How did Einstein come up with the thought of a space fabric?

[Zack K]

I've always wondered how we came to come up with such an idea. Was he one day sitting around and thinking, then made a random assumption and go "ah hah!". Or did his idea come up through his calculations on the nature of how gravity should cause interaction? Is their a literal fabric of space (of course it's not like the 2d plane mentioned in pop science), or is that just an analogy to help our human minds understand the nature of gravity and time? If that case is true can't I say the same thing for forces such as electromagnetism? That a proton is attracted to an electron because of this quantum fabric that causes like charges to attract. Also was Einstein just happen to be the one to come up with that ambitious idea and it happen to be right?

 

[Orodruin]

He didn’t. The idea of a spacetime ”fabric” is a strongly overpopularized description of GR.

 

[Zack K]

He didn’t. The idea of a spacetime ”fabric” is a strongly overpopularized description of GR.

So he never coined the term of a space fabric? So what medium does light and gravity travel through then, because I doubt he all he did was come up with some equations on general relativity.

 

[Ibix]

Is their a literal fabric of space (of course it's not like the 2d plane mentioned in pop science), or is that just an analogy to help our human minds understand the nature of gravity and time?

It isn't a fabric. That's just an analogy.

I've always wondered how we came to come up with such an idea. Was he one day sitting around and thinking, then made a random assumption and go "ah hah!". Or did his idea come up through his calculations on the nature of how gravity should cause interaction?

Einstein developed a from-scratch derivation of the Lorentz transforms in his 1905 paper, which was when he published Special Relativity. Minkowski pointed out in 1908 that Einstein's maths was equivalent to a claim that we exist in a (3+1)d manifold, which is the beginning of the notion of spacetime. But one side effect of Special Relativity is that it is completely incompatible with Newtonian gravity. Attempts to understand special relativity in non-inertial frames eventually led to the insight that you could model gravity as a curved manifold.

can't I say the same thing for forces such as electromagnetism?

The key difference between gravity and electromagnetism is that everything is affected the same by gravity - there are no "gravitationally neutral" particles. So it's possible to model gravity as a curved background that everything moves in, while if you try the same thing with electromagnetism you need to explain why a charged particle follows a curved path and an uncharged one doesn't.

I believe Kaluza and Klein made an attempt to do this. I don't think it was terribly successful, but I don't know much about it.

Also was Einstein just happen to be the one to come up with that ambitious idea and it happen to be right?

Einstein did "just happen" to be the one to develop this in some senses. His PhD supervisor, Lorentz, and others had actually put together most of the maths already - in fact, Poincare's 1904 review paper includes everything Einstein published in 1905. He just didn't realize the significance - he thinks of the Lorentz transforms as a patch for electromagnetic theory, rather than a fundamental change in the way we think about everything. Had Einstein not had his insight, someone else would have. The same can be said of General Relativity - David Hilbert was very close to the same ideas.

 

[Dale]

I've always wondered how we came to come up with such an idea. Was he one day sitting around and thinking, then made a random assumption and go "ah hah!".

As @Ibix mentioned above it was Minkowski that came up with the idea of flat spacetime in SR (no gravity). In analyzing the SR flat spacetime model some things became apparent. Inertial objects (as measured by accelerometers) have straight worldlines, and objects at rest with respect to each other are parallel world-lines and never intersect.

So, when thinking about gravity, you can have two inertial objects that are both straight worldlines (accelerometers read 0) and are initially at rest wrt each other (parallel) and yet they collide. This is only possible in curved geometry. Hence the idea of using a curved manifold to describe gravity

 

[weirdoguy]

So what medium does light and gravity travel through then

None. This is the basic lesson from relativity.

 

[phinds]

None. This is the basic lesson from relativity.

Uh ... I think it's more the basic lesson from Michelson and Morley, which was part of the background behind Special Relativity.

 

[pervect]

I've always wondered how we came to come up with such an idea. Was he one day sitting around and thinking, then made a random assumption and go "ah hah!". Or did his idea come up through his calculations on the nature of how gravity should cause interaction? Is their a literal fabric of space (of course it's not like the 2d plane mentioned in pop science), or is that just an analogy to help our human minds understand the nature of gravity and time? If that case is true can't I say the same thing for forces such as electromagnetism? That a proton is attracted to an electron because of this quantum fabric that causes like charges to attract. Also was Einstein just happen to be the one to come up with that ambitious idea and it happen to be right?

I don't know the origin of the idea of space-time as a fabric, whether it can be attributed to Einstein or not, and if not, where did it originate from.

