GR lacks absolute space, but what is absolute space?

[name123]

GR lacks absolute space, but does Newtonian physics also? If not what does GR lacking absolute space mean?

I had thought in Newtonian physics that there existed an absolute space in which Newton's laws are true, and that an inertial frame was a reference frame in relative uniform motion to absolute space. Is that wrong? I was given the impression by a staff member here that it was, and I was advised not to read the wikipedia article ( https://en.wikipedia.org/wiki/Galilean_invariance ) which stated:

Among the axioms from Newton's theory are:

1. There exists an absolute space, in which Newton's laws are true. An inertial frame is a reference frame in relative uniform motion to absolute space.
2. All inertial frames share a universal time.

But I find that somewhat confusing because in the Stanford Encyclopedia of Philosophy it also states https://plato.stanford.edu/entries/Newton-stm/ "Newton defined the true motion of a body to be its motion through absolute space."

What I particularly found confusing is while I had pointed out, using a wiki article ( https://en.wikipedia.org/wiki/Absolute_time_and_space ) that "...within the context of Newtonian mechanics, the modern view is that absolute space is unnecessary. Instead, the notion of inertial frame of reference has taken precedence, that is, a preferred set of frames of reference that move uniformly with respect to one another" the staff member replied not that yes he held the modern view that absolute space was unnecessary, but stated that I had misunderstood what absolute space meant. So if anyone could clear up that misunderstanding that would be useful, as before coming to the forum I had not realized that I had misunderstood it.

I had thought GR lacking absolute space meant that its inertial frames should not be thought to be reference frames moving relative to absolute space, to that there was no true movement as I think Newtonian stated.

 

[PeterDonis]

This is one of those cases where ordinary language just doesn't work very well. What you are seeing is attempts on the part of various people to try to describe the differences between Newtonian mechanics and relativity using words instead of math. They are, very confusingly, using the same term, "absolute space", to either refer to different things in the math, or to refer to nothing at all in the math.

It's hard to go too deeply into the math at the "B" level; as I've commented before, the real cure for this is to spend time working through a textbook (or actually two, one for Newtonian mechanics and one for relativity) to see how the differences actually play out. But we can at least make a start.

Let's restrict attention to inertial frames (although even here there is an issue because the definition of "inertial frame" as it actually works out in practice is not quite the same in Newtonian physics and relativity--but we'll get to that). The general concept of an inertial frame is the same in both Newtonian physics and relativity: it is a frame in which the principle of inertia--bodies not being acted on by a force move in straight lines at constant speed--holds good. So in any given inertial frame, we can define coordinates ##x, y, z, t## and say that anybody not being acted on by a force will move in such a way that the coordinate derivatives ##dx/dt##, ##dy/dt##, and ##dz/dt## will be constants, which we can call ##v_x##, ##v_y##, and ##v_z##. For simplicity and to save typing, we will ignore the ##y## and ##z## dimensions and assume we are dealing with objects moving only in the ##x## direction, so we just have ##dx/dt = v## for anybody not being acted on by a force.

Also, both Newtonian physics and relativity have the same concept of a "principle of relativity": basically, that the laws of physics should take the same form when expressed in terms of the coordinates of any inertial frame. (Note that this is just the "special" principle of relativity at this point--we are only talking about inertial frames and inertial coordinates. Trying to extend this to the "general" principle of relativity brings in other issues that I don't think we're ready to tackle at this point.)

The two key differences between Newtonian mechanics and relativity are now easy to state:

(1) The transformation we use to convert from coordinates in one inertial frame to coordinates in another frame is different in Newtonian mechanics vs. relativity. In Newtonian mechanics, we use the Galilean transformation:

$$
x' = x - vt
$$
$$
t' = t
$$

Whereas in relativity, we use the Lorentz transformation:

$$
x' = \gamma \left( x - v t \right)
$$
$$
t' = \gamma \left( t - \frac{v}{c^2} x \right)
$$

(2) In Newtonian mechanics, gravity is a force; in relativity, it isn't. So, for example, in Newtonian mechanics, I can define an inertial frame centered on a gravitating body, like the Earth, that covers the whole Earth and its vicinity. I can do this even though bodies left to move freely (i.e., no rockets pushing them, etc.) will not move in straight lines at constant speeds in this frame; their motion will not be described by ##dx / dt = v## where ##v## is constant. (Note that here the ##x## direction means along some chosen radial line, and we are only considering radial motion for the time being.) But that's ok in Newtonian physics, because gravity is a force, and we account for the coordinate acceleration of such bodies--the fact that ##dx / dt## varies with time--by saying that the Earth's gravity is exerting a force on them, and the principle of inertia only applies to bodies on which no force is being exerted.

