Posts tagged ‘special relativity’

June 9th, 2013

The Philosophy of Science Directory

by Max Andrews

This is a compilation of posts, which focus on the philosophy of science. These posts will cover a broad spectrum within the philosophy of science ranging from multiverse scenarios, scientific theory, epistemology, and metaphysics.

  1. MA Philosophy Thesis: “The Fine-Tuning of Nomic Behavior in Multiverse Scenarios”
  2. Natural Law and Scientific Explanation
  3. Science and Efficient Causation
  4. Which Comes First, Philosophy or Science?
  5. The Postulates of Special Relativity
  6. There’s No Such Thing as Creation Science–There’s Just Science
  7. Time Travel and Bilking Arguments
  8. “It’s Just a Theory”–What’s a Scientific Theory?
  9. Exceptions to a Finite Universe
  10. Teleology in Science
  11. Duhemian Science
  12. The Relationship Between Philosophy and Science
  13. The History of the Multiverse and the Philosophy of Science
  14. Where’s the Line of Demarcation Between Science and Pseudoscience?
  15. Miracles and the Modern Worldview
  16. Mass-Density Link Simpliciter
  17. Scientific Nihilism
  18. Q&A 10: The Problem of Defining Science
  19. Q&A 6: Scientism and Inference to the Best Explanation
  20. The Quantum Universe and the Universal Wave Function
  21. The History and Macro-Ontology of the Many Worlds Interpretation of Quantum Physics
    read more »

April 27th, 2013

Lorentzian Transformations

by Max Andrews

The fundamental question raised by these postulates of special relativity is how different coordinate systems (reference frames) are related, i.e., how one transforms between them. (x, y, z, t) denotes the coordinates of some event in frame S, what are the coordinates (x’, y’, z’, t’) in the frame S’ moving at the velocity v relative to S? But first, a clarification on proper time and coordinate time:

Proper time is time measured between events by use of a single clock, where these events occur at the same place as the clock.  It depends not only on the events but also on the motion of the clock between the events.  An accelerated clock will measure a shorter proper  time between two events than a non-accelerated (inertial) clock between the same events.

May 30th, 2012

The Lorentz Transformations

by Max Andrews

The fundamental question raised by these postulates of special relativity is how different coordinate systems (reference frames) are related, i.e., how one transforms between them. (x, y, z, t) denotes the coordinates of some event in frame S, what are the coordinates (x’, y’, z’, t’) in the frame S’ moving at the velocity v relative to S? But first, a clarification on proper time and coordinate time:

Proper time is time measured between events by use of a single clock, where these events occur at the same place as the clock.  It depends not only on the events but also on the motion of the clock between the events.  An accelerated clock will measure a shorter proper  time between two events than a non-accelerated (inertial) clock between the same events.

In standard special relativity, we often want to express results in terms of a spacetime coordinate system relative to an implied observer.  In this case, an event is specified by one time coordinate and three spatial coordinates.  The time measured by the time coordinate is referred to as coordinate time, to distinguish it from proper time.

May 29th, 2012

The Postulates of Special Relativity

by Max Andrews

Albert Einstein felt the strong need to affirm Galilean relativity, which applied only to mechanical laws, that he decided to extend it to include electromagnetic and optical laws.  He adopted the principle that no physical experiment (mechanical, optical, electromagnetic, or any physical law whatsoever) can distinguish between a state of absolute rest and a state of constant velocity.  With the help of the German mathematician Herman Minkowski (who taught us to think in terms of spacetime rather than space and time individually.  Einstein introduced a new principle of relativity and revolutionized mechanics.

There are two postulates of special relativity but the consequences are profound.

  1. Postulate 1 (Principle of Relativity): The laws of nature are the same in all inertial frames.
  2. Postulate 2 (Constancy of the Velocity of Light): The speed of light in empty space is an absolute constant of nature and is independent of the motion of the emitting body.
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May 15th, 2012

How Einstein got to E=mc^2

by Max Andrews

In 1865 James Clerk Maxwell had unified electricity and magnetism by developing his equations of electromagnetism. It was soon realized that these equations supported wave-like solutions in a region free of electrical charges or currents, otherwise known as vacuums.  Later experiments identified light as having electromagnetic properties and Maxwell’s equations predicted that light waves should propagate at a finite speed c (about 300,000 km/s).  With his Newtonian ideas of absolute space and time firmly entrenched, most physicists thought that this speed was correct only in one special frame, absolute rest, and it was thought that electromagnetic waves were supported by an unseen medium called the ether, which is at rest in this frame.

