In the vacuum of space, light moves at a constant, finite speed. A peculiar consequence of this fact, discovered by Albert Einstein in 1905, is a phenomenon called the relativity of simultaneity.
Imagine you are sitting on a train moving at constant speed. If the blinds are drawn, you can’t tell you are moving. A light bulb on a chain in the centre of the car hangs straight down. When someone turns it on (Figure 1, panel A), being in the centre of the car, its light reaches the two sides simultaneously (panel B). Then, a moment later the light reaches the front and back of the car simultaneously (panel C), having travelled at the exact same speed in all four directions.
Einstein wondered how this situation would be described from the perspective of someone sitting outside the train not moving with the car (bottom row, panels D–G). From this vantage, the light is still found to reach the two sides simultaneously (panel E). But if the train is moving forward, in the moment it takes the light to travel to the front and back of the car, the back has moved closer to the light source and the front has moved further away (panels F and G). The light bulb moves too, but this doesn’t matter since the light reaching the front and back depends on the bulb’s earlier position (the faded ghost in panels D–G), the speed of the train, and the position of the front or back when the light finally gets there, plus the constant finite speed of light. Given these four values, we can calculate the total distance the light travels in either direction of its journey.
Light travels significantly faster than trains and other terrestrial things, so the difference this phenomenon produces is normally imperceptible to us. But that doesn’t change the fact that the passengers on a train describe the two events when the light reaches the front of the car and when it reaches the back, as simultaneous (panel C), while another reference frame — such as a hovering drone looking down at the moving train from above — says the back of the car intercepts the light en route to it (panel F) before the forward-travelling light catches up to the outbound front (panel G).
Of course, how much faster matters, and we can put it in numbers. For a car 25 metres long travelling at 300 kilometres per hour, the drone finds the light reaching the back about 23 millionths of a billionth of a second before it reaches the front. That gap grows in proportion to two things: the relative speed of the two frames, and the distance between the two events along the direction of motion. Over a train car it is far too small to notice (Figure 1 draws the train at four tenths of the speed of light, about a million and a half times faster than any train, so that the effect can be seen at all). Across the distances between stars, it is not.
In any event, we therefore find that, because the speed of light is constant and finite, two synchronous events are not described as synchronous from another, relatively moving perspective.
A Stubbornly Persistent Illusion?
On the basis of this phenomenon, it has been argued that in reality there is no objective “now”, and that time does not pass — that the apparent passage of time may even be psychological. Einstein himself wrote on the passing of his friend Michele Besso, “Now he has departed from this strange world a little ahead of me. That means nothing. People like us, who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion.”
Together with Einstein, physicists and philosophers have often argued on the basis of relativity that in reality there is no objective sense of simultaneity — that if, for instance, in your current reference frame you’d rightly say that a star several hundred light-years away is “right now” exploding, you could stand up and walk away from it and just as well conclude that it won’t explode for another minute or so.
That is the train’s rule applied over a vastly greater distance: walking speed is tiny, but carried across several hundred light-years it shifts which distant events count as happening in sync with “right now” by about a minute. None of this is about what you see — the explosion’s light will not reach you for centuries either way. It is about which distant events are described as happening at the same time as you.
By extension, travelling at different speeds (running, driving, flying, etc) and at different locations, it may be argued that if there is no objective now, and if all relative “nows” are on equal footing, then perhaps reality encompasses all of spacetime — every event that ever happens anywhere across the universe throughout all of eternity — with time nothing but a stubbornly persistent illusion. Some even claim spacetime itself exists, though under any reasonable definition of “existence” that is categorically false — albeit a good source for a favourite trope in science fiction.
But is there really no objective now? Equivalently, is there not one persistent definition of simultaneity corresponding to one definition of existing space — the three-dimensional universe — relative to which objects can be said to be moving or at rest, and events can be described to occur truly simultaneously or not?
From the perspective of modern cosmology, it seems that there is — but before we can understand why, it is helpful to first take a closer look at the Problem of Now in relativity.
The Problem of Now, Concretely
The argument that there is no objective space, and motion is a purely relative phenomenon, rests on an absence. If we cannot observe the presence of one objective space that persists throughout time, and if we cannot measure our own motion through that space, then we cannot define an objective sense of “now” in reality. That, in a nutshell, is the argument on which the Problem of Now in modern physics rests.
