Ethical Relativism
and
Einstein's Theory of Special Relativity
There is a history of scientific discoveries and theories being generalized from the often rather narrow domain of thought in which they apply to a much larger domain of thought. Often these generalizations are used to justify social policies which, if not for their 'scientific justification', would be rather hard to accept. An example is the generalization of the Darwin's theory of natural selection in the context of biological (species) evolution to 'social Darwinism' in the context of sociology. This generalization of Darwinism in the late 1800's and early 1900's was used to justify the development of social policy and laws that allowed for robber barons to reduce their workers to virtual slaves because, 'it is the nature of things that the strong survive and the weak die, as science has shown us'. Laws were passed to allow and encourage the accumulation of wealth on the part of the corporate leaders, and laws were passed banning unionization and worker rights, all under the cover of 'scientific justification'.
Such abuse of scientific theories is often possible because the theories are not thoroughly understood by the public or policy makers. Another example can be found in the generalization Einstein's theory of special relativity to the field of ethics. In ethics, we distinguish between two kinds of ethical theories absolutist and relativist. An ethical absolutist will claim that moral laws are like physical laws in that they exist and are immutable. That is to say, just as Newton's laws of mechanics [Principia Mathematica, 1687] (supplanted by special relativity the case of large velocities) describe the way objects in the universe move now, they way the have always moved, the way they will always move, and that any careful observer will agree that the motions of objects can, in fact, be described by these 'laws'. These laws are not matters of convention, varying over time or space, and are independent of the observer. Hence, we call them laws. The relativist, on the other hand, will argue that morality is relative to the extent that what a person will regard a moral action will depend on his/her society and place in that society. Thus, what is moral now in the United States of America, might not be moral now in Uzbekistan (for example), or even in the United States of America one hundred years ago or one hundred years in the future.
Now, there have been ethical absolutists and relativists since the ancient Greeks - ethical relativism was not invented after Einstein published his 1905 paper on special relativity ["The Electrodynamics of Moving Bodies", Annalen der Physick] as ethicists thumped themselves on the forehead and said to themselves, "Ah! If physical laws are relative, so must moral laws be!". Not anymore than sociologists thumped themselves on the forehead after the publication of Darwin's Origin of the Species [1859]. Instead, just as people already supporting certain social policies appealed to Darwin's theory as additional support and justification for their policies, some people use (or abuse, as the case may be) Einstein's theory as additional support and justification of ethical relativism. The move is not at all hard to understand "Hey, Einstein demonstrated everything's relative, right? And who are we to argue with Einstein?!?".
Well, if we understand Einstein's theory in the first place, then our argument is not with him, but with the people who seek to use his theory to support and justify ethical relativism. And the fact of the matter is, that what we need to understand about Einstein's theory can be achieved with nothing more than 'college' algebra. The fact that two observers in motion relative to one another will measure the length of an object to be different, i.e. length contraction, and that two such observers will also measure the time between the same two events to be different, i.e. time dilation, are the hallmark consequences of special relativity that people know, though don't understand, and that ethical relativists trade upon in trying to sell their ethical position.
The theory, and hence the consequences of the theory, are mysterious to most people, because, "Hey, we're talking about relativity, right?!? If it took Einstein to figure this stuff out, then surely it's beyond us.". Well, not really, because it's nothing more than 'college' algebra. So let's derive time dilation in a way that anyone with a college education can handle.
Consider two observers, one standing on a railway platform - call this observer O', the other riding in a boxcar moving from left to right with a velocity v - call this observer O, as depicted in the following drawing
Each observer exists in a frame of reference, both of which are in motion relative to one another. As the boxcar passes from the left to the right, O', standing on the platform, sees it and O in it moving to the right with velocity v, while, O, riding in the boxcar, sees O' moving to the left at velocity v. Both observers feel themselves to be at rest and the see the other observer as the one in motion!
In the middle of the boxcar's floor is something that can emit a beam of light directly up, say, a laser, and something that can detect light, say, a photo-diode, and in the middle of the roof of the boxcar is a mirror which will reflect light emitted by the laser down to the photo-diode.