In relativity, however, we don't do this. Instead we observe that, since bodies moving solely under gravity feel no force (they are weightless), the obvious conclusion is that gravity is not a force; it's something else. (The something else turns out to be spacetime curvature, but we haven't got that far yet.) And that means that we can't define an inertial frame centered on a gravitating body like the Earth that covers the whole Earth and its vicinity, because bodies that are not being subjected to any force do not move in straight lines at constant speeds in such a frame. The best we can do is to define local inertial frames, covering small regions of space (and small intervals of time) that we are interested in.

Notice that nowhere in any of the above did I have to talk about "absolute space". So what is all this stuff about "absolute space" that appears in all these different sources? Again, it's very confusing because that term can refer to different things. Some examples:

- Newton, as far as I can tell, meant by "absolute space" something like "we can't distinguish inertial motion from rest, but we can distinguish non-inertial motion from rest, so there must be some kind of absolute nature of space that let's us do that". In other places Newton refers to the thought experiment of a bucket full of water: if the bucket is not spinning relative to the distant stars, then the surface of the water in the bucket is flat; but if the bucket is spinning relative to the distant stars, then the surface of the water is concave. The standard Newtonian account attributes this to "centrifugal force" acting on the water in the bucket; but why should "centrifugal force" act when the bucket is spinning relative to the distant stars? This sort of thing is what Newton was thinking of when he talked about "absolute space". But as you can see this has nothing whatever to do with relativity of inertial motion, or transformation between frames, or using coordinates centered on one object vs. another, or any of that.

- Some sources, like the Wikipedia page that talks about the "modern view" that absolute space is not required in Newtonian physics, are basically treating "absolute space" as referring to nothing at all in the math. They are looking at the things I described above--the fact that we can talk about Galilean vs. Lorentz invariance, the (special) principle of relativity, choosing inertial coordinates, etc., without ever mentioning "absolute space" at all, and concluding that the term just isn't useful at all.

- The Stanford Encyclopedia of Philosophy quote looks to me like it's trying to extend Newton's observations about non-inertial motion, which I described above, to the case of inertial motion--but that doesn't work, because of the special principle of relativity. There does appear to be a way to tell if you are rotating relative to the distant stars, but there is no way to tell if you are moving in a straight line at a constant speed relative to the distant stars. So the two cases are not the same, but the encyclopedia is trying to treat them as if they are.

To me the simplest way to avoid all of this confusion is to avoid the term "absolute space" and just go straight to the actual physics you are trying to describe. The two key differences I described above should be enough to do that, at least as a start.

 

[Dale]

The other thing to recognize is that in science the great minds that come up with new theories are not considered to be infallible prophets whose words are the ultimate authority. What we today call Newtonian mechanics is different from what was originally described by Newton and what we today call General Relativity is different from what was originally described by Einstein. They were the first to propose their respective theories, not the final word.

Newton did speak of absolute space, but modern Newtonian mechanics does not use that concept. It was removed by Galileo. The quotes of Newton are of historical or philosophical interest only.

 

[PeterDonis]

It was removed by Galileo.

Saying it this way might be a bit misleading, since Galileo worked before Newton did (he died before Newton was born). Galileo enunciated the (special) principle of relativity, which was indeed a "removal" of absolute space at least in part (by establishing the relativity of inertial motion). But Galileo did not, AFAIK, address the concerns about non-inertial motion, such as rotation, that I mentioned before and which Newton appears to have spent considerable time wondering about. Our current resolution of that issue did not really come until GR was fully understood (and not all physicists even agree that GR resolves it).

Your points about past scientists not being infallible authorities is spot on, though.

 

[Dale]

Saying it this way might be a bit misleading, since Galileo worked before Newton did (he died before Newton was born).