If we think back to the train car and the drone, we can see why. There, the temptation is to say that the drone hovering in a fixed place above ground defines “at rest” and that the train is “really moving” — that the top row in Figure 1 shows the situation relative to the actual state of affairs in the bottom row. But we know that the Earth is rapidly spinning and orbiting the Sun, the Sun is orbiting the Milky Way, the Milky Way is moving relative to nearby galaxies, the Local Group… — you get the picture. Therefore, since both the train and the drone really are moving, neither reference frame can be properly defined as the one that’s truly at rest in an absolute sense. Therefore, either should be taken to define an equally valid, relative state of rest. That, of course, is why we call it the theory of relativity.
But it is worth being exact about what relativity itself requires here. Its principle is that the laws of physics take the same form in every frame moving at a steady speed, so no experiment done inside the closed train car can tell the passengers whether they are moving. That is a statement about the laws. It does not say that nothing in the universe singles out a state of rest. And whether something does is a question about what is out there — which is a matter for observation to decide, not theory alone.
On the other hand, if there is an absolute state of rest and an objectively well-defined “now”, what science would require is a concrete measurement showing that the associated space has always persisted as such, along with a way to measure velocity through it from anywhere in the universe and at any time. That would make the one state of rest objectively well-defined relative to all others. Such a space could then be said to “exist” in the usual sense, with Earth and all of us existing in it, and it would provide consistent definitions of “now” and of “motion”.
The Cosmic Now
Cosmology delivers this, and we have already made the required measurements through the cosmic microwave background (Figure 2). The CMB shows that our universe — the three-dimensional expanding space in which we live and evolve — has existed for approximately 13.8 billion years; that space has expanded by an integrated factor of 1090 since the CMB formed; and that our solar system is moving through it with a velocity of 369.82 km/s towards the constellation Crater. The integrated expansion of space throughout cosmic time has been so precise, in every direction we look, that across the sky we can measure anisotropies at a few parts in a hundred thousand that were imprinted on the CMB at the time it was formed — a feature that would be impossible to see if space were not objectively defined and expansion had been different here and there.
The CMB is light released when the universe was about 380,000 years old. Until then the universe was a hot, nearly uniform gas of hydrogen and helium. But once it cooled below roughly 3,000 kelvin, electrons settled onto atomic nuclei, the gas became transparent, and the light filling it was set free. As space has expanded since, every wavelength of that light has been stretched by the same factor, and its temperature has fallen by that same factor — from about 2,970 kelvin then to 2.7255 kelvin today (Figure 2, panel A) — all due to a uniform expansion of space by that factor of 1090 since the CMB was released.
Our velocity through the universe is read from the same light. Moving towards a source of light compresses its waves, making it look slightly hotter; moving away stretches them, making it look cooler. Towards Crater the CMB is warmer than average by 0.0033621 kelvin (Figure 2, panel B). Divide that by the average, 2.7255 kelvin, and you get 0.0012336 — our speed as a fraction of the speed of light. Multiply by the speed of light and it is 369.82 km/s.
That is our speed through the universe, and it’s in the direction of the constellation Crater. And anyone anywhere in the universe could make a similar measurement, by observing the CMB’s temperature gradient wherever and whenever they find themselves.
Once that motion is taken out, what remains is the few-parts-in-a-hundred-thousand pattern (Figure 2, panel C) — and that pattern is the gravitational imprint of matter as it was distributed when the light was released, not a difference in how space has expanded. So whatever difference there has been in the expansion of space itself, from one direction to another, must be smaller still: less than a few parts in a hundred thousand, in every direction.
That uniformity also makes the CMB a clock. Its temperature falls as space expands, and space has expanded the same way everywhere, so any observer anywhere who is at rest relative to the CMB and measures 2.7255 kelvin is at the same moment of cosmic time as we are. The set of those events, across the whole universe, is what “now” objectively is — fixed by the universe rather than by anyone’s motion, simultaneous regardless of relative synchrony, to the precision with which the CMB is uniform.
On this observation, Einstein’s relativity of simultaneity still applies to local phenomena as a matter of relative perspective: neither the train nor the drone gets to say they are the one that is truly at rest, and both frames of reference can be used to describe reality, just as Einstein found. But contrary to his belief, our modern observations also imply that time is more than a mere illusion. The implication from modern cosmology is that the universe exists, and events happen all across space in the course of cosmic time — and these events may be described as synchronous or not, depending on one’s motion through the universe, though there is in reality an objective measure of absolute simultaneity.
Leave a Reply