Formulating a relativistically invariant version of quantum mechanics was a challenge that took the greatest minds in physics many years to overcome, and was finally achieved by Paul Dirac in the late s.
Different frames of reference, including different positions and motions, would see different laws of physics and would disagree on reality if a theory is not relativistically invariant. The fact that we have a symmetry under 'boosts,' or velocity transformations, tells us we have a conserved quantity: linear momentum. This is much more difficult to comprehend when momentum isn't simply a quantity associated with a particle, but is rather a quantum mechanical operator.
The result of his efforts yielded what's now known as the Dirac equation, which describes realistic particles like the electron, and also accounts for:. This was a great leap forward, and the Dirac equation did an excellent job of describing many of the earliest known fundamental particles, including the electron, positron, muon, and even to some extent the proton, neutron, and neutrino. A Universe where electrons and protons are free and collide with photons transitions to a neutral one that's transparent to photons as the Universe expands and cools.
The scattering between electrons and electrons, as well as electrons and photons, can be well-described by the Dirac equation, but photon-photon interactions, which occur in reality, are not. But it couldn't account for everything. Photons, for instance, couldn't be fully described by the Dirac equation, as they had the wrong particle properties. Electron-electron interactions were well-described, but photon-photon interactions were not. Explaining phenomena like radioactive decay were entirely impossible within even Dirac's framework of relativistic quantum mechanics.
Even with this enormous advance, a major component of the story was missing. The big problem was that quantum mechanics, even relativistic quantum mechanics, wasn't quantum enough to describe everything in our Universe. If you have a point charge and a metal conductor nearby, it's an exercise in classical physics alone to calculate the electric field and its strength at every point in space. In quantum mechanics, we discuss how particles respond to that electric field, but the field itself is not quantized as well. This seems to be the biggest flaw in the formulation of quantum mechanics.
Think about what happens if you put two electrons close to one another. If you're thinking classically, you'll think of these electrons as each generating an electric field, and also a magnetic field if they're in motion. Then the other electron, seeing the field s generated by the first one, will experience a force as it interacts with the external field. This works both ways, and in this way, a force is exchanged.
This would work just as well for an electric field as it would for any other type of field: like a gravitational field. Electrons have mass as well as charge, so if you place them in a gravitational field, they'd respond based on their mass the same way their electric charge would compel them to respond to an electric field. Even in General Relativity, where mass and energy curve space, that curved space is continuous, just like any other field.
If two objects of matter and antimatter at rest annihilate, they produce photons of an extremely specific energy. If they produce those photons after falling deeper into a region of gravitational curvature, the energy should be higher. In General Relativity, the field carries energy away in waves: gravitational radiation. But, at a quantum level, we strongly suspect that just as electromagnetic waves are made up of quanta photons , gravitational waves should be made up of quanta gravitons as well.
This is one reason why General Relativity is incomplete. Fields push on particles located at certain positions and change their momenta. But in a Universe where positions and momenta are uncertain, and need to be treated like operators rather than a physical quantity with a value, we're short-changing ourselves by allowing our treatment of fields to remain classical.
The fabric of spacetime, illustrated, with ripples and deformations due to mass. A new theory must be more than identical to General Relativity; it must make novel, distinct predictions. As General Relativity offers only a classical, non-quantum description of space, we fully expect that its eventual successor will contain space that is quantized as well, although this space could be either discrete or continuous.
That was the big advance of the idea of quantum field theory , or its related theoretical advance: second quantization. All of a sudden, processes that weren't predicted but are observed in the Universe, like:.
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Glashov who have thrown some doubts upon such a rather complex process, as reported in a review by Mosher . Thus the theory by Higgs consists of a multistage process by which a heavy boson is first being produced, and then decays into all other particles, thereby being given their correct rest masses.
In a study of the quantum mechanical energy levels of the harmonic oscillator, M. The related electromagnetic vacuum fluctuations were investigated by Casimir  who predicted that two metal plates will in the vacuum attract each other when being separated by a small spacing. This is due to the fact that only small wavelength: of the fluctuations can exist in the spacing, whereas their full spectrum exerts a force on the outsides of the plates.
