Special Relativity*
Einstein’s theory of special relativity arose from a perceived conflict between the constancy of Newton’s laws of motion, which hold true in any inertial frame of reference where bodies are moving at constant velocity in relation to each other, and Maxwell’s equations for electromagnetism where the speed of light appears as a physical constant.
Einstein’s achievement was to realise that Newton’s laws and Maxwell’s equations needed some adjustment to take into account the speed of light as a universal constant so that the laws of physics are the same in all reference frames, and our perceptions of distance and time are dependent on our own particular frames of reference. Special relativity takes no account of gravity, and is most manifest when things are moving extremely fast.
Observers at rest and those in constant velocity relative motion are on an equal footing
Simply put, Einstein postulated that the concept of motion is relative - observers, those who claim to be at rest and those undergoing constant velocity relative motion, are on an equal footing and both can proclaim that they are stationary and the rest of the world is moving about them. Their different perspectives are the same. To utilise an earthly example, imagine you are sitting in a train which appears to be stationary at a railway station. You look up and seen another train beside you. One train has started moving, but for the moment you cannot tell whether it is the one you are on or the one beside you. It appears for an instant that you are on the moving train and the other still stands still, but when you look around you and see objects outside on the other side of your train, you realise that your train has not moved and it is the other train which has in fact started pulling out from the station going in the opposite direction[1].
It may seem strange, but Einstein said both viewpoints are correct and that a person on each train can regard himself or herself as still and those on the other moving. Both trains are in ‘relative motion’ one to the other, even though the passengers on board each may think themselves respectively to be the ones who are still. As I sit here at my computer, I imagine myself being stationary, but as the Earth revolves and moves in its orbit around the sun, you and I and all the things about us really hurtling through space at millions of miles per hour. So when we talk about the speed of something moving about on Earth, we really have to take into account the Earth’s speed and work out what its speed is. These principles are far more evident and obvious in outer space. It’s just that here on earth, while we think ourselves stationary, we really aren’t, because everything about us is revolving and moving at exactly the same speed.
Continuing the train example in another context, imagine that you are on a train and that all the curtains in the carriage you are sitting in are drawn. If the train is moving at a constant speed and there are no wobbles or turns, everything in the carriage will look the same whether it is moving or not, and there is no way you can tell whether the train was sitting still on the tracks or moving at high speed. So again, you have to make a relative comparison with other things outside the train, to see whether you are the one who is moving or sitting still.
Changing the focus, imagine people travelling on the deck of a ship which is travelling close to the shore. Someone at the top of the mast drops a ball to the deck below. To the people on board, it drops to the deck in a straight line. But to the people on shore, it appears to fall on a curved path as the ship travels forward. It is only by looking at the shoreline that the people on deck perceive a relative motion between the ship and the shore. It can appear as though the shoreline is moving and the ship standing still, even though those on board know that they’re the ones who are actually moving[2].
Another scenario: Tom is sitting in his London studio typing while his wife is on a long distance flight from London to Sydney. When takeoff restrictions are relaxed, she get up , strolls the length of the plane and then returns to her seat. Has she come back to where she started. From Tom’s perspective, yes. However, from Tom’s perspective, both she and the plane a moving at 500 mph. Assuming her round trip took 5 minutes, this means she’s 40 miles further away from London.
But let’s extend the analogy. Tom has been sitting at his desk typing for five minutes. Is he in the same place as he was when he started? From his perspective, yes. However, the Earth is rotating - at Tom’s latitude, at around 600 miles per hour. In so doing, he has spun around 50 miles through space (in more equatorial skies, his wife's plane has spun closer to eighty).
Let’s go further. If we step back further, the Earth is orbiting the Sun at 67,000 miles per hour. while our entire solar system is orbiting the galactic core at 514,000 miles per hour. That makes over 40,000 miles of interstellar travel in five minutes. From this perspective, our planet was last 'here' one galactic year ago - the time it takes to complete a single orbit of the Milky Way, which is a quarter of a billion terrestrial years.
And even this doesn't provide an ultimate frame of reference, because the galaxies themselves are moving apart at vast and variable speeds - and there's no end to what may lie beyond. As physicists Brian Cox and Jeff Forshaw would say "there is no way, not even in principle, of deciding what is standing still and what is moving ... it only ever makes sense to speak of motion relative to something else." [2.1]
How this ‘relativity’ between different observers comes about: the standard by which these things are measured is the speed of light, a constant
Another of Einstein’s thought experiments on this subject had to do with the speed of light. When he was a teenage boy aged 16, he imagined himself catching up with and actually riding a beam of light. “If light were a wave, then no matter how fast it travelled, I should be able to catch up with its peaks and valleys. But then what would I see? Would light stand still? Would time stand still? Would I ride this wave forever?”, he asked. In his thought experiment, Einstein was comparing riding a beam of light to catching a wave and imagined he could catch up with it[3].
