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As I understand it Newton's Laws imply that space is relative, as the laws of physics are the same in all inertial frames and as such there is no way, even in principle, to distinguish a frame that is truly at rest (absolute space). Hence the concept is physically meaningless, and the positions of (and distances between) physical objects, events, etc. are relative to the frame in which one is observing them from. Advancing on to Special Relativity, by postulating that the speed of light (in vacuum) is constant in all frames of reference, we are forced to conclude that time is relative also (as if it weren't then different observers would observe a different speed of light (in vacuum)). This leads to the result that the concepts of space and time are no longer completely separate and independent of one another and instead intertwined (as an event that occurs at rest over some time period in one frame, will occur over some spatial interval and a different time interval in another frame). Hence they should be considered as should be considered as a single entity, called spacetime.

Sorry for the waffling so far, just want to check that my understanding is correct up to this point?!

My main question is, given that space and time are (individually) relative quantities, is spacetime itself relative, or can it be considered absolute (as after all, it is the mathematical space of all possible events and exists independently of the physical events that occur within it)?

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  • $\begingroup$ The distances between two objects are frame independent in Galilean Relativity. Like that used in Newtonian Mechanics. $\endgroup$ – Timaeus Sep 16 '15 at 16:43
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There is a property of spacetime which is independent of frame of reference.

The geometrical properties of the spacetime are described by the metric tensor, $ \eta _{\alpha \beta} =diag({-1,1,1,1})$ is SR (flat spacetime) or more generally $ g_{\alpha \beta} $ (any spacetime) in GR. This tensor specifies the distance between two infinitesimally close spacetime events, for example $ (t_1,x_1,y_1,z_1) $ and $ (t_1+dt,x_2+dx,y_2+dy,z_2+dz) $ in cartesian coordinates. The representation of this tensor is depending on your your choise of coordinates, but it describes the same physical (more accurate - geometrical) object. With the metric tensor you can calculate proper distances (called lorentz invariants in SR) between any two spacetime coordinates, quantities which are invariant under any coordinate transformation (= independent of frame of reference you're using, not necessarily inertial).

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Spacetime is absolute.

In general you can make spacetime as a 4d Lorentzian manifold.

If you only care about Minkowski spacetime then you can make an affine space, a set of points with a binary subtraction that gives a vector in a 4d vector space with a nondegenerate bilinear form that has a Lorentzian signature.

You can even imagine it as a subset of a larger space. But absolutely nothing has to be relative about spacetime, it is a manifold. And you can stick frames or coordinates on top of it but that doesn't change anything.

But you can do the same with Galilean spacetime, have a manifold like $\mathbb E$ (like $\mathbb R$ with a distance that is based on the absolute value of the subtract of two real numbers, so like $\mathbb R$ bit without a preferred origin). Then make a fiber over it with $\mathbb E^3$ as a fiber. So you can make absolute objects if you want them and make relative objects if you want them.

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What you wrote is a bit confused.

In classical physics the state of motion of physical objects is relative to reference frames, however the metric structures, separately spatial and temporal, are absolute. Distances and angles between parts of a body are independent from the reference frame you adopt to represent the body, though the body and its parts may have different velocities and describe different trajectories in time depending on the reference frame. Also temporal distances between events are absolute in classical physics. Restricting ourselves to a subclass of reference frames, the inertial ones, other absolute quantities arise: accelerations and forces.

Spacetime, both in classical and relativistic physics is the collection of events, minimal spatial and temporal determinations representing all what happened, happens and will happen. Events are absolute, they are given a priori before fixing any reference frame on the spacetime. In this sense spacetime is absolute.

For the sake of simplicity I will consider special relativity only in the rest of my answer.

In relativistic physics, differently form classical physics, distances, angles and temporal distances turn out to be relative, they depend on the adopted (inertial) reference frame.