This tends to push them together. Such a net differential force was first shown to exist by Lamoreaux  , in using a sensitive torsional pendulum device. Part of these quantum fluctuations also carry electric charge as pointed out by Abbott . Even if all these fluctuations are at the same low ZPE level, their spatial inhomogeneity can thus produce a pressure gradient. With these basic concepts as starting points, a revised quantum electrodynamic theory RQED can be elaborated as follows. It is first noticed that the Lorentz invariant field equations in a sourceless state are given by d'Alembert where.
Taking the electromagnetic sources in the vacuum state into account in a formally correct Lorentz invariant formulation, the field equations have to be modified by adding the four-current density. The resulting Equation 5 is identical with its corresponding conventional form for a medium containing particles of given electronic charge and mass. But in the present situation it applies instead to a nonzero charge density.
This leads to the final form. Equation 10 thus defines the modulus of the vector C which can have several components, such as in the case of cylindrical waves.
In a three-dimensional representation the new extended Lorentz invariant field equations of the vacuum state are thus given by. These equations are also gauge invariant, because their new added parts include the field strength E as in conventional theory, i. In analogy with conventional theory as described by Heitler  , the present quantized field equations become identical with the original ones, in which the potentials and current densities are replaced by their expectation values.
Relevant and specific quantum conditions, such as that of the spin, can then be imposed on the corresponding general solutions. Equations 5 - 14 have new features and lead to new results, not being available from conventional theory:. In the present theory the Lorentz invariance is extended into a multidimensional form represented by the velocity vector C.
Thus the velocity constant c of Equation 3 does not become identical with the velocity of propagation of an individual photon. Radially convergent generating functions result in particle models with vanishing net electric charge, whereas divergent such functions lead to a nonzero net charge, a point-charge-like geometry, and a modified renormalization process.
All particle models have source terms due to broken symmetry which leads to steady states with nonzero rest masses, and often with an associated spin. There are both particles with net electric charge such as the electron, muon and tauon, and those with vanishing net charge such as the photon, Z boson, the so called Higgs particle, and the neutrino. The present particle models are axisymmetric, with the exception of the neutrino for which chirality has to be taken into account. Such a spinless photon of plane-wave geometry would propagate exactly at the velocity c of Equation 3.
An acceptable form in a limited region of space is on the other hand provided by a wave-packet solution in cylindrical geometry. This reduction occurs only in the ninth decimal as compared to the value of c, see Ref. The nonzero spin is then associated with a very small but nonzero rest mass. This is confirmed by experiments as described in Ch.
Particles with net integrated charge, such as the electron, muon and tauon, are represented by models as follows:. This gives an example where relativity is linked with quantum mechanics through the present theory.
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There are also particles with vanishing net charge, the models of which can be obtained in terms of a convergent generating function:. The latter has no net charge, no eigenmagnetic field, no spin, and a minimum mass of GeV within limits of a few percent    . This deduced particle model has all the basic properties of the particle detected at CERN  .
But it has no relation to the theory by Higgs. So far the internal particle structure has been considered in this context. We now turn to the mutual short-range interaction between particles, in particular under the influence of their intrinsic charge geometry. As an example, we consider a tentative model of the neutron, given by three individual quarks which are mutually bound to each other to form a triangular configuration  , as described in current investigations  .
In a first simplified treatment, equal models are used for each of the quarks. Thus Q i is an order of magnitude larger than the elementary charge e. The remaining 97 percent are thus in a force-free state. With the Ansatz 18 the integrated force with density 15 therefore becomes comparatively small. This is in particular the case when comparing such an eigenforce to the force that arises between two mutually interacting quarks in the present triangular configuration. This can be done by adding a small part being radially convergent and having the correct sign.
And that is just the start of a broader critique. Smolin thinks the small-scale approach to physics is inherently incomplete. Current versions of quantum field theory do a fine job explaining how individual particles or small systems of particles behave, but they fail to take into account what is needed to have a sensible theory of the cosmos as a whole.
