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. [7]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: every object can move through time and space, but its 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.

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 under­stand far more about the thing we call 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? Why is it that this space­time does not strictly define things like posi­tion 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]

Why is this impor­tant? When we probe the micro­scopic realm, we dis­cover that 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. Until we can dis­cover an ulti­mate ref­er­ence frame that does not dis­solve 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, then that pic­ture should nat­u­rally 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] If we con­tinue to divide a region of space, or an interval of time, 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 (l_p) because below that size space itself retains no def­i­n­i­tion. Likewise, time cannot be divided into units smaller than the Planck time (t_p) because the dimen­sion of time does not retain def­i­n­i­tion beyond that scale.

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.

All of these clues lead to the idea that space­time is a fluid — that it has a gran­ular struc­ture. This point deserves some rumi­na­tion because this con­di­tion tech­ni­cally requires the lit­eral phys­ical exis­tence of addi­tional dimen­sions. It 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 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.’ Ultimately, it will be our under­standing of dimen­sions that deter­mines our new heading. Learning how to read the legend of our new map (how to under­stand the dimen­sions in that map) will enable us to finally resolve the mys­teries revealed by Newton and his bucket.

[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 (l_p), and the Planck time (t_p). There also exists a min­imum dis­crete value for mass called the Planck mass (m_p), Planck charge (q_p), and Planck tem­per­a­ture (T_p).

l_P = 1.616252(81) ´ 10-³⁵ m

t_P = 5.39124(11) ´ 10-⁴⁴ s

m_P = 2.17644(11) ´ 10-⁸ kg

_qp = 1.875545870(47) x 10^-18 C

T_p = 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:

l_P / t_P = c,        l_P³ / m_P t_P² = G,        m_P l_P² / t_P = ħ

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

l_P = Ö ħG/c³,     t_P = Ö ħG/c⁵,      m_P = 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.