Let an object in a rest frame simultaneously emit two light waves with the same energy E/2 in opposite directions (now having equal but opposite momenta), the object remains at rest, but its energy decreases by E.  By the Doppler effect, in another frame, which is moving at the velocity v in one of those directions, the object will appear to lose energy equal to

May 1st, 2012

A Failure of Creationist Cosmology

by Max Andrews

Einstein’s GTR [and aspects of STR] has made incredible contributions to natural theology.[1]  Given the fixed speed of light, that nothing can travel faster than light, and the billions of light-years separation between the earth and other stars, it follows that the universe is billions of years old.[2]  This has created a problem for young-earth creationists.[3] Current estimations for the age of the universe have been set at 13.73±2 billion years old.  Young-earth creationists have adopted three main approaches:  (1) embrace a fictitious history of the universe in the spirit of Philip Gosse’s 1857 work Omphalos; (2) view the speed of light as having decayed over time; and/or (3) interpret Einstein’s GTR so that during an “ordinary day as measured on earth, billions of years worth of physical processes take place in the distant cosmos.”[4]

October 7th, 2011

Neutrinos Faster Than Light or Extra Dimensions?

by Max Andrews

Source: CERN Press

By now we’ve all heard of the news coming out of CERN and OPERA on 23 September that the Italian accelerator, OPERA, measured neutrinos traveling faster than the speed of light.  I didn’t comment on the finding right away because I wanted to do some research on the claims and on what exactly happened.  So here are my two-cents.

So, what exactly is a neutrino?  A neutrino is a fundamental particle and crucial for the standard model of particle physics.  The neutrino comes tin three types: [associated with] the electron, muon, and tauon, which are fermions and part of leptons.  The have no electric charge and interact only via the weak nuclear force (see the Oxford Companion to Cosmology for more on this).  These particle are incredibly difficult to detect and pass through our bodies all the time (this is a nice little Italian cartoon that has an excellent depiction of neutrinos).

So, what happened?  CERN sent the neutrinos 730lm to the Italian accelerator OPERA.  The journey only took 2.43 milliseconds and the scientists timed it to within 10 nanoseconds. (A millisecond is a thousandth of a second, 1/1,000s and a nanosecond is a billionth of a second, 1/1,000,000,000s).  The neutrinos arrived 60 nanoseconds earlier than they would have if they were traveling at the speed of light (c = 299,792,458 m/s). There are three options of what could have happened.

  1. Option One.  The experiment was in error and the calculations are simply incorrect.
  2. Option Two.  The speed of light is not the cosmic speed limit and there must be slight adjustments for relativity theory.
  3. Option Three.  The neutrinos took a shortcut through extra dimensions.

Option One: Experimental Error.  The OPERA team spent three years trying to calculate and find every error they could possibly find.  The neutrinos are produced by colliding protons into a graphite target to produce pions and travel a 1km tunnel and decay to produce neutrinos.  Electronic delays in the timing system that records when protons arrive at the graphite target introduce uncertainty.  However, this margin of error is 5 nanoseconds. Where the pions decay is also unknown, which produces an error of 0.2 ns.  Measuring the distance is also difficult because the OPERA lab in Gran Sasso is inside of a mountain, which is undetectable to GPS.  However, the distance can still be calculated to within 20 cm.  The error is 0.67 ns.  With the other errors taken into consideration, the total error bar is 7.4 ns.  Remember, if experimental error is going to be the prevalent option the errors have to account for 60 nanoseconds.

Option Two: Adjusting Relativity.  If it really is the case that the neutrinos did travel faster than the speed of light then Einstein isn’t completely thrown to the curb.  There must be a theory that will account for this that will be closer to the truth.  This has historical precedence.  Newtonian physics were thought to explain the universe until Einstein came around with the concept of relativity.  Newton wasn’t necessarily wrong, Einstein just provided a more accurate theory.  If neutrinos can travel faster than c then we need another Einsteinian discovery.  Not that big of deal.