Hmm, that is funny. I have been at this for decades and I never noticed that the dates were wrong for that.

Since we are talking about history, do you know who it was that showed that Newton's laws respect Galilean relativity.

 

[PeterDonis]

do you know who it was that showed that Newton's laws respect Galilean relativity

I had always thought Newton did that, but I don't have a handy reference to back that up.

 

[Ibix]

I had always thought Newton did that, but I don't have a handy reference to back that up.

The quotation from Principia that name123 gave in the other thread hinges on the notion that the absolute frame Newton believes in is undetectable. That suggests he understood the Galilean invariance of his laws then, no?

 

[PeterDonis]

That suggests he understood the Galilean invariance of his laws then, no?

Yes, I think you're right.

 

[name123]

Yes, I think you're right.

The point in the thread that you closed when I mentioned the wiki page, was that in Newtonian physics if one were to consider the following scenario:

Imagine three marbles A, B & C with each with 2 small lasers attached. All in the same rest frame, separated from each other by a light year, and forming an isosceles triangle (where AB and AC are the same length, and the centre of BC is a kilometre from A), and that the lasers of each pointed to the marbles adjacent to them in the triangle (so like pointing to the adjacent vertices). And imagine that there were two equally sized space ships, D & E each having the external shape of of opposing halves of a cylinder bisected along its axis. D and E both travel fast towards the midpoint of BC from opposite directions along a line perpendicular to BC and which transects BC at its midpoint. Imagine that, from the perspective of D and E, that in the last 30 seconds of their journey, they decelerate as fast as the laws of physics allow and come together to form a cylinder 100m in diameter with its axis orientated along BC. I'll refer to the cylinder as F. Imagine F has enough mass to (from F's perspective) pull A towards it at a rate of 0.01 mm per second from where A was when F was formed (so the rate will increase as A gets closer). Over time A will be pulled towards F such that they touch.​

Newtonian physics predicts and explains that in such a scenario the magnitude of change in A's velocity vector (relative to absolute space) in the direction of F > than the magnitude of change in F's velocity vector (relative to absolute space) in the direction of A.

It does not (as far as I understand) predict or explain that in the scenario, relative to absolute space, A's velocity vector undergoing no change, and F, B and C undergoing a change in their velocity vectors relative to absolute space instead. Because, from what I understand, in Newtonian physics there is no explanation for why A's position would remain constant relative to absolute space, but not F, B, and Cs'.

From what I have read it does seem that Newton understood the idea of Galilean invariance of his laws, and as mentioned from in the post on the GR interpretation of a scenario GR interpretation of a scenario

https://en.wikipedia.org/wiki/Absolute_time_and_space you will see a quote from Isaac Newton from (I assume) Philosophiæ Naturalis Principia Mathematica.

Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies: and which is vulgarly taken for immovable space ... Absolute motion is the translation of a body from one absolute place into another: and relative motion, the translation from one relative place into another ...

— Isaac Newton​

It seems clear that he understood relative Galilean invariance and I find it strange that you are claiming to be struggling to understand what Newton meant by absolute space, since I would guess that it is the intuitive understanding of space. And is a concept easy to understand when following the history of the concept development of physics.

The larger point that I am trying to make is that absolute space (seems to me) is compatible with Newtonian physics, and that furthermore there do not seem to be explanations (in terms of the forces posited in Newtonian physics) for scenarios such as the one mentioned without absolute space in Newtonian physics ( I suggest reading the GR interpretation of a scenario thread (that was closed by PeterDonis https://www.physicsforums.com/threads/gr-interpretation-of-a-scenario.902163/page-3#post-5682492), as I give examples of the difference in having absolute space (not the post of PeterDonis obviously), if what I am trying to convey in this post is unclear). .

I assume that Newton's ideas regarding absolute space are a matter of historical fact, and I assume that people understood him at the time, so quite surprising that the concept might become incomprehensible to a scholar later.

Is absolute space any less compatible with GR than it is with Newtonian physics?

It may not seem a big issue but consider the "Andromeda paradox" https://en.wikipedia.org/wiki/Rietdijk–Putnam_argument

With absolute space, there is absolute time, both in GR and as Newton pointed out, in Newtonian physics. In both you cannot tell what absolute space is (and in GR therefore not absolute time).