However there is another, more abstract, object which is absolute. It is the so-called Lorentzian distance between pairs of events $e,e'$. $$\Delta s^2(e,e') = -c^2 (t-t')^2 + \sum_{k=1}^3 (x_k-x'_k)^2$$ Above $(t,x_1,x_2,x_3)$ are the coordinates of the event $e$ in an inertial reference frame and $(t',x'_1,x'_2,x'_3)$ are the coordinates of the event $e'$ in the same reference frame. If, keeping fixed $e,e'$, you change reference frame so that $(s,y_1,y_2,y_3)$ are the new coordinates of the event $e$ and $(s',y'_1,y'_2,y'_3)$ are the new coordinates of $e'$, you have however $$-c^2 (t-t')^2 + \sum_{k=1}^3 (x_k-x'_k)^2= -c^2 (s-s')^2 + \sum_{k=1}^3 (y_k-y'_k)^2$$ This abstract identity can be used to build up all relativistic kinematic.

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  • $\begingroup$ Isn't it the case though that position and velocity are relative quantities in classical (Newtonian) physics - this is required for $\mathbf{F}=m\mathbf{a}$ to hold in all inertial frames?! Also, in hindsight I realise that I didn't word my original question particularly well, distances are absolute in Newtonian physics if they are measured at equal times (i.e. simultaneously) in two different inertial frames, however they are relative if they are measured at different times... $\endgroup$ – Will Sep 17 '15 at 7:48
  • $\begingroup$ Well, distances, by defintion, in classical or relativistic physics are computed between simultaneous events corresponding to points of physical bodies (simultaneous in the considered reference frame). This notion of distance is absolute in classical physics and relative in relativistic physics. $\endgroup$ – Valter Moretti Sep 17 '15 at 7:52
  • $\begingroup$ ...for example, consider the case in which there is a person standing on a platform and a person on a train travelling at speed $v$ relative to the platform. Suppose that the person on the train throws a ball vertically into the air at coordinates $(t_{0},x)$ (relative to their frame), according to the person on the platform will assign coordinates $(t_{0},x')$ to the same event... $\endgroup$ – Will Sep 17 '15 at 7:55
  • $\begingroup$ ...The ball will fall back into the person's hand at some later time $t$, however, in this time interval the train will have travelled a distance $v(t-t_{0})$ relative to the person on the platform. Therefore, according to the person on the train the ball will have travelled $0$ distance in the $x$-direction, however, according to the person on the platform it will have travelled a distance $v(t-t_{0})$. Sorry, I realise this is trivial and don't want to be insulting, but just want to check that my understanding is correct?! $\endgroup$ – Will Sep 17 '15 at 7:56
  • $\begingroup$ This is obvious, because it is just mathematics. The physically non obvious fact (actually false) is that the length of a solid ruler is the same if measured in a reference where the ruler is at rest or in a reference where it is viewed in motion. $\endgroup$ – Valter Moretti Sep 17 '15 at 7:59
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[...] distances between physical objects [...] are relative to the frame in which one is observing them from.

No, on several grounds:

  • if a pair of physical objects (a.k.a. "material points", "participants" ...) was and remained at rest to each other then it is properly and unambiguously characterized by a value of their distance between each other,

  • the determination of distance ratios, e.g. comparing the distance between two particular physical objects (which were and remained at rest to each other) to the distance between two particular members of a (suitable, namely inertial) frame (which were and remained at rest to each other, but which had both not been at rest wrt. either one of the aforementioned particular physical objects), does not introduce any ambiguity either, and

  • the determinations, trial by trial, which pairs of physical objects had been at rest between each other, and which not, are not made by plain observation but by measurement; i.e. they're derived from given observational data (described below in more detail) by application of a specific evaluation operation. Likewise, determinations of distance ratios (between suitable pairs) is not by plain observation, but by measurement.

we are forced to conclude that time is relative also

No: any pair of indications ("positions of the little hand" etc.) of each physical object ("material point", "participant" ...) is certainly properly and unambiguously characterized by a value of this object's duration from one indication to the other;
and determinations of duration ratios are certainly unambiguous as well.

And this certainly fits well with the chronometric definition of distance (values, for suitable pairs as described above) as $$\text{distance} := c~\frac{\text{ping duration}}{2},$$ where the symbol $c$ is (subsequently) identified as signal front speed.

an event that occurs at rest over some time period in one frame, will occur over some spatial interval and a different time interval in another frame

That's an incorrect use of the technical term "event" as exactly one coincidence (as far as it can be resolved). What might be said instead is the following:
If one participant indicated having met and passed several other participants not in coincidence, but in succession, then these other participants were and remained separate from each other.

Is spacetime absolute?

