Relativistic time dilation and thermodynamics

qbit

I have a question relating to relativistic time dilation and thermodynamics. I have put the question in the context of a thought experiment. This I have done as I can not find the particular terminology needed to ask a more succinct question. I have also taken some liberty to try to make the question more enjoyable to read.

A brilliant but mad scientist removes the living, conscious brain and eyes from a test subject, Eric, and sustains Eric's disembodied mind, with sight, in a glass tank with nutrient fluid. But Eric's view of the world is limited to the dark cupboard he has been placed in and a keyhole in the cupboard door. Through the keyhole is the laboratory of his captor, however the view is narrow and he can make out only a pendulum on what could be a chronometer on a desk. Suspended in space and deprived of all but one of his senses, Eric's existence was bleak.
Determined not to let his predicament undo what was left of his sanity, Eric directed his attention. He observed that the pendulum was in motion and performed its intended function, swinging side to side in a regular, periodic motion. This marked time for him where he otherwise had no notion. With no fingers or toes to tap, heart beat or teeth to chatter, Eric could only mark time by recalling songs and tunes. His experience of time passing was entirely subjective if not for the pendulum.
Each oscillation of the pendulum marked a unit of time and those units of time appeared to pass relatively quickly over some large periods of time (he estimated to be about two hours), and relatively slow over other, large periods of time. This observation Eric attributed to his state of mind. For example, a large period time before he slept was associated with a relative quickening of pendulum, that is, a time when he was drowsy. The reverse effect was observed when he was alert.
Days could have passed but Eric could not know for sure as the laboratory lighting was artificial and not influenced by diurnal cycle when a mote of dust, suspended in his nutrient solution, appeared before his eye. Caught in an eddy, the mote appeared to possess precise cyclical motion. He now observed two oscillators which he could compare and for a while, they were perfectly synchronous.
In time, the pendulum and mote became asynchronous. Not in a constant manner but rather the oscillation of the pendulum was increasing to become relatively faster. It could be argued, thought Eric, that the oscillations of the mote were decreasing to become relatively slower, however the relative transpiration of time would only confuse that which was to happen next.
While his mote remained at constant oscillation, the oscillation rate of the pendulum increased to such a rate that it was a blur. Could it be, thought Eric, that time outside his cupboard was transpiring much faster? Or could the chronometer instead be hot, unwinding its spring faster and faster as the increase in kinetic energy drove the mechanism to run faster and a faster? How can Eric tell the difference?
Eventually, the pendulum oscillated at near light speed compared to his mote. If the pendulum had within it another, miniature chronometer, would the same relativistic time dilation effects be observed when taking measurements from this second chronometer if the pendulum was hot as compared to an increased transpiration of time?

Thanks in advance.

Matterwave

Relativistic time dilation happen for one observer in one reference frame looking at another reference frame's clock which is moving relative to him. If Eric is in the same reference frame as the pendulum, he should be able to detect no time dilation at all (other than perhaps subjective results due to his inability to internally keep time).

harrylin

I guess you mean that the pendulum's swing speed reached nearly c? Note that you can't tell that by comparing it with the mote, as that doesn't tell you the limit speed.
Those are not relativistic time dilation effects. For that you need a system that is moving at very high speed relative to the observer (not the case here) or a difference in gravitational potential (which is also not the case here).

qbit

Matterwave,

Thanks, I take your point. But I had rather hoped to portray a situation where this is not the case. Let's say Erics mote completes one cycle for every 2.9^8 cycles of the pendulum. The miniature clock built into this blur of a pendulum would not be in the same reference frame by my reckoning.

harrylin,

Thanks for you reply. Maybe I've over complication the example by using chronometers that undergo acceleration. Anyway, it is my understanding that time dilation is an effect experienced by any pair of objects in relative uniform motion, except when that motion is equal to zero (and exponentially significant when when approaching c). There is no such thing as an absolute reference frame to determine a 'speed limit'. The pendulum simply can not reach c relative to the mote or Eric or his cupboard.

I would disagree. The miniature clock on board the pendulum, or if you like, in the reference frame of the pendulum, or is you prefer, in the system of the pendulum is supposed to be moving at near light speed relative to the mote. They are, to my mind, not the same system or reference frame.

But yes, I have omitted any gravitational effects for simplicity.

