Both. The bulge due to our rotation is much larger but is constant in time and uniform with longitude since the whole planet spins at the same rate. There is also a bulge due to the Moon and a smaller bulge due to the tidal effect of the Sun, that creates the difference between "spring" and "neap" tides.

https://oceanservice.noaa.gov/facts/springtide.html

Thanks George (quick off the mark!). I think you are saying that presumably those tidal effects affect the Earth's mantle too, and over time have led to deformation from a spherical in addition to the rotation bulge. What is niggling me about this question, though, is the absence of background stars. Does the space defined by the Sun and Earth define enough space to spin against? It seems crazy to me, but possibly correct nonetheless, that the Earth's spin depends on space defined by those far away stars. Hence the thought experiment: is one star enough?

In principle the question whether the earth is spinning and space stands still or whether space is spinning and the earth stands still is a matter of choice of your reference frame. Inside that reference frame you have to fit your forces of nature to the observations.

Under the condition that you chose the earth to stand still you have to conclude that space rotates around you and that this rotating space has an influence on the gravity field. This then makes the equator bulge with respect to the poles. Also all stars move with an ever faster speed around you the further away they are. Soon you find stars that move faster than the speed of light. But that does't matter because it is space it self that is rotating around you.

Under the condition that you chose the earth to rotate you have to conclude that space stands still and then the rotation with its centrifugal force cancels a littlebit of the gravity and makes the equator bulge.

Now you can chose what model gives the simplest explanation of the observations and take that one as the best.

Based on this thinking you might continue.

If we assume that the earth rotates but its position is static then we have to invent special celestial mechanics to make all planes and the sun move around the earth according to observations. As soon as we decide that the sun is the centre the observation of the planet movements can be explained in a much simpler way.

Now we can expand our observation further out and see if we should continue in this process. We know from special relativity that nothing can go faster through space than the speed of light. If we keep the sun as the centre of the universe then we have to see that the line from the sun to the centre of our galaxy is rotating. With that somewhere out in space stars have to move faster than the speed of light to stay on the observed position. But this doesn't matter because again it is space it self that is moveing.

Out of this observation we came to the explanation that even the sun can't be the centre of the universe and that we gave up the search of a centre.

Now let me make a few more steps.

In your memory you might have the time that you played in the kindergarten. That place was big and you could move around. When you come back there years later you notice how that place did become small. Why you experience that that place became small? This is because we take the distance from our eyes to the ground as our reference height. With that reference frame we have to conclude that the kindergarten did shrink. The world did shrink. Under that assumption stars moved towards us with a speed faster than the speed of light, but that doesn't matter because space itself is moving and not the stars in space.

Why this example? We have moved on from this reference frame and use different lengths as a reference. In the new reference frame we acknowledge that we our self did grow. It is not our immediate experience but with the observation that other people grow we easy accept that also we did grow.

Yet in this reference frame, that we all have accepted, there are stars, galaxies and galaxy clusters that move away from us with a speed faster than the speed of light. But again, this doesn't matter because it is space it self that is expanding.

Why we discarded all other reference frames where some part of space moved faster than the speed of light and we keep this expanding reference frame where again part of space moves faster than the speed of light?

There is a reference frame where nothing, not even space, is moving faster than the speed of light. That frame is the comoving reference frame.

When we accept that reference frame then in there all matter is shrinking.

In order to explain our observations we have to find properties of matter that allow that matter shrinks. In the reference frame where matter is constant we have to find properties of space to explain its expansion.

These properties are the Friedmann equations.

I have an article that is accepted for publication in the Journal of High Energy Physics, Gravitation and Cosmology, JHEPGC, that shows why the calculations that lead to the Friedmann equations have problems. It also elaborates more on the Idea to use the comoving reference frame as the closest to reality.

I hope my answer is not to long and didn't deviate too much from the initial question.

Thanks Paul, my first impression of your answer is that you are correct. I had not considered that the effect of a rotating Earth in a non -rotating space was indistinguishable from a non-rotating Earth in a rotating space, and that, therefore, it is just an arbitrary choice of reference frame. Though clearly the sensible choice is to choose the background stars as non rotating, particularly when this is coupled with the ideas of vacuum energy, which makes space a more physical thing. So in my question where the background stars are made to disappear, we still have the surrounding vacuum energy, which we can treat in the same way as the background stars - is this right?

What your answer infers, by the way, is that even if the Earth was the only object in the universe, we could still determine its spin by measuring the bulge etc.

Yes, I like this. I had discounted the idea of a rotating universe as nonphysical because of special relativity speed limits. Your answer clarifies this. Thanks again.

Hello Peter, you are welcome.