I can quote a bit from a different analogy Einstein used, in his popularization, "Relativity: The Special and General Theory"

https://www.bartleby.com/173/24.html

This idea, based on a heated marble slab, is rather different than the idea of space-time as a fabric, though the fabric idea certainly works too. The underlying math is the same, and one can credit Gauss with originating the math.

THE SURFACE of a marble table is spread out in front of me. I can get from anyone point on this table to any other point by passing continuously from one point to a “ neighbouring” one, and repeating this process a (large) number of times, or, in other words, by going from point to point without executing jumps.” I am sure the reader will appreciate with sufficient clearness, what I mean here by “neighbouring” and by “jumps” (if he is not too pedantic). We express this property of the surface by describing the latter as a continuum. 1
Let us now imagine that a large number of little rods of equal length have been made, their lengths being small compared with the dimensions of the marble slab. When I say they are of equal length, I mean that one can be laid on any other without the ends overlapping. We next lay four of these little rods on the marble slab so that they constitute a quadrilateral figure (a square), the diagonals of which are equally long. To ensure the equality of the diagonals, we make use of a little testing-rod. To this square we add similar ones, each of which has one rod in common with the first. We proceed in like manner with each of these squares until finally the whole marble slab is laid out with squares. The arrangement is such, that each side of a square belongs to two squares and each corner to four squares. 2
It is a veritable wonder that we can carry our this business without getting into the greatest difficulties. We only need to think of the following. If at any moment three squares meet at a corner, then two sides of the fourth square are already laid, and as a consequence, the arrangement of the remaining two sides of the square is already completely determined. But I am now no longer able to adjust the quadrilateral so that its diagonals may be equal. If they are equal of their own accord, then this is an especial favour of the marble slab and of the little rods about which I can only be thankfully surprised. We must needs experience many such surprises if the construction is to be successful. 3
If everything has really gone smoothly, then I say that the points of the marble slab constitute a Euclidean continuum with respect to the little rod, which has been used as a “distance” (line-interval). By choosing one corner of a square as “origin,” I can characterise every other corner of a square with reference to this origin by means of two numbers. I only need state how many rods I must pass over when, starting from the origin, I proceed towards the “right” and then “upwards,” in order to arrive at the corner of the square under consideration. These two numbers are then the “ Cartesian co-ordinates” of this corner with reference to the “Cartesian co-ordinate system” which is determined by the arrangement of little rods. 4
By making use of the following modification of this abstract experiment, we recognise that there must also be cases in which the experiment would be unsuccessful. We shall suppose that the rods “expand” by an amount proportional to the increase of temperature. We heat the central part of the marble slab, but not the periphery, in which case two of our little rods can still be brought into coincidence at every position on the table. But our construction of squares must necessarily come into disorder during the heating, because the little rods on the central region of the table expand, whereas those on the outer part do not. 5
With reference to our little rods—defined as unit lengths—the marble slab is no longer a Euclidean continuum, and we are also no longer in the position of defining Cartesian co-ordinates directly with their aid, since the above construction can no longer be carried out. But since there are other things which are not influenced in a similar manner to the little rods (or perhaps not at all) by the temperature of the table, it is possible quite naturally to maintain the point of view that the marble slab is a “Euclidean continuum.” This can be done in a satisfactory manner by making a more subtle stipulation about the measurement or the comparison of lengths. 6
But if rods of every kind (i.e. of every material) were to behave in the same way as regards the influence of temperature when they are on the variably heated marble slab, and if we had no other means of detecting the effect of temperature than the geometrical behaviour of our rods in experiments analogous to the one described above, then our best plan would be to assign the distance one to two points on the slab, provided that the ends of one of our rods could be made to coincide with these two points; for how else should we define the distance without our proceeding being in the highest measure grossly arbitrary? The method of Cartesian co-ordinates must then be discarded, and replaced by another which does not assume the validity of Euclidean geometry for rigid bodies.1 The reader will notice that the situation depicted here corresponds to the one brought about by the general postulate of relativity (Section XXIII). 7
NOTE:—Gauss undertook the task of treating this two-dimensional geometry from first principles, without making use of the fact that the surface belongs to a Euclidean continuum of three dimensions. If we imagine constructions to be made with rigid rods in the surface (similar to that above with the marble slab), we should find that different laws hold for these from those resulting on the basis of Euclidean plane geometry. The surface is not a Euclidean continuum with respect to the rods, and we cannot define Cartesian co-ordinates in the surface. Gauss indicated the principles according to which we can treat the geometrical relationships in the surface, and thus pointed out the way to the method of Riemann of treating multi-dimensional, non-Euclidean continua. Thus it is that mathematicians long ago solved the formal problems to which we are led by the general postulate of relativity.