No comment on time passing vs. temperature?

harrylin

OK so you have a miniature clock in the swinging pendulum itself - I'm afraid that I mixed up your chronometers, sorry for the misunderstanding! - you confused me with your "chronometer spring", a pendulum clock has no unwinding spring but weights. In that case, yes that miniature clock inside the swinging pendulum will be slow compared to the pendulum clock (your "chronometer"?), although not completely stopped as the pendulum is moving at different velocities. Note that even the clock is not the full time keeping system as this made up of the clock and the Earth* which serves as balance spring for the pendulum. And this system is in rest relative to the brain.
I suspect that that aspect will be solved by itself when the above is solved.
However, I basically didn't comment on that last question because it is quite unclear to me what you mean with it.

*Interestingly for a similar reason Einstein excluded pendulum clocks from his example in 1905, see footnote 7 of http://www.fourmilab.ch/etexts/einstein/specrel/www/

qbit

harrylin,

I am beginning to regret my choice of a pendulum for Eric's external clock. Not only does it add confusion to the (thought) experiment by, as you note, possess a pivot that could confine the pendulum to one plane of motion (a swing, I think you call it) or two planes of motion; thermal expansion of pendulum clock mechanisms generally cause the clock to lose time. Precisely the opposite to the phenomenon I'm posing the question about.
A more prosaic but more accurate portrayal of the problem would have been to use an elastic particle in a box that marked time by periodically bouncing from one wall to another.
Anyway, I've included an illustration of Eric's world view with digital timer built into the bob.
In the particle in a box scenario, the timer would be built into the particle.
After posting the question, it has since occurred to me that I may have answered my own question: perhaps the only real way for Eric to determine the difference between a 'hot' oscillator and an oscillator for which time transpires more rapidly is to observe that time dilation on the inboard timer. Of course I'm not including any sneaky workarounds like measuring the EM emission spectrum.
But perhaps the question itself is obtuse. What I'm trying to ask is how is it possible to be certain that the arrow of time is constant for all material things or bodies. My premising being that all bodies must undergo change for any real measurement of time to be observed. Yet the rate at which bodies change is dependent on temperature. Even the change of translational motion of a body might be put into terms of change in temperature. I think it essentially comes down to, this: currently we say all objects move concurrently in time and may posses different temperatures (let's omit thermal gradients within bodies and conduction and thermal radian for the sake of the argument - yes, a big ask, but hard to distil the idea with all that included). Could we instead say all objects have a constant temperature but age differently. Now, I am aware that this method of analysis is possibly about as useful as suggesting that the Sun revolves around the Earth (for which there exists a complicated relationship) as compared to the Earth about the Sun (which is a far more simple and conventional). But I wish to ask if this could be the case: could time be temperature dependent?

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harrylin

I suppose that you mean if proper time rate is constant. That rate is determined relative to a co-moving clock. Thus another way to put it, is asking if the indications of two co-moving "perfect" time keepers, of which one is a reference clock, have a constant ratio independent of the velocity, all other parameters kept constant (ceteris paribus). That is indeed what SR postulates.
That doesn't make any sense to me; we can measure the temperature of objects, and temperature and time are defined very differently.
Also, take a light clock:
- http://simple.wikipedia.org/wiki/Lig.../Time_dilation
- http://en.wikipedia.org/wiki/Time_dilation
What is its temperature?
No, good clocks are compensated for temperature. We can measure their temperature and correct for the effect of higher or lower temperature on clock rate. Typically reference clocks are kept at constant temperature.

qbit

Apologies for the very delayed reply, harrylin. I've been in hospital. However, I have had a good opportunity to rethink and restate the problem.

For time to transpire, there must be change. Alternatively, we could assume that a system is frozen and time marches on anyway. But note that this is a layer of abstraction. It assumes 'external time'*.
Take a system, A, in a state of change. Consider that for this system, without our abstract idea of external time, internally, no time transpires. There must be a second system in a state of change, B, to which A can be compared for the passage of time to be meaningful. This makes more sense when A is an observer system and B is any given system in a state of change. Let's take the relative motion of the boundaries confining A and B to be zero. Note that A must be a system in a state of change to process the information that B is in a state of change. As an aside, one can deduce that A can not observe a rate of change greater than itself.
Now if one considers the above cogent, I also ask that one consider the following. Take the boundaries containing A and B to be relatively stationary. The greatest rate of change allowable is the speed of light in a vacuum, c. If system A's internal particle(s) move at c compared to system B's particles, then there is no greater rate of change and time progresses as fast as physically possible for A. A is as 'hot' a physically possible and B is absolute zero, classically speaking. If B had observer status, the same can't be said to be true from B's perspective. B is frozen both thermodynamically and in the subjective time discussed above.
Please note that the relative motion and hence time dilation of the particles in A and B has not been mentioned thus far. It is apparent that the situation is symmetrical between the particle(s) in A and B. Their reference frames are moving at c relative to each other and any clocks on board A particles would appear frozