# Chapter 2

## Section 3: Einstein’s Absolute Spacetime

Like Newton’s model, Einstein’s model of physical reality evokes an absolute benchmark, an ultimate reference frame in Nature he called absolute spacetime. Therefore, according to general relativity, a bucket in an otherwise empty universe can be accelerating or spinning. Spacetime provides the reference by which we can define this acceleration because of the intimate correlation it depicts between motion through space and motion through time.

If an object travels through spacetime in a consistent unchanging manner, then it is not accelerating. However, if an object changes its motion through spacetime — by changing its direction, or its speed — then the object has accelerated. Since any change in an object’s experience of time demands a change in its experience of space, and visa versa, spacetime is the benchmark for acceleration. It is every object’s constant motion through spacetime that makes spacetime the ultimate reference frame — at least macroscopically. This is why Einstein labeled the absolute benchmark ‘absolute spacetime.’

To make this a little clearer, consider the following: objects can move through time and space, but their combined movement through time and space is always equal to the speed of light (c). At the two ends of the spectrum an object can be moving only through space, wherein it doesn’t progress through time at all, or only through time, wherein it doesn’t progress through space at all. As an object takes on different velocities it trades travel through time for travel through space, but it does not change its total magnitude of spacetime travel.

Einstein’s concept of absolute spacetime is a definite improvement over Newton’s absolute space, but it cannot be the complete answer because it does not reveal why other measures in Nature are strictly relational. It gives us an ultimate reference frame (a spacetime field of zero curvature) but the structure of that reference frame does not give us an explanation for why position, velocity, etc. are relational quantities.

This is as far as we have come in our quest to discover Nature’s ultimate reference frame. We are still with a complete geometric description of spacetime – one that is capable of simultaneously providing us with a reference that defines acceleration, and explaining why relational measures (position, velocity, etc.) are not uniquely fixed by that reference frame.

To go further we need to have a richer understanding of spacetime than we currently do. We have established that spacetime is something, but what is it? Space is part of it, time is part of it, warps and ripples are some of its properties, and it constructs the reference by which acceleration gets its meaning. But what is this thing we call spacetime? How are we to fully map or understand it? What is it about the structure of spacetime that does not allow position and velocity to be strictly defined? Why does spacetime, which plays the role of ultimate reference for acceleration, fail to play the role of ultimate reference for position, time, and velocity?

While we ponder what spacetime is, let’s discuss some of the clues about space and time that have been discovered more recently. (Answers to the questions posed in this chapter require an introduction to our new model of spacetime. They can be found after that introduction – see Chapter 10.)

## Modern Clues for an Ultimate Reference Frame

Quantum physics has found that the ultramicroscopic realm is suffused with quantum jitters. What does this mean? Well, the usual answer tends to include talk of fields and/or vacuum fluctuations, both of which seem to avoid a graphic explanation by answering with terms just as confusing. This isn’t done with any intent to mislead. The truth is that a complete picture of spacetime is still missing, so any talk about quantum jitters (or any of the other quantum mechanical occurrences) tends to be technical or mathematical. Nevertheless, these observations can serve as glimpses into the structure of spacetime. They can give us clues about how the structure of spacetime must be – clues that will assist us in our goal of constructing a complete map.

Hendrik Casimir envisaged one of those clues. He predicted that two uncharged metal plates (or mirrors) will move toward each other when they are placed in a vacuum and are arranged parallel to each other. Since the gravitational force between these two plates is far too weak to explain this movement and nothing other than space is included in the system, this effect is very intriguing.

To explain this motion, Casimir suggested that the quantum fluctuations of space itself are analogous to a pressure caused by the combined motions of many molecules. Based on this assumption, he showed that when the two plates are placed extremely close to each other the ‘molecular pressure’ of space should slightly decrease between the plates because of the respective differences in ‘molecular motion’ inside and outside the plates. (Figure 2-6) In other words, if spacetime truly has some sort of associated pressure, then the two plates will be “pushed” together because only particles with a wavelength/energy [8]smaller than the gap between the plates can be within the gap, whereas particles of any wavelength/energy can be on the outside of the plates. The result is that there are more particles pushing the plates together than pushing them apart. Because of this, the plates clash together like a pair of tiny cymbals. Or in other words, the system ends up with less space between the plates. Casimir claimed that the interactive geometry of space itself would cause this motion. We now refer to it as the Casimir effect.

[FIGURE PLACEHOLDER]

Figure 2-6 The Casimir Effect.

