Is time relative?

In the previous post ( I gave a simplified account of why time and position are considered relative, in which each observer has his own version of what “here” and “now” means. We need some means of describing what an observer sees. An absolute position would be like GPS coordinates. Everybody agrees where the equator is, and we have made Greenwich a reference point for longitude, but in the general Universe there are no obvious reference points. Without a reference point, “here” is meaningless unless expressed as a distance from something else, and this has been well established since Galileo’s time, if not earlier. There was thought to be “aether” through which everything travelled, but Michelson and Morley provided evidence there was no such thing. The formalism of Einstein’s relativity puts time in a similar position, and it dilates as velocities approach that of light. This is accounted for with what is called “space-time”, in which time is just another relative coordinate.
All observed evidence is in accord with this, and an example is the lifetime of muons. The muon is an elementary particle that decays to an electron with a half-life of about 1.5 microseconds. However, if the muons were travelling at about 98% the velocity of light, applying the Lorentz-Fitzgerald factor for time dilation, as required by special relativity, it has been shown that this half-life is about 5 times longer, and most importantly, muons behave as if they live five times longer when travelling at such velocities. From an observer considering the muon’s point of view, the reason it lasts longer is because the distance it thinks it has travelled is shorter. This suggests that time is relative, and the equations of relativity invariably give the correct prediction of a measurement.
Consider a space traveller. According to relativity, if the traveller heads off at near the speed of light and travels far enough, then comes back, time has essentially stopped for the traveller, but not for whoever is left behind. That was the basis of my scifi trilogy “Gaius Claudius Scaevola”. Within the trilogy, Scaevola starts in Roman times, gets abducted by aliens, and returns sometime like the 23rd century, and he has aged a few years only. The principle of relativity is that all clocks in a moving ship must slow down equally; as Feynman remarks in Six not so easy pieces, if this were not so, you could use something like the rate of development of a cancer to work out the absolute velocity of a space ship. To further quote Feynman, “if no way of measuring time gives anything but a slower rate, we shall have to say, in a certain sense, that time itself appears to be slower in the space ship”. The best-known application is the GPS system. Without the equations of General Relativity, this simply would not work.
Nevertheless, I believe there is a way of measuring an absolute time. Suppose a similar traveller headed off to a galaxy five hundred light years away at light speed, and, in accord with relative time, came back a billion years later without having aged. Now suppose he and another physicist from the future decided to measure the age of the Universe, that is the time from the big bang. The equipment is set up and gives a meter reading. Surely both must obtain the same reading since they see the same dial, yet according to the traveller, the Universe should be only13.8 billion years old, while the measurement gives it at 14.8 billion years old. There is only one possibility: the Universe is 14.8 billion years old, and all that has happened is that the traveller has simply not observed the passing of a billion years. The point is, when considering distance, there is no reference position. When considering time, there IS a reference time, and the expansion of the universe provides a fixed clock that is a reference visible to any observer. Worse, you could in principle work out the age of the Universe from within the ship, so in principle you could use this to work out the speed, apart from the fact that determining the age of the Universe is not exactly accurate. So why does muon decay slow?
Suppose we start with no muons, then at time t we shall have nt muons, given by (assuming the number of decays are proportional to the number there)
n_t=n_0 e^(-kt)
Now it is obvious that you get the same result if either k or t is dilated.
What is k? It is the “constant” that is characteristic of the decay, and it can be considered as the barrier to decay, or the tendency of the particle to hold together. Is there any way that could change? Does it have to be constant?
This gets a bit more difficult, but Einstein’s relativity can actually be represented in a slightly different way than usual. For those with a grasp of physics, I recommend Feynman’s “Six not so easy pieces”. When Feynman says they are not so easy, he is not joking. Nevertheless one point he makes is that Einstein’s special theory of relativity can be represented solely in terms of a mass enhancement due to velocities near the speed of light. What that means is that as the muon (or the space traveller) approaches the speed of light, it gets more massive. If that energy is concentrated on the muon, then the added mass might dilate k by increasing the barrier to decomposition. It is not necessarily time that is changing, but rather the physical relationships dependent on time. Does it matter? In my view, yes. I would like to think in science we are trying to determine what nature does, and not that which happens to be convenient at the time.
In many cases in science, like the equation above, there can be more than one reason why an equation works. Another point is that the essence of a scientific theory should be able to be conveyed without the use of difficult mathematics, although, of course, to make specific use of the concepts, difficult mathematics are needed. What the scientists should do is to ask questions of a theory, and then test the answers.
As an example of such a question, we might ask, did Michelson and Morley really prove there is no aether? My view is, no they did not, although that does not mean there is aether. The reason is this. If light always has the same velocity relative to the aether, it must interact with it. That means there is an interaction between aether and electromagnetism. Now molecules have local electromagnetic fields, and such molecules travel fast and randomly, and might very well “trap” aether. Think about a river flowing, with reeds along the bank. The water flows strongly, but if you try to measure the flow in a reed-bed, the water is virtually stationary. In the same way, the random motion of air might trap aether near the earth’s surface. What science suggests now is simple: repeat the Michelson Morley experiment outside the space station. Suppose the answer was still zero. Then Einstein’s theory is firm. Suppose the answer is not zero? Actually, the equations of Einstein’s relativity would not change all that much, and would actually become a little more complicated, but the differences would probably not be discernible in any current experiment. What do I think? That is actually irrelevant. The whole point of science is to ask questions, to try and uncover further aspects of nature. For it is what nature does that is relevant, not what we want it to do. What do you think?