 

[whatif]

So what medium does light and gravity travel through then

None. This is the basic lesson from relativity.

Uh ... I think it's more the basic lesson from Michelson and Morley, which was part of the background behind Special Relativity.

However, space is measurable and has properties of known value, does it not? So space is something physical, is it not?

 

[Dale]

So space is something physical, is it not?

Sure, but it is not a medium. All media have a unique rest frame and momentum etc. Spacetime does not.

 

[PAllen]

It isn't a fabric. That's just an analogy.
Einstein developed a from-scratch derivation of the Lorentz transforms in his 1905 paper, which was when he published Special Relativity. Minkowski pointed out in 1908 that Einstein's maths was equivalent to a claim that we exist in a (3+1)d manifold, which is the beginning of the notion of spacetime. But one side effect of Special Relativity is that it is completely incompatible with Newtonian gravity. Attempts to understand special relativity in non-inertial frames eventually led to the insight that you could model gravity as a curved manifold.
The key difference between gravity and electromagnetism is that everything is affected the same by gravity - there are no "gravitationally neutral" particles. So it's possible to model gravity as a curved background that everything moves in, while if you try the same thing with electromagnetism you need to explain why a charged particle follows a curved path and an uncharged one doesn't.

I believe Kaluza and Klein made an attempt to do this. I don't think it was terribly successful, but I don't know much about it.
Einstein did "just happen" to be the one to develop this in some senses. His PhD supervisor, Lorentz, and others had actually put together most of the maths already - in fact, Poincare's 1904 review paper includes everything Einstein published in 1905. He just didn't realize the significance - he thinks of the Lorentz transforms as a patch for electromagnetic theory, rather than a fundamental change in the way we think about everything. Had Einstein not had his insight, someone else would have. The same can be said of General Relativity - David Hilbert was very close to the same ideas.

Actually, I think Poincare did not include the resolution of stellar abberation that Einstein developed. Einstein’s 1905 papaer contained the first satisfactory explanation of this. I also think that Poincare did not work out that energy of an EM wave transforms identically to frequency (SR Doppler factor applies to both).

 

[Orodruin]

However, space is measurable and has properties of known value, does it not? So space is something physical, is it not?

I would say spacetime is something physical. Space is an arbitrary convention imposed on spacetime.

 

[whatif]

Space is an arbitrary convention imposed on spacetime.

What does that mean? What is it that is merely arbitrary and what is the convention?

 

[Orodruin]

What does that mean? What is it that is merely arbitrary and what is the convention?

Arbitrary = You can choose what "space" means in different ways and neither is more correct than the other.
Convention = An agreed upon convention that is typically used. Typical conventions are using Minkowski coordinates for SR or using comoving coordinates in cosmology. "Space" is then considered to be the hypersurfaces of simultaneity in spacetime, but this splitting is not unique, nor does it single out one single possibility (such as Minkowski coordinates in SR, where you can change the meaning of "space" by basing your split of spacetime into space and time on a different inertial frame).

 

[folkethefat]

Why is time different from space? the arrow of time and so. Or maybe, what is the leading theoretical explanation for the difference?

 

[Dale]

Why is time different from space?

It has a different sign in the signature and a different number of dimensions.

 

[Ibix]

Why is time different from space?

Time and space aren't uniquely defined in relativity, and what one person calls time another person will call a mix of time and space. So if we can't agree on a meaning of time and space it's difficult to say that there is a difference.

Relativity does make a distinction between timelike and spacelike intervals. Everyone will agree that atimelike interval is more "time-y" than "space-y", and you can always describe someone who would call it just "time". Vice versa for spacelike intervals. As Dale says, the rigorous statement of this follows from the fact that the metric of spacetime has one minus sign in its canonical form.

Relativity, in common with all our fundamental theories, doesn't explain why time has one direction and never runs in reverse. It's perfectly happy in reverse. The "arrow of time", as I understand it, comes from thermodynamics. The universe started in a high-entropy state and is heading to a low-entropy state because that's what probability says.

 

[folkethefat]

thanks for your answers!

 

[1977ub]

This discussion about space or time being real is a bit like things like momentum or energy which can be described as mathematically real "bookkeeping" quantities - ?