Although Casimir made this prediction in 1948, equipment sensitive enough to measure this effect wasn’t technologically available until 1996. During this time span, Casimir’s prediction was widely assumed to be just a quirk of mathematics. Then, in 1997 Steve Lamoreaux produced a convincing demonstration of the effect. [9] Today, “dealing with the Casimir effect has become a matter of urgency for nanotechnologists.” (Saswato Das, 2008) The Casimir effect strongly argues that quantum field jitters are the result of the interactions of some theoretical ‘molecules’ or ‘atoms’ that somehow compose the medium of space. [10]

This is important because as we approach the microscopic realm spacetime loses its function as the ultimate reference frame. This is a significant problem, because if we no longer have an ultimate reference frame, then all of the questions introduced by Newton’s bucket become unanswered again. So long as our understanding of spacetime dissolves on the microscopic scales, we will remain in this cloud of confusion. This is why it is important for us to study the clues that the microscopic realm can offer. If we can use them to depict a new picture of Nature, that picture might reveal the ultimate reference frame. The clarity that would come from such a coherent theory is what we are after.

Einstein’s vision of human transcendence requires that we accept nothing less than a theory that gives a completely coherent account of individual phenomena. Working toward such a theory requires that we become aware of all of the unique phenomena in Nature that require explanation and that we actively investigate those phenomena. Every unexplained occurrence tells us something about the shortcomings of our existing fragmentary maps (or descriptions) of physical reality. Most of those clues point toward the need for stricter scrutiny of the microscopic realm. This is where our unexplained mysteries originate, and this is where we will find our most valuable clues by which to rewrite a richer, complete map of physical reality. Let’s investigate some more of those clues.

In 2005, Theodore A. Jacobson and Renaud Parentani showed that “the propagation of sound in an uneven fluid flow is closely analogous to the propagation of light in a curved space-time.” This work suggests that “spacetime may, like a material fluid, be granular and possess a preferred frame of reference that manifests itself on fine scales…” (Jacobson and Parentani 2005, 70)

Further support of this inference comes from Stephen Hawking’s famous argument that black holes are not truly black. Back in the 1970s Hawking predicted that black holes emit thermal radiation, but relativity demands that any radiation emitted from the surface of a black hole will be infinitely stretched as it propagates away — making it impossible to measure. This infinite stretching assumes that spacetime is infinitely divisible. But if we treat spacetime as granular, then we can depict it as a fluid system. When we do this, “The fluid’s molecular structure cuts off the infinite stretching and replaces the microscopic mysteries of spacetime by known physics.” (Jacobson and Parentani 2005, 70)

This approach would support Hawking’s claim, but so far no one has come up with a framework for physical reality that depicts a granular structure for spacetime. One reason for this may be that such a framework must be what physicists call a background independent formulation. This means that the framework cannot presuppose the fluctuations of quantum fields, or the vibrations of string theory, to be stuck within spacetime. Instead, this formulation is required to explain quantum effects as the result of interactions within a spaceless and timeless framework. By definition this requirement can only be met in a higher-dimensional model, but to date, higher-dimensional models have escaped intuitive depiction.

Another clue we have about the microscopic realm is that theoretical minimum discrete values for space and time exist. [11] According to modern physics we cannot infinitely divide a region of space, or an interval of time, into smaller and smaller amounts because we will eventually arrive at a scale where further division of those parameters yields meaningless results. Space cannot be divided into units smaller than the Planck length (lp) and time cannot be divided into units smaller than the Planck time (tp).

To make sense of this consider a more familiar analogy. We cannot infinitely divide a chunk of pure gold into smaller and smaller chunks because eventually we reach the limit of one gold atom. Any further division forces us to transcend the very definition of gold. Therefore, we cannot meaningfully talk about less than one gold atom in terms of gold.

Today there is a plethora of evidence supporting the physical existence of these minimum limits. The Planck constants are universally accepted values within the formulation of quantum mechanics. The Swedish mathematician Oskar Klein originally picked the Planck length in 1926 as a unique value because it is the only length that could naturally appear in a quantum theory of gravity. Since gravity is directly connected to the shape of space, this value seemed a necessary requirement. The Planck time is a unique value because it is the only value that can be combined with the Planck length to yield c, the speed of spacetime – otherwise known as the speed of light.

The existence of these Planck values restricts all measures of distance and time to whole number multiples of the Planck units. In space two objects can be a distance of 77 Planck lengths apart, but they cannot be 77.5 Planck length units apart. Two events can occur 33 Planck time units apart, but they cannot occur 33.5 Planck time units (chronons) apart.

These clues suggest that spacetime may be best thought of as a fluid — a medium that has granular structure. (Later we will consider spacetime as a particular kind of fluid – a superfluid.) This point deserves some rumination because if we are going to take this condition seriously, then we are going to have to allow the literal physical existence of additional dimensions (regions that define what is between the atoms of space). A quantized structure for spacetime means that the full map of Nature must be dimensionally richer than we have assumed. If we figure out how to comprehend and explore those dimensions, then a whole new realm might open up to us. But before we can even start to comprehend, or explore, unfamiliar dimensions it is pertinent that we understand exactly what a dimension is. Therefore, we turn now to define and explore what physicists mean by ‘dimensions.’