Now, before going any further, we must consider Einstein's postulates, because it is the postulates that give rise to the relativistic effects of time dilation and length contraction. Einstein's postulates are
These seem like a fairly innocuous statements, but the second postulate is really quite contrary to our common experience. If I was standing in front of a moving car, and the driver were to shoot a gun at me, the velocity of the bullet in the driver's frame of reference would be whatever the muzzle velocity of the gun is, say vg. If the car were moving at velocity vc toward me, the bullet's velocity would be vg+vc in my frame of reference, which is to say, I would the bullet coming at the speed vg+vc. If the car were moving away from me, the bullet's velocity would be vg-vc in my frame of reference - and if the car's velocity were greater than the bullet's (in the driver's frame of reference), then the bullet, like the car, would be moving away from me! For physical objects like bullets, indeed, for anything except light, velocities are simply additive.
Einstein postulated that light was different if the driver of the car had been shooting a laser at me, it would not matter if the car was moving toward me or away from me - the light would have the same velocity in my frame of reference (approximately 3x108 meters per second or 186,283 miles per second!) in both cases! Again, this is contrary to everything else in our experience, and this postulate was the intellectual leap that demonstrated Einstein's brilliance.
So, in what follows, we'll not add the boxcar's velocity to the light's velocity when considering the light's velocity in O''s frame of reference. The fact that, in O''s frame of reference, the light moves from the left to the right, in addition to moving from the bottom of the boxcar to the top of the boxcar and back, as depicted on the right ( i.e. the red path), has no effect on it's velocity as measured by O', i.e. O' measures the velocity of the light to be c just as O does.
How much time does O measure the roundtrip of the light to take? In O 's frame of reference, the light follows the path on the left ( i.e. the blue path), and since the boxcar's height is d, in going from the bottom to the top and back, the light travels 2d in O's frame of reference. Velocity is distance traveled divided by the time traveled, so the travel time, t, of the light is 2d/c - as measured by O.
How much time does O' measure the roundtrip of the light to take? In O''s frame of reference, the light follows the red path. In the time the light takes to complete its trip from the bottom of the boxcar to the top and back, call it t', the boxcar moves to the right, in O' 's frame of reference, a distance vt', and the light takes t'/2 to travel from the bottom of the boxcar to the top. In this time, the boxcar has moved to the right, again, in O''s frame of reference, a distance vt'/2, and the distance traveled by the light during this time is its velocity c multiplied by t'/2, or simply ct'/2 - because the speed of light is the same for all observers.
And this is where the college algebra begins these three distances, vt'/2 and ct'/2, and the boxcar's height, d, form a right triangle, with the distance traveled by the light, ct'/2, being the hypotenuse of the right triangle. Pythagoras's theorem is that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides, or in this case
We need to solve this equation for t'. Going one step at a time
A little manipulation of this last equation will make some things a little bit easier to see. If c2 is factored out of the denominator
we see, first, v/c, i.e. the famous b (the Greek letter beta ) factor - when one says an object is moving .9c or nine-tenths the speed of light, the nine-tenths is the b factor. Second, we see the 2d/c, which was the travel time t for the light as measured by O! So
Because physicists don't like to write more than they have to, and because the quantity in front of the t in this equation shows up time and again, they have given it a name as well, and it is called the g (the Greek letter gamma) factor, hence
One can derive the length contraction formula in a similar way. In that case, one considers not a laser emitting light up and a mirror reflecting the laser light back down, but instead a laser emitting light to the right (or left - it makes no difference) and a mirror reflecting the laser light back to the left, all as the boxcar moves past O'. The algebra is a little more complicated, but not that much. In any case, the result is
where l is the length of the boxcar as measured by O, and l' is the length of boxcar as measured by O'.
We should make some observations now. For reasons that we haven't given here, in the vacuum of space, nothing can travel faster than light. So if we limit ourselves to boxcars moving through space, b is always less than 1 - all velocities v must be smaller than c. Thus, b is always less than 1, b2 is always less than 1, (1-b2 ) is always less than 1, and finally, the square root of this quantity is always less than 1. g is one over this last quantity, so g is always bigger than 1! O, who is at rest with respect to the boxcar, measured the length of the boxcar to be l, and O' who was moving relative to the boxcar, measured it to be l'=l/g. But g is always bigger than 1, and dividing one number by a number bigger than 1 makes the number smaller, so l' must be smaller than l - the length of the boxcar is contracted from the point of view of any observer moving relative to it! On the other hand, t'=g t, and as g is always bigger than 1, t' is always bigger than t - the time it takes for something to happen in a frame is lengthened or dilated from the point of view of any observer moving relative to it!
