as defined by Sciama but it's just a potential with the units kilograms over meters okay so
what but what you can do obviously here pull it to the other side of the equation and then you
have your expression for the local acceleration which is basically the inverse Square law m /
R^2 but what's missing here is a gravitational constant and here it is okay this term c^2 over
the sum over the masses over the respective distances that's a gravitational constant okay
and we know that the coincidence is there as as as far as orders of magnitude are considered it's
the correct order of magnitude 6. 67 * 10- 11 m^3/s^2 kg; this is the gravitational
constant and he derives it from this very simple ansatz of this Vector potential so if you go here
you can Define this is nothing else than the thing I showed before the gravitational constant so you
have really a unifying pict picture here in which from the same formalism the origin of inertia
and the origin of gravity arises I I I'm just baffled by this I'm just this this still just
blows my mind and let's let's read what how Fay comments on this and we recognize Big G as
the Newton gravitational constant but the difference is now that G is not a universal constant
as some godness some arbitary number invented by the Creator you don't want that as a physicist ...
Rather it is inversely proportional to the gravitational potential of the entire universe
the smallness of G and it's very tiny and thus the weakness of the gravitational force is simply
an outcome of the vastness of our observable universe in relation to any nearby Mass (isn't
that beautiful!) moreover the appearent constancy of G is merely a consequence of the relative
constancy of the cosmological environment the most groundbreaking result of Sciama's model is
however that gravity necessarily exists as a direct result of March's principle that is of
the necessity to define a law of inertia in a wholly relational manner that's referring to the
bucket problem and the two interpretations of we might see that uh curved surface yeah in a wholly
relational manner in the absence of any absolute physical structures since the mass of the universe
is not homogeneously distributed the inertial field which defines motion and the absence of
other forces cannot be homogeneous either the expression of this necessary in homogeneity
is the inertial field of the inertial field is simply what gravity is so I mean yeah as I
said I think you have I have to you have to let that sink in in a little bit but it's really
a bold and beautiful result and it's a result that properly realizes Mach's principle Mach
had suspected that inertia had its origin in all masses in the universe and as a consequence he
also suggested that gravity has its origin in all masses in the universe and that if you remember
implicates a little bit the equivalence principle that later was used by Einstein to derive general
relativity in which you say gravity and inertia is essentially the same thing and here we have
a formalism a model from which it really comes out and of course another consequence of that
Mach's principle is that you can now compute the gravitational constant it's it's as I have
mentioned many times it's very unsatisfactory from an epistemological point of view that you need to
postulate a god-given constant that rules all the universe no you want to understand you want to
compute that number and this is what can be done in Sciama's model that realizes Mach's principle now
it's really I'm you see I'm I'm really excited I'm I'm really enthusiastic about it but to be
fair to be honest there are still some problems how to connect this with other known facts and
um Sciama also was aware of this and he had a thesis in which he introduces also a metric I think
that's the correct way to replace one day the vector potential and he also mentions that's very
interesting a refractive index of space and that points to another very smart idea in um gravity
an idea I have made a lot of videos about that of a paper of Robert Dicke now what did Robert Dicke
do he basically applies the same formula also as in Sciama's paper even if he was not aware of it
but what dick does is developing a the theory of variable speed of light that explains the effects
of general relativity such as light deflection red shift and Shapiro time delay interestingly
this also relates to an old idea of Einstein Einstein in 1911 thought about variable speed
of light and actually variable speed of light was Einstein's first idea when he considered the
equivalence principle but let's remember general relativity is fantastic and describes the results
in a very elegant manner but it lacks explanatory power in two very important aspects it does
not compute the gravitational constant and it does not explain this strange coincidence
of our dynamical and visual measurements of what means being at rest I should mention
here also Erwin Schrödinger who also suggested in 1925 that the potential of the entire universe
might be the square of the speed of light which is Sciama's basic formula so you see all this
is very nicely interlinked I've made a playlist about this variable speed of flight theories with
all different aspects history Mach's principle also there is also a nice relation to Dirac's large numbers
and to modern problems of Hubble redshift and Dark Energy the only thing which is missing
is that really spectacular Insight of Denis Sciama in 1953 that explanation or that unification of
gravity and inertia and yeah I like very much this caricature you see here uh a rotating bucket
and Newton is in the center and here is Einstein struggling with rotating frames and accelerated
motion and general covariance and so on and out there far distant in the universe is ma and you're
tempted to place here also Denis Sciama because I think he really made an essential contribution
even if it might not be completely worked out . but I think the idea is really great and well it's
it's it's very ironic that I mean Mach formulated the idea or his objections to Newton's gravity in
1883 and it took 70 years until 1953 for Sciama to solve the problem now we have another 70 years 20
of which I was unaware that the solution existed so progress sometimes seems very slow in physics
and I guess it's a general problem of our way of thinking we focus too much on details on parts of
what is important and we are focusing too much on the present we're lacking the holistic view so
to speak. so I My Philosophy is a little bit like Wittgenstein's if you want to understand something
if you want to solve a problem go to the place where there is oversight go to a place where you
see the big picture even if the details of that picture might not be clear. Yet but we certainly
have a problem in modern physics we develop fancy theories but if you look for instant I mean how
clueless Richard Feynman was about the problem of inertia he was curious and interested but he
was clueless in the end and and the result was already published so I think we have a problem
with our current scientific culture and this is addressed in my my book Make Physics Great
Again let's take a view on the real important problems I'm tempted to say let me know in the
comments what you think about but honestly if you want to delve into this problem you have
to read something you have to work and well a starting point is as I said the the papers I
mentioned and my VSL playlist here is a paper in the Annalen der Physik about the early version of these
thoughts and there is also a book Einstein's Lost Key that deals entirely with variable speed of light
and this Machian ideas and the relation to Schrödinger and Sciama and Dicke who substantially improved
Einstein's thoughts and also Dirac's large numbers I think it's very interesting that we can today have
a look at all this because these people had no internet had no search engines they were unaware
of their best ideas no Einstein didn't know Dirac, Dirac didn't know Einstein's best idea that's very kind
of tragic and I tried to give a summary of all these theories centered around variable speed of
light and machian ideas. if you enjoy the video don't forget to like it and if you're interested
in fundamental physics subscribe to this channel.