Option Three: Extra Dimensions.  It may be the case that the neutrinos, when travel with an incredible amount of energy, travel through the smaller curled up dimensions.  Consider the neutrinos traveling into the fourth dimension, this would actually make the distance much shorter.  Hopefully this illustration will help.  Take a piece of paper and draw a straight line across the paper.  Label one end of the line A and the other B.  This line is one-dimensional.  Take the paper and fold it so it creates an upward arch.  Now, if you were to travel from A to B by going through the paper instead of curving around the outside of the paper then the distance would be shorter.  This may, perhaps, be what happened to the neutrinos. (For more information on the discovery see New Scientist No. 2832, October 1-7 2011).

I tend to lean more towards option three, that the neutrinos passed through the smaller extra dimensions.  This would be an incredible development that would contribute to and, possibly, confirm a prediction of string theory.  Part of this may be wishful thinking on my part but this may potentially be an incredible empirical find that would confirm the mathematics.  Now, what about further philosophical or theological implications?  I don’t think this has too much of an impact on philosophy or theology that hasn’t already been addressed concerning the philosophy of science or of scientific theology.  For more on these implications see “The Relationship Between Science and Philosophy,” “Einstein, the Big Bang, and Natural Theology,” “Einstein on Free Will,” and “Einstein’s Impact on the Epistemic Method.”

August 10th, 2011

Einstein, The Big Bang, and Natural Theology

by Max Andrews

Einstein’s General Theory of Relativity (GTR) had predicted that the universe was either expanding or contracting.  Einstein found the notion of a beginning to the universe so distasteful that he introduced a “fudge factor” to his field equation to keep a Steady State universe, an eternal equilibrium.[1]  Einstein introduced a term called the cosmological constant.  The cosmological constant was a force so weak, which factored into the geometric curvature of space, that it would make no difference on an eternal universe.

In the 1920’s Edwin Hubble was studying the Andromeda nebula.  At least since the time of Kant scientists wondered what these distant enormous objects were (galaxies).  Kant conjectured that they might be island universes in their own right.[2]  With further study, Hubble noticed that these galaxies had a red shift; the galaxies were appearing redder than they should have and Hubble postulated that these galaxies were moving away from one another.  What was being observed was the same thing that the Doppler effect has on sound.  The trajectory of an object has an effect on the wavelength of the sound, or in this case, light.

As a result of Hubble’s discovery and Einstein’s own equations the Russian mathematician Alexander Friedman and the Belgian priest and physicist Georges Édouard Lemaître suggested that the universe had a finite past and was not static and eternal.  There was now a problem with the cosmological constant; it cannot simply be deleted from Einstein’s equations. The cosmological constant could balance the equation from describing the geometric curvature (left hand side of the equation) to describing the energy momentum (right hand side of the equation).   If this expansion is extrapolated the equations of motion then (and even now) can only go but so far—until the universe comes to a singularity. With reluctance Einstein conceded the steady state model in the late 1920’s, though many scientists would not accept the implications of an expanding universe (its finitude).  One critic, Fred Hoyle, dubbed such an event the “Big Bang” in mockery and the name stuck.[3]

Einstein’s GTR [and aspects of STR] has made incredible contributions to natural theology.[4]  Given the fixed speed of light, that nothing can travel faster than light, and the billions of light-years separation between the earth and other stars, it follows that the universe is billions of years old.[5]  This has created a problem for young-earth creationists.[6] Current estimations for the age of the universe have been set at 13.73±2 billion years old.  Young-earth creationists have adopted three main approaches:  (1) embrace a fictitious history of the universe in the spirit of Philip Gosse’s 1857 work Omphalos; (2) view the speed of light as having decayed over time; and/or (3) interpret Einstein’s GTR so that during an “ordinary day as measured on earth, billions of years worth of physical processes take place in the distant cosmos.”[7]

Regarding a fictitious history of the universe, the argument states that all present light, which appears to be billions of light years away, was created in transit with an appearance of age.  So, when supernovae exploding in a galaxy millions or billions of light years away, the young-earth creationist [advocate of a fictitious history] must adopt the approach that no supernovae ever exploded.[8]  Einstein and the scientific theologian’s epistemic method reject such an interpretation.  Einstein’s method of inquiry based the natural order as having an ontological status of genuine reality and the discoveries are made a posteriori; no such method of inquiry is tenable under a fictitious history.  Einstein’s epistemology has influenced Big Bang theists and scientific theologians regarding GTR and the objectivity of the natural order.  It appears, objectively, that the universe really is billions of years old.