The difference, while not mathematically significant, has an impact on peoples lives. In the one case (with no absolute space) children could have the idea that whatever they can do must have been their destiny (consider some school massacres) , in the other (where there is absolute space ) free will easily be thought to exist (with absolute space is absolute time: the future is not already set). So while people could have a political agenda to lead people away from God on a weak argument of introducing operational definitions for space and time. https://en.wikipedia.org/wiki/Absolute_time_and_space (under the Differing View section):

These views opposing absolute space and time may be seen from a modern stance as an attempt to introduce operational definitions for space and time, a perspective made explicit in the special theory of relativity.​

I think it should be mentioned, to the children, that these decisions (regarding the existence of absolute space) were made with regards to operational definitions and not how people might need consider it. The example given shows (I think) how with or without absolute space the explanation by Newtonian physics is not equivalent. Assuming the post history on this forum is honest, you can see in post https://www.physicsforums.com/threads/gr-interpretation-of-a-scenario.902163/page-2#post-5681337 that the staff mentor Nugartory thought that you would need to introduce fictitious forces to explain the scenario where A did not move (motion was truly relative). It could be modeled mathematically either way. The difference is with which scenarios it could be explained by the theoretical model of what was going on. If it could be explained in both, then both are compatible. My question to the forum is:

Is absolute space any less compatible with GR than it is with Newtonian physics?

If this is a political forum with some agenda, then I won't find it surprising if you again close the thread. If not then please explain whether it is by necessity, or choice. I do not think I am the only one interested.

 

[PeterDonis]

Newtonian physics predicts and explains that in such a scenario the magnitude of change in A's velocity vector (relative to absolute space) in the direction of F > than the magnitude of change in F's velocity vector (relative to absolute space) in the direction of A.

No, that is not what Newtonian physics predicts. Newtonian physics predicts that, in an inertial frame in which A and F start out at rest at some instant of time, the magnitude of A's coordinate acceleration will be much larger than the magnitude of F's coordinate acceleration. There is nothing in the actual prediction of Newtonian physics for this scenario that can be described as "absolute space".

I assume that Newton's ideas regarding absolute space are a matter of historical fact

Yes, they are. But that is not the same as saying they are part of Newtonian physics, the model that Newton and many others after him actually used to make predictions. This is the key distinction that you are missing, and have been missing all through this discussion. You keep quoting statements of Newton that, however historically interesting they are, are not part of the actual physics he used. They are just statements of his personal opinions.

If you want to find out what, if any, role the concept of "absolute space" plays in Newtonian physics, or GR, the first thing you need to do is to look at the actual physics--the actual models that are used to make predictions. You need to find what concept in those models corresponds to the term "absolute space". And then you need to see what role that concept plays in making predictions.

If you do that for the scenario you posed, you will find, as I said above, that there is no concept in the Newtonian analysis that corresponds to "absolute space". You have been told this before, but instead of either (a) accepting it, or (b) going into the actual model and finding such a concept, you are continuing to repeat your mistaken understanding. That is not the way to have a productive discussion.

The difference, while not mathematically significant, has an impact on peoples lives. In the one case (with no absolute space) children could have the idea that whatever they can do must have been their destiny (consider some school massacres) , in the other (where there is absolute space ) free will easily be thought to exist (with absolute space is absolute time: the future is not already set).

The concept you are talking about now is determinism vs. free will, which is not the same concept as "absolute space" (or "absolute time"). Nor is it a physical concept, so it's off limits for discussion here anyway.

Is absolute space any less compatible with GR than it is with Newtonian physics?

You have already been told the answer to this question: "absolute space" does not play any role in the actual physical models used in either Newtonian physics or GR.

If this is a political forum with some agenda, then I won't find it surprising if you again close thread. If not then please explain whether it is by necessity, or choice.

This thread is being closed because you are refusing to listen to what you have already been told. Plus, you are confused about what concept you are talking about. Plus, you are dragging in things that have nothing to do with physics.

I do not think I am the only one interested.

Then how come nobody else has posted in this thread except you, two moderators, and one Science Advisor, and the latter three were only posting in order to respond to you or clarify points in those responses?

 

[PeterDonis]

This thread is closed.