A more fruitful path forward, he suggests, is to consider the universe as a single enormous system, and to build a new kind of theory that can apply to the whole thing. And we already have a theory that provides a framework for that approach: general relativity.
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Even something as basic as inertia the resistance of your car to move until forced to by the engine, and its tendency to keep moving after you take your foot off the accelerator can be thought of as connected to the gravitational field of every other particle in the universe.
Consider a thought problem, closely related to the one that originally led Einstein to this idea in What if the universe were entirely empty except for two astronauts. One of them is spinning, the other is stationary. The spinning one feels dizzy, doing cartwheels in space. But which one of the two is spinning? Without any external reference, Einstein argued, there is no way to say which one is correct, and no reason why one should feel an effect different from what the other experiences. The distinction between the two astronauts makes sense only when you reintroduce the rest of the universe.
In the classic interpretation of general relativity, then, inertia exists only because you can measure it against the entire cosmic gravitational field. What holds true in that thought problem holds true for every object in the real world: The behavior of each part is inextricably related to that of every other part. It is also, Smolin thinks, a promising way to obtain bigger answers about how nature really works, across all scales.
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Smolin is keenly aware that he is pushing against the prevailing devotion to small-scale, quantum-style thinking. Much as all of the parts of the universe are linked across space, they may also be linked across time, he suggests. His arguments led him to hypothesize that the laws of physics evolve over the history of the universe. Over the years, he has developed two detailed proposals for how this might happen. His theory of cosmological natural selection, which he hammered out in the s, envisions black holes as cosmic eggs that hatch new universes.
More recently, he has developed a provocative hypothesis about the emergence of the laws of quantum mechanics, called the principle of precedence —and this one seems much more readily put to the test. If you perform an experiment that has been performed before, you expect the outcome will be the same as in the past. Strike a match and it bursts into flame; strike another match the same way and … you get the idea.
Smolin hypothesizes that those laws actually may emerge over time, as quantum systems copy the behavior of similar systems in the past. One possible way to catch emergence in the act is by running an experiment that has never been done before, so there is no past version that is, no precedent for it to copy. Such an experiment might involve the creation of a highly complex quantum system, containing many components that exist in a novel entangled state. If the principle of precedence is correct, the initial response of the system will be essentially random.
As the experiment is repeated, however, precedence builds up and the response should become predictable … in theory. Although precedence can play out at the atomic scale, its influence would be system-wide, cosmic. Getting the two classes of physics theories to work together, though important, is not enough, either.
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What he wants to know—what we all want to know—is why the universe is the way it is. Why does time move forward and not backward? How did we end up here, with these laws and this universe, not some others? Like Hogan, he is less concerned about the outcome of any one experiment than he is with the larger program of seeking fundamental truths. For Smolin, that means being able to tell a complete, coherent story about the universe; it means being able to predict experiments, but also to explain the unique properties that made atoms, planets, rainbows, and people.
Here again he draws inspiration from Einstein. The most likely way to get the big answers is to engage with the universe as a whole. If you wanted to pick a referee in the big-small debate, you could hardly do better than Sean Carroll, an expert in cosmology, field theory, and gravitational physics at Caltech.
He knows his way around relativity, he knows his way around quantum mechanics, and he has a healthy sense of the absurd: He calls his personal blog Preposterous Universe. Right off the bat, Carroll awards most of the points to the quantum side. That has been the prevailing view ever since the s, when Einstein tried and repeatedly failed to find flaws in the counterintuitive predictions of quantum theory.
No matter how the theories shake out, the large scale is inescapably important, because it is the world we inhabit and observe. Taking a larger view, the real issue is not general relativity versus quantum field theory, Carroll explains, but classical dynamics versus quantum dynamics. Relativity, despite its perceived strangeness, is classical in how it regards cause and effect; quantum mechanics most definitely is not.
Einstein was optimistic that some deeper discoveries would uncover a classical, deterministic reality hiding beneath quantum mechanics, but no such order has yet been found. The demonstrated reality of spooky action at a distance argues that such order does not exist. There are still huge gaps in what quantum theory can explain.
In the case of time, then, the jury is still out.