However, as his thought processes developed, he realised that no matter how hard you chase after a light beam, it still moves away from you at the same speed – the speed of light. It is the same speed – a massive 670 million miles per hour - whether you are moving towards it, running away from it, or standing still. In other words, the speed of light is a far away winner, an absolute, the cosmic speed limit, but the benchmark nevertheless. It is always the same, no matter where you happen to be or what you happen to be doing. Nothing can travel faster than the speed of light.
Repercussions as regards time
The discovery that the speed of light is a constant proved to have important repercussions on the way we view space and time which are not obvious and contrary to our perceptions of "normal" common sense, because our affairs are conducted at such miniscule velocities by comparison. Before Einstein, everyone thought that time was the same for everyone. However, Einstein realised that if the speed of light is a constant and does not change, then other factors in the equation, such as time and spatial measurements must; that time must pass differently for a person travelling at great speed than it does for someone who is standing still, and that as you get closer to the speed of light, the more time will slow down, until it finally stops altogether and becomes “now forever”[5]. Perhaps that is what the afterlife is: forever living in the eternal present flitting through the universe at light speed as a neutrino - or perhaps even a muon!
Shakespeare realised that time travels at different speeds for different individuals: that for some it trots (the young woman between the time she gets engaged and when she marries), for some it ambles (the priest who doesn’t know his Latin), for some it gallops (the thief on his way to the gallows) and for some it stands still (lawyers on vacation)[5]. But Einstein had a different perspective.
According to his theory of special relativity (relativity without gravity with a flat spacetime, be it remembered):
- space and time are interwoven and relative to one’s state of motion;
- the speed of light is a constant - nothing can travel faster than the speed of light, and it is only the speed of light which saves the universe from being “as non-objective as a roomful of art critics”, because everything else is relative;[6]
- the passage of time occurs at different rates when one (or both) observers are in motion;
- clocks moving relative to one another record the passage of time at different rates; they fall out of synchronisation and therefore give different notions of simultaneity; a moving clock ticks more slowly than a stationary one.
To illustrate the principles governing the warping of time in the context of motion, Brian Greene uses the example of a peace treaty being signed on a carriage in a moving train when neither party wishes to lose the tactical advantage of having his opponent sign before him[7]. It is agreed that both parties, sitting at opposite ends of the carriage, will sign simultaneously when a light bulb is switched on in the train. Both parties sign when this occurs and both are happy with the result, but on the platform it appears that the person facing the direction in which the train is travelling has signed the treaty first - because the light from the bulb reached him first. The light took longer to reach the person at the other end of the carriage because it had further to travel[8]. Since special relativity is most manifest when things are moving at close to the speed of light, these effects are unnoticeable in our earthly environment, but the example serves to illustrate the point.
One might say that Einstein had abandoned the traditional meaning of ‘simultaneous’ as ‘happening at the same space-time space-instant’; and redefined it in terms of what different observers in different vantage points observer could see[9]. The quantum mechanics guru, Niels Bohr, expressed it by saying that:
“In the past, the statement that two events are simultaneous was considered an objective assertion, one that could be communicated quite simply and that was open to verification by any observer. Today, we know that ‘simultaneity’ contains a subjective element, inasmuch as two events that appear simultaneous to an observer at rest are not necessarily simultaneous to an observer in motion. However, the relativistic description is also objective inasmuch as every observer can deduce by calculation what the other observer will perceive or has perceived”[10].
Repercussions as regards space and time: the concept of spacetime
Spacetime is a region of space considered over an interval of time. A region of spacetime is a record of all things that happen in some region of space during a particular span of time. Absolute time does not exist; absolute space does not exist, but absolute spacetime does.[11]
To illustrate these concepts of space and time (spacetime) in special relativity, imagine a vehicle travelling due south at a constant speed of 100 kph. It then goes into a long series of curves and hairpin bends as it ascends an incline and then descends into an adjacent valley. The vehicle must now share some of its speed, hitherto used solely for travelling south, for use in travelling back and forth. This example incorporates the three space dimensions: back and forth, left and right, up and down.
Now incorporate the time dimension. Imagine a car parked outside your house. It is moving in time, just as you the observer are. It now speeds off, meaning that some of its motion through time is diverted through space, and its speed through time slows down when it diverts some of its motion through time into motion through space, leaving their combined total unchanged. This means that the car’s progress through time slows down and therefore time elapses more slowly for the moving car and its driver than it elapses for you and everything else that remains stationary. This may all seem contrary to “common sense” and our own everyday experience, and in earthly terms the time difference is so small that we don’t notice it, and our timepieces do not record any difference at all.
Repercussions as regards measurement and distance
Special relativity declares a similar law for all motion: moving at light speed through space leaves no motion for travelling through time, so time stops when travelling at the speed of light through space.[12] Since space and time are relative, observers in different inertial reference frames moving at constant velocity will not necessarily reckon distance and time in exactly the same way. From their different vantage points, they will not always agree as to the length, width or depth of things spatial or the duration of things in time, and everyone will have their own idea about what he or she sees with no scientific way of resolving the disagreement. So no matter how fast a person is moving, his reckoning of an inch and a second will always change so as to leave undiminished the speed of light.