The second argument was a denial that the speed of light has been a constant [approximately] 300,000 km/s.  As previously discussed, Einstein’s E=mc2 states that energy is proportional to the mass of an object multiplied by the speed of light squared.  If c decays then that would imply that there has been a change in the quantity of energy in the universe.  This creates a problem for thermodynamics.  Thermodynamics would not be the only problem; many other constants would need to change as well to preserve the stability of a life-permitting cosmos such as Planck’s constant h (h-bar).  Suddenly the objection is not only with c because that would in turn change all of physics.[9]  All of this would be done to circumvent an old universe suggested by a constant speed of light.[10]  Before Einstein’s relativity theories, this would not have been a problem for the young-earth creationist.

The third foremost-misconstrued aspect of Einstein’s equations by natural theologians has been to misinterpret GTR and time dilation.  The mathematics of this theory shows that while God makes the universe in six days in the earth’s reference frame (“Earth Standard Time”), the light has ample time in the extra-terrestrial reference frame to travel the required distances.[11]  The problem with this theory is that there are mathematical errors in its use of Einstein’s GTR.

One misunderstanding is the theory’s use of the Cosmological Principle.  It wrongly assumes that the long-time-scale implications of Big Bang cosmology are crucially dependent on the global validity of the principle and that the relaxation of this assumption, through the introduction of a boundary to the matter of the universe, produces dramatic differences in the gravitational properties of the universe.[12]  A second misunderstanding is the nature of time.  The theory wrongly affirms that the physical clock synchronization properties, which occur in the standard Big Bang model are due to the boundary conditions implied by the Cosmological Principle and that modification of these boundary conditions can change the way physical clocks behave.  Clocks in either our bounded or unbounded universe will behave exactly the same way whether on earth or at a distant galaxy provided there are identical interior matter distributions.[13] The third misunderstanding to be discussed is how GTR relates to event horizons (the point where escaping a mass’s gravity becomes impossible).  The theory wrongly affirms that observers who pass through event horizons observe dramatic changes in the rate of time passage in distant parts of the universe when it is the case that no such changes occur.[14]  Einstein’s impact on young-earth creationism has been profound and, arguably, has overthrown the tenability of young-earth creationism altogether.[15]

Einstein’s impact on natural theology has not been completely negative, as in the case for young-earth creationists, but for scientific theologians [and old-earth creationists] he has been a catalyst for epistemic and religious advances.  It is important to understand that as a GTR-based theory, the model does not describe the expansion of the material content of the universe into preexisting, Newtonian space, but rather the expansion of space itself.  The standard Big Bang model, as the Friedman-Lemaître model came to be called, thus described a universe that is not eternal in the past, but which came into being a g finite time ago.  Moreover, the origin it posits is an absolute origin ex nihilo.[16]  Christian theologians and philosophers already had arguments for a beginning of the universe based on necessity, contingency, and the concept of an actual infinite, but Einstein’s equations, which led the Standard Model, gave a mathematical and physical description of the universe that supported the Christian doctrine of creation.  The metaphysical concept of creatio ex nihilo now had empirical evidence.

In the 1960’s there was a dramatic increase in a series of dialogue on the relationship between science and religion.[17]  Natural theology [by the tasks of primarily scientists and philosophers] has sought to demonstrate that God is a necessary element in any comprehensive explanation of the universe is a long tradition, one that the Darwinian crusade sought to eliminate.  It might be legitimate to say that this renewed relationship between science and religion is a return to normal if Einstein was right when he said that “science without religion is lame. Religion without science is blind.”[18]


            [1] Guillermo Gonzalez and Jay Wesley Richards. The Privileged Planet: How Our Place in the Cosmos Is Designed for Discovery (Washington, DC: Regnery, 2004), 171.

            [2] Gonzalez and Richards, 169.

            [3] Gonzalez and Richards, 171.