According to Einstein's profound insight:
"All our well-substantiated space-time propositions amount to the determination of space-time coincidences {such as} encounters between two or more material points."

Therefore, as far as the immediate observational data is considered "absolute" to begin with, namely the determinations of coincidence (or, as may derived, of sequence) of observations of each participant (and including the consistent determinations of the identities of the various participants),
any conclusions concerning "space-time propositions" (such as the causal structure of a set of events under consideration, and consequently their description as a (suitably generalized) metric space, as well as the derived geometric or kinematic relations between participants (distance ratios, speeds, etc.),
may be called "absolute", too.

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Space-Time is absolute. Absolute-Motion also exists.

However, this absolute motion is only considered to be absolute relative to the absolute 4 dimensional environment known as Space-Time. If one proceeds to analyze the outcome of this ongoing absolute motion that takes place within the absolute Space-Time, the outcome of this analysis is the discovery of Special Relativity and the derivation of all of its mathematical equations, including the Lorentz transformation equations.

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  • $\begingroup$ To see proof of the above statement, watch the 9 mini YouTube videos at goo.gl/fz4R0I $\endgroup$ – Sean Oct 9 '15 at 15:21
  • $\begingroup$ I watched that video, it is simply you admitting that you have no education in the actual physics and then speculating physics that is almost not entirely unlike the reality of relativity and then pulling out the equations without a sound mathematical process. While I have no objection whatsoever to your posting that video on YouTube, I do seriously call into question your definition of the word "proof". I suggest, if I may be so bold, that you learn the true relativity first. That should put you in a position where explaining your ideas and methods is much easier and more persuasive. $\endgroup$ – Jim Jul 20 '16 at 11:21
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Short answer: Yes, spacetime is relative.

Einstein's relativity mixes space and time when transforming from one set of coordinates to another, however there is no preferred frame. This is part of the criteria known as Lorentz invariance. If you are given the physical results of an experiment, there is no way to determine which particular inertial frame it was performed in.

In modern physics (general relativity, quantum field theory) time and space are always treated on an equal footing. All currently verified theories and observed phenomena are Lorentz invariant. However there are several hypotheses kicking around in the physics community (e.g. certain theories of modified gravity) which break Lorentz invariance by creating vectorial gravitational fields (as opposed to the tensorial fields in Einsteinian gravity) which have a unique direction, implying an absolute rest frame. Such theories are completely unconfirmed, so for now the answer is that as far as we know, all frames are equal.

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  • $\begingroup$ Surely though spacetime as a geometric structure describing the universe is (in some sense) observer independent, as otherwise there would be an infinity of spacetimes (one for each frame of reference). As far as I understand it Lorentz invariance means that that laws of physics are the same in all coordinate systems. However, the underlying spacetime manifold exists independently of any particular coordinate system... $\endgroup$ – Will May 12 '15 at 16:02
  • $\begingroup$ ...Each coordinate system just assigns a particular 'label' to a given point on the manifold, however, this point exists on the manifold independently of such a label, and has the same 'position' on the manifold regardless of the coordinate system used to describe it. This seems to me to be absolute (certainly in the sense that Newton meant it - a space of fixed points that remain fixed and whose relations with other points (distance between, etc.) remain fixed. $\endgroup$ – Will May 12 '15 at 16:05
  • $\begingroup$ Spacetime is not just some mathematical description. The physical curvature of space (the mixing of space and time) is a physically measurable quantity. A theory can still be co-ordinate independent and break Lorentz invariant. See this interesting (but long!) talk for details youtube.com/watch?v=iu7LDGhSi1A (about 35:00 onwards it discusses potential new theories which break Lorentz invariance). $\endgroup$ – Jack Richings May 12 '15 at 16:09
  • $\begingroup$ Put simply, Newton was wrong. As far as we know Einstein was right, but Newton was not. $\endgroup$ – Jack Richings May 12 '15 at 16:10
  • $\begingroup$ This breaks Lorentz symmetry: Parity_violation - "Although parity is conserved in electromagnetism, strong interactions and gravity, it turns out to be violated in weak interactions." as seen here CPT_symmetry"A consequence of this derivation is that a violation of CPT automatically indicates a Lorentz violation." $\endgroup$ – Helder Velez May 12 '15 at 16:15

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