Physicists refer to the measurement of a thing made by an observer at rest relative to the thing as the "proper" measurement (in our example, the proper measurements are those made by O), but they aren't really making the value judgment the word "proper" implies. The "proper" length is really nothing more than the longest any observer in an inertial reference frame will accurately measure an object to be, and the "proper" time is really nothing more than the shortest period of time any observer in an inertial reference frame will accurately measure for any given time interval. Ask a physicist, and (s)he will tell you that there is no privileged frame of reference for making measurements.
So what has all this to do with ethical relativity? We don't usually use the language of "measurement" when discussing our estimation of the morality of a particular act, but people do sometimes talk about a 'moral yardstick'. I consider a particular act, I hold my moral yardstick up to it, and judge it to be moral or immoral. Well, we've derived the way in which the two most basic physical measurements we can make, the length of object and the time it takes for something to happen, are relative, i.e. the measurement depends on the situation of the person making the measurement. If these fundamental physical measurements are relative, then must not all measurements be relative? Perhaps.
But perhaps not. Arguments by analogy are notoriously tricky, and seemingly valid arguments by analogy often turn out to be worthless. Suppose for a moment this argument by analogy is valid. What conclusions can we draw as a result?
Not what a more radical breed of ethical relativist asserts that members of one society at one point in history cannot judge the morality of the members of another society (at a possibly different time in history). This kind of radical relativist claims there is no 'privileged frame of ethical reference', i.e. no society in a position to assert that its moral judgments are superior to any other society's moral judgments. But this goes too far.
Special relativity does not assert that the boxcar does not, in fact, have one and only one length - it only asserts that each observer's measurement of this length will depend on their frame of reference. We might argue about whether or not the boxcar actually exists, but if we grant that it does, then it seems that it must have some length, and the issue is our measurement of this length. And if I measure the boxcar's length in my frame of reference, I can know what an observer in any other frame of reference will measure it to be, given that I know the velocity of that observer's frame reference relative to my own. That is to say, I can judge the validity of his/her measurement. I can make the claim given that observer's situation, the correct answer is l, and if that observer measure's the boxcars length, and gets anything other than l, (s)he is simply wrong.
In the United State of America of the early 21st century, this more radical breed of ethical relativism is often espoused under the guise of a liberal and intellectual political correctness. Its proponents claim they simply generalize Einstein's claim that all measurements are relative. But an understanding of Einstein's theory of special relativity, which requires nothing more than college algebra and Einstein's postulates, is asserted to be beyond the reach of all but the intellectual elites. These elites then claim that, as they understand Einstein, and we do not, we should take their word it that we are in no position to judge people not of our society or time.
This is not the case.
And one can go further recall Einstein's first postulate! He claimed that physical laws were the same for all inertial observers. If one is going to generalize physical (special) relativity to address ethical relativity, what of the first postulate? And here one is confronted starkly by problem of arguing by analogy what does it mean to be an "inertial observer" in an ethical context? One can dodge the full force of this question if one focuses on the second postulate, by doing exactly what we did, that is, by getting caught up the physics! But to even bother with doing so, one must first grant that people in a society constitute inertial observers in an ethical context, or the argument by analogy doesn't even get off the ground!
So, if we grant that we constitute inertial observers in the ethical context, no ethical relativist can appeal to Einstein's physical theory to justify their ethical theory because the generalization of Einstein's first postulate is a flat contradiction of the ethical relativist's fundamental claim. To generalize Einstein's first postulate is to assert that moral laws exist, and that they are the same for all people in all cultures and all times. But if moral laws exist and are immutable, then why do societies' moral codes vary so greatly?
Well, it has taken us something longer than 2500yrs to come to our current understanding of physics. And the fact that our physical theories, and the physical laws they purport, have changed over time and varied from society to society is taken by very few as evidence that physical laws lack a universal existence or are mutable over time. Likewise, the certainty with which every scientist anticipates refinement as possible upheaval in current theories, strikes very few as evidence for this claim.
Perhaps Einstein's theory of special relativity is an apt analogy for ethical theory, if only it is correctly understood.