Thus: “(s)ize and all the measurements associated with it, such as length, width and height, are all relative. They have no meaning unless they can be compared with something else. Our standardised form of measurement - inches, feet, yards, miles quarts, pints and so on – give us frames of reference to measure things. But they are still arbitrary units that have merely been defined so we can relate to and interact with our world. None of them are fixed and absolute”[13].
To illustrate the point, Bill Bryson utilises a much quoted example from Bertrand Russell’s The ABC of Relativity[14]. It is another train example. Russell asks the reader to envision a train 100 yards long moving at 60% of the speed of light. To someone standing on the platform watching it pass, the train appears to be only 80 yards long and everything on it appears to be similarly compressed. “If we could hear the passengers on the train speak, their voices would appear slurred and sluggish, like a record played at too slow a speed, and their movements would appear similarly ponderous. Even the clocks on the train would seem to be running at only 4/5ths of their normal speed”.[15] But the people on the train would have no sense of these distortions. To them, it is those on the platform who would look weirdly compressed and slowed down.
These relative effects are the same as regards all our earthly travels, only the distinctions are too small for us to be aware of. And time - which after all is just another form of measurement - is exactly the same.
* For all the relevant concepts here considered, see the excellent BBC documentary, "Inside Einstein’s Mind – The Enigma of Space and Time", NOVA/WGBH, BBC4 (2015) at https://www.youtube.com/watch?v=lgeB4b1WR0Y. It is an excellent overview and covers issues such as:
- Einstein’s thought experiments in the fields of special relativity, premised upon Maxwell’s discovery that light is an electro-magnetic wave that travels at a fixed speed,
- general relativity, the equivalence of gravity and acceleration, the geometry of spacetime, the curvature of space, the shaping of spacetime by matter causing us to feel gravity; how the distribution of matter and energy determines the curvature of spacetime as described by the equation Gμν = 8πTμν; the fact that clocks tick faster at altitude where gravity is weaker,
- the consequences of general relativity which Einstein could not foresee: “We understand general relativity today better than Einstein ever did”: Sean Carroll, research professor in the Department of Physics at the California Institute of Technology; black holes, made not from matter but solely from warped space and time; gravitational waves; the universe’s expansion denoting that it once had a beginning in the form of the big bang, dark energy being responsible for 70% of all the ‘stuff’ of the universe;
- and finally, the fact that Einstein never really related to quantum mechanical concepts, leaving us even today with the legacy of an ongoing quest for a theory uniting the very small and the classically large.
[1] The train examples, save the one from Bertrand Russell, are drawn from Brian Greene, The Elegant Universe, Vintage 1999, 29-30. For an elaboration of Einstein's thought experiment from the different perspectives of stationary observers and those on the train itself, see the interactive at http://channel.nationalgeographic.com/genius/interactives/genius-thought-experiment/ from the National Geographic's ten episode series on Einstein's life and work (2017).
[2] The ship examples are drawn from Gary Moring, The Complete Idiot’s Guide to Understanding Einstein, Penguin, 159-161.
[2.1] These scenarios extracted from Tom Chatfield’s article “Everything is relative”’, NewPhilosopher, special edition on Time, Issue 22, November 2018- January 2019, p 39.
[3] Citation from Moring, Ibid. See also Sabine Hossenfelder, “Head Trip – Einstein’s thought experiments”, Scientific American, September 2015, at 37.
[4] Moring, Ibid.
[5] As you like it, Act 3, sc 2, 280-301. Cf Henri Bergson’s view of time, which was beyond the province of science alone, he said, being closely intertwined with the ‘vital impulse’ of life and creative expression. Jimena Canales, The Philosopher and he Scientist: Einstein, Bergson and the debate that changed our understanding of time, Princeton University Press, 2015.
[6] Michael Guillen, Five Equations that changed the world, Hyperion, New York, 1995, 246.
[7] Greene (2000), 34-37. Dana Mackenzie utilises a similar example in The Universe in Zero Words, op cit, 160.
[8] Gary Moring uses the example of lightning ‘simultaneously’ striking two poles an equal distance apart and the different perspectives of a stationary observer standing at the mid-point between the poles (who sees both events occur at the same time) and one in motion at the mid-point who sees the strike occur first on the pole he is travelling towards, because the light has a shorter distance to travel from the pole that the train is travelling towards than the one he is travelling away from: Gary Moring, The Complete Idiot’s Guide to Understanding Einstein, Penguin, 168-9.
[9] Robert P. Crease, The Great Equations – Breakthroughs in Science from Pythagoras to Heisenberg, Norton, New York, 2008, 239.
[10] Cited by Werner Heisenberg in his essay Science and Religion, incorporating the different views concerning science and religion by the then young physicists, Heisenberg, Paul Dirac, Wolfgang Pauli and Niels Bohr reproduced in Ray Younis, Metaphysics and Reality (in the 21st Century) CCE course, 1 December 2012.
[11] Greene (2005), 53,59
[12] Greene (2005), 49
[13] Moring, op cit, 164.
[14] In A Brief History of nearly Everything, Broadway Books, 2003, 124-5.
[15] Ibid.