Maybe I have to clarify. In current physical understanding it is nonphysical if matter moves through space with a speed faster than the speed of light. However it is accepted that space itself moves faster than the speed of light. This is the big issue with the expanding space. The wavelength of the light from a distance where the redshift z = 1, is measured here as double the wavelength of a similar source here. That means that that place in space would be moving away from us with the speed of light. We receive light with z = 10 or more. There is clear agreement that this is interpreted as that space itself is expanding and not that those galaxies are moving through space with that speed.

So, although we have mostly accepted that we are closest to reality when we assume that space doesn't rotate around any axis, we still assume that space is expanding. Rotation needs some axis, some reference of place. Expansion doesn't need a central point of reference, yet it needs a reference of size.

What I propose is to ditch also that reference of size. I think that we are closer to reality if we assume that space is constant and therefore we shrink.

A version of my thinking is uploaded here in researchgate. You might want to have a look there. Good luck.

The question has been discussed in the past at least since Newton (~1700) and thus has a vast literature. Key words for searching: "Mach's principle"

https://en.wikipedia.org/wiki/Mach%27s_principle

Hi Daniel, do you agree with Paul's answer that, to paraphrase, everything is relative: not just velocity but also rotation and expansion? I am aware of Mach's principle, and understand that Einstein's GR has superseded and incorporated it, and therefore that should be the starting point for an answer.. I studied GR at postgrad level but I always had difficulty interpreting the maths physically, e.g. we can write down a metric external to a spinning star (Kerr) , but in reality the spinning star is itself in an expanding universe, so the spinning star metric is implicitly relative to the space defined by the universe as a whole. I am guessing that no one has come up with an analytical solution for a spinning local metric inside an expanding space metric? If this did exist then we could, I would imagine, formally investigate Paul's theory by changing frame to rotate with the star. But that is just a hunch.

Hi Peter,

Well the famous bucket as discussed by Newton can be told to rotate with respect to an inertial frame if the surface of water has a parabolic shape, and not rotate if the water level is flat. So rotation can be measured locally and is not relative. Likewise an oblate fluid planet is absolutely rotating.

The velocity of light limit in GR is only assumed for local physical problems, so there is no contradiction for solutions of GR equations where distant space points separate with supraluminal speed. GR is a differential theory, so it describes local constraints in space time. To find solutions one needs boundary conditions. Since analytical solutions are tedious to find, people usually choose simple boundary conditions, such as static flat space at large distance from a star. GR proper boundary conditions are not specified by the theory as far as I am aware, one needs additional arguments (such as causality) for restricting the choice of boundary conditions (Gödel's solutions are known to violate causality so are improper). But expanding or moderately rotating space time boundary conditions could be adopted I guess. GR numerical codes should be able to handle such choices in principle. As the scales of the universe and the scale of a star are very different, nobody should expect much effect on the numerical solutions close to the star, as between the star and the universe an Euclidian flat space is a very good approximation over many powers of ten of scale.

Hello, Based on Mach's principle you can distinguish between a rotating universe around a static frame and a rotating frame in a non-rotating universe. I am allowed to use any frame but have to explain all extra properties like centrifugal force. If everybody is happy with that explanation then 'who cares?'. Only our poor philosophical physicists, or physical philosophers ;), that try to find out what would be the closest to reality discuss what is better. In that discussion I state that it seems we have settled for a non-rotating universe. But nobody seems to take the same approch to the expansion of space. For me this expanding space is a relative movement in a private frame of some one who insists that his size is absolute over time.

You can try to come to a genius solution of the properties of space that mathematically explains centrifugal forces. However it is fare easier to talk about these fires when a body rotates in a static environment. in the same way we spend years of genius research to come up on answers how we can explain the first part of the start of the universe and why it seems to accelerate in the expansion while it would be far simpler to search for properties of matter that allow all matter to shrink.

A far away supernova at z=1 lasts 40 days. A nearby similar supernova lasts 20 days. So in a static universe matter shrinks linear to the duration of time. It sounds exotic but this is the result of only a coordinate transformation. So as soon as you accept that space is constant then the rest is a given fact. The story why and how nature works so that the observations are explained is the task of the scientists.

In the expanding universe we explain the length difference of the supernova event by the stretching of space. Space itself stretches it. It is a property of space.

in the static universe we explain the length difference of the supernova event by the shrinking of matter. Matter mass, length, and time shrink linear. Thus the density of mass rises with the square because the volume shrinks with the cube. Out of this it looks acceptable that the speed of shrinking accelerates. So we don't need a hypothetical dark energy that nobody can find.

Look in my article for further details.

I hope I can find a person who has so much knowledge of GR and cosmology that he either can say I am right or can point me where I am wrong. Until now those scientists that tried to question my views failed to prove me wrong.

Peter Bollada, you studied GR. Try to prove me wrong. If you succeed you help me lose a bad view, if you fail you have reached a huge understanding of GR and nature and I hope you spread the Idea.

I wish you success with your study.

Paul