            [4] Natural theology supposes that the belief in God must rest upon an evidential basis.  Belief in God is thus not a properly basic belief.  Through the development of Einstein’s work, natural theology was undergoing barrage of attack from theologians such as Karl Barth.  Barth’s polemic against natural theology can be seen as a principled attempt to safeguard the integrity of divine revelation against human attempts to construct their own notions of God, or undermine the necessity of revelation. Alister E. McGrath, The Science of God: An Introduction to Scientific Theology (Grand Rapids, MI: Eerdmans, 2004), 81-82.

            [5] It is worth noting that space itself can travel faster than the speed of light, Einstein’s STR permits this.  It is expected that space begin to exceed this cosmic speed limit relatively soon.  William Dembski, The End of Christianity (Nashville, TN: B&H, 2009), 65.

            [6] Young-earth creationists have an epistemic method that begins with the Bible and shapes the rest of nature and science according to that specific interpretation rendered.  Their conclusion is that the six days of creation are a literal 24-hour day period and the universe is roughly six to ten thousand years old.

            [7] These are the three primary approaches as they relate to Einstein’s work.  Young-earth creationists have certainly developed scores of other arguments, but these are the most relevant and most cited.  D. Russell Humphreys, Starlight and Time: Solving the Puzzle of Distant Starlight in a Young Universe (Green Forest, AR: Master, 1994), 37 quoted in Dembski, 65.

            [8] Dembski, 66-67.

            [9] Dembski, 67-68.

            [10] There are models consistent with a 13.7 billion year old universe that suggests a change in the speed of light.  Recent varying-speed-of-light (VSL) theories have been suggested as a possible alternative to cosmic inflation for solving the horizon problem, the problem of causality over long distances in initial inflation, suggesting that the speed of light was once much greater.  This is not a popular view since it is difficult to construct explicit models permitting such a suitable variation.  Other constants have been suggested to change (a theory of varying fundamental constants) in part due to superstring theory and eternal inflation.  Even so with these theories and cosmic models, there are still more-fundamental (in contrast to varying) constants in the parent universes (preceding universes in the multiverse models).  Even with a theory of varying fundamental constants Einstein’s equations [of STR] still stand in such models. Andrew R. Liddle, and Jon Loveday, The Oxford Companion to Cosmology (Oxford:  Oxford University Press, 2009), 316.

            [11] Humphreys, 13.

            [12] Samuel R. Conner and Don N. Page, “Starlight and time is the Big Bang,” CEN Technical Journal 12 no. 2 (1998): 174.

            [13] Ibid.

            [14] Ibid.

            [15] In Conner and Page’s response to young-earth creationism’s cosmology they assume five mathematical and methodological points.  (1) GTR is an accurate description of gravity.  (2) Gravity is the most important force acting over cosmologically large distances, so that the conventional application of GTR to cosmology is valid.  (3) The fundamental parameters of nature, such as the gravitational constant G and the speed of light c, are invariant over the observable history of the universe.  (4) The visible region of the universe is approximately homogenous and isotropic on large distance scales.  Lastly, (5) the events which we witness by the light of distant galaxies and quasi-stellar objects are real events and not appearances impressed onto the universe by the intention of the Creator.  Ibid, 175.  The first two assumptions directly reinforce Einstein’s GTR equations.  The third assumption, as previously discussed, relates to Einstein’s STR equations.  The fourth assumption relates to the balancing of Einstein’s field equations and its adjustment after Hubble’s discovery of expansion.  The final assumption relates to Einstein’s epistemic method of reality having real ontological value in an epistemic inquiry.

            [16] Paul Copan and William Lane Craig, Creation Out of Nothing: A Biblical, Philosophical, and Scientific Exploration (Leicester, England: Apollos, 2004), 222-223.

            [17] These efforts were predominately made by scientists and not theologians.  Such landmark works were Ian Barbour’s Issues in Science and Religion (1966) and later Paul Davies’ God and the New Physics (1983). Rodney Stark, For the Glory of God: How Monotheism Led to Reformations, Science, Witch-Hunts, and the End of Slavery (Princeton, NJ: Princeton University Press, 2003), 197.

            [18] Albert Einstein, Ideas and Opinions, Trans. and rev. Sonja Bargmann (New York: Three Rivers, 1982), 46. Stark, 197.