6 thoughts on “Is time relative?

  1. “There is only one possibility: the Universe is 14.8 billion years old, and all that has happened is that the traveller has simply not observed the passing of a billion years.”

    This is the twin paradox in a slightly different form. One traveller has accelerated with respect to the distant stars, and so was in a non-inertial frame of reference.

    • Yes, except it is no paradox. There is no dispute that those on the ship age more slowly, in accord with relativity. But if they are simply moving more slowly through time, then time is not necessarily relative. Thus in my muon example, it is not necessarily time that is dilated, but rather the barrier to decay is enhanced.

  2. …if you were sitting in the dining room of the space ship, along with the accompanying muon, and could convince it to measure its own mass, they are pretty sensitive about these things, I’ve heard. Would you find that it’s physical attributes were any different than when you took off? I would think that you wouldn’t. If so, the observer of the “increase” in its mass is not in the ship but outside it and the increase is not the muon’s own measurement of itself but one made by an observer as we streak past. I think there is a question, of whose answer I do not know, what is the effect of that speedily passage on the observation?

    • Yes, the measurement inside the space ship would be the same as on the ground because the relative velocity between you and the muon is near zero. To an external observer the muon would be heavier, but inside the space ship, both you and the muon experience the same Lorentz-Fitzgerald contraction that the external observer has to apply. The Lorentz-Fitzgerald contraction arises because irrespective of the relative velocity of the object, light from it always arrives at exactly the velocity c. For the observer inside the space ship, if the muon is considered to have a time dilation with respect to an external observer, you and your clock experience the same dilation, so when you measure the muon’s lifetime it is the same as when you were on Earth and you cannot tell that you are travelling from within the ship. It is actually essentially the same argument as Galileo used!

      • So, the measured weight of the muon is a fact if you are next to it. Then, if you are not actually measuring what it is you are simply observing, you are just making inferences from what you observe.
        So, when you observe a traveler in a spaceship going by at the speed of light your observations are not measurements, per se, only inferences. Does this present an issue when we try to describe “facts” that we only can observe?
        When one asks, “Who is right?” there seems to be an “observational” right ans, and a scientifically determined “right” ans. Further, it seems that one must always include whether a fact is observationally determined, with the various caveats, or measured, “scientifically.”
        My recollection of my educational system (USA in the 60s, 70s and 80s-and probably on-going) is that there was (is) no mention that there is a difference. “People get heavier”,
        I believe, that problem has caused many to have issues with the observational and factual data surrounding “close-to-speed-of-light” velocities. I realize that people professionally discussing these things are aware of the various caveats surrounding the data they are working with, but, as in so many cases, it is like trying to learn calculus when your professor continually skips the 5 “obvious” (to a true believer) steps in a proof.
        The student learns only to solve problems by rote. Of course, in many situations that only produces automatons, something that we constantly complain about, but hesitate to take the time out of our busy schedules to fix. Besides, what professor doesn’t want to feel like a demi God? 🙂
        At any rate, c included (I postulate), I do appreciate this conversation and your time.

  3. All data coming into a scientific experiment are observations, but what most people forget is that the observation comes essentially as a pointer reading, i.e. your equipment gave a reading of so many millivolts. If the equipment is a spectrometer, the machine itself will do so much mathematics, using perhaps, Beer’s law, to present the scientist with an absorption. The scientist then uses the concentrations he has measured out, and the assumption that the material has not undergone any chemical transformation, to record an extinction coefficient. This extinction coefficient may then be used to estimate the amount of the material in other samples, but again there are assumptions, such as Beer’s law actually applies, there isn’t some other species present, etc. So any conclusions drawn have a number of implied assumptions in them. Generally these have been found to hold thousands of times before, so there is seldom a problem, but once you take your experiment outside the conditions where there is plenty of back-up data, there are risks. At that point we rely on theory. What I have written about relativity and how a muon’s lifetime varies is based on theory that has generally been found to always predict what we observe, but many of the possible experiments cannot be carried out, so up to a point I guess we don’t actually know.

    Your comments on educational systems are valid. I know when I was doing my honours year, it became obvious that the lecturers on quantum mechanics had no understanding at all, and they were merely reproducing pages of formal textbooks. Feel free to take up more of my time; part of the reason I am blogging, and for that matter writing fiction, is to try and promote the scientific way of thinking.

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