[Continue to Chapter Three]

From the forthcoming book:

### Einstein’s Intuition by Thad Roberts

Represented by
Sam Fleishman
Literary Artists Representatives
New York, New York

NOTES:

[1] “Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you these same flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speeds to all sides of the cabin; and, in throwing something to your friend, you need throw it no more strongly in some direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction. When you have obtained all these things carefully, have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still.” Galileo Galilei, Dialogue Concerning the Two Chief World Systems, 1632, translated by Stillman Drake, p. 186; Walter Isaacson, Einstein, pp. 108-9.

[2] Kip Thorne, 1979, Quote from Einstein by Walter Isaacson, p. 133.

[3] al-Farabi, 1951, ‘Farabi’s Article on Vacuum,’ N. Lugal and A. Sayili (ed. and trans.), Ankara: Turk Tarih Kurumu Basimevi.

[4] Isaac Newton, Principia, Scholium on Absolute Space and Time Florian Cajori, trans., Berkeley: University of California Press, 1934; reprinted in The Scientific Background to Modern Philosophy, Edited by Michael R. Matthews, Hackett Publishing Company Indianapolis/Cambridge, 1989, pp. 139-146: Cohen, I. Bernard. The Newtonian Revolution. Cambridge: Cambridge University Press, 1980; Manuel, Frank E. A Portrait of Isaac Newton. Cambridge, Massachusetts: Harvard University Press, 1968; Westfall, Richard S.Never at Rest: A Biography of Isaac Newton. Cambridge: Cambridge University Press, 1980.

[5] Leibniz said, “I hold space to be something merely relative, as time is… I hold it to be an order of coexistences, as time is an order of successions.” H. G. Alexander, ‘The Leibniz-Clarke Correspondence,’ Manchester University Press (1956), 3rd paper, §4; Olaf Dryer ‘Relational Physics and Quantum Space, arXivig –qc/0404054v1, April 13, 2004.

[6] Of course a universe containing only a bucket of water could not possess enough gravity by which to keep the water from floating away. So in this case, since we mean to discuss acceleration in general, imagine instead that you were positioned inside a large bucket. If the bucket were spinning you would feel a pull toward its outside edge. Mach’s claim is that without another reference by which to define the spinning of the bucket it cannot be spinning. Therefore, in this view, it is impossible in an otherwise empty universe, to feel a pull toward the walls of the bucket.

[7] Ironically, Einstein began his intellectual endeavor by trying to prove that Mach was correct in his relational approach.

[8] In quantum mechanics everything has a particle-wave duality. Everything, therefore, has an associated wavelength.

[9] The publication on this demonstration can be found at – Physical Review Letters, DOI:10.1103/PhysRevLett.78.5

[10] Even without the Casimir effect as an explanation vacuum energy would still hold as a valid and secure claim through the well-established phenomenon known as Lamb shift. The inference goes like this: since predictions for the wavelengths of light absorbed and emitted by molecules (which only match observation if physicists assume that vibrating molecules contain zero point energy) can be extended to explain how “vacuum fluctuations alter the frequencies of light that hydrogen atoms absorb and emit,” zero-point energy must be inherent in vacuum fluctuations. The “same basic theory that works for molecules says that the vacuum contains zero-point energy too, there is no reason to believe otherwise.” (David Shiga, “Something for Nothing,” New Scientist, October 2005: 34-37.)

[11]These values are called the Planck length (lp), and the Planck time (tp). There also exists a minimum discrete value for mass called the Planck mass (mp), Planck charge (qp), and Planck temperature (Tp).

lP = 1.616252(81) ´ 10-35 m

tP = 5.39124(11) ´ 10-44 s

mP = 2.17644(11) ´ 10-8 kg

qp = 1.875545870(47) x 10-18 C

Tp = 1.416785(71) x 1032 K

(Italicized digits are theoretical.)

If we interpret the medium of spacetime as a molecular or atomic composite, then these parameters can be easily understood as the physical values that relate to the individual ‘molecules’ or ‘atoms’ of that medium. Support for this interpretation comes from the fact that the constants of general relativity and quantum mechanics are natural derivatives of these fundamental constants.

The primary constants of general relativity and quantum mechanics are:

(c is the characteristic speed of spacetime, colloquially referred to as the speed of light,  is Planck’s constant, and G is the gravitational constant,.)

These constants can be derived from the fundamental constants of the space quanta in the following manner:

lP / tP = c,        lP3 / mP tP2 = G,        mP lP2 / tP = ħ

Working backwards we can solve for lp , mp and tp in terms of the general relativistic and quantum mechanical constants (measured values) in this manner:

lP = Ö ħG/c3,     tP = Ö ħG/c5,      mP = Ö ħc/G

There are many other constants of Nature that appear all throughout physics, chemistry, electronics etc., that also turn out to be natural composites of the Planck parameters. For example: the magnetic constant (μ0), the electric constant (ε0), the Boltzmann constant (k), and the characteristic impedance of the vacuum (Z0). We will discuss these relationships, and several others, in greater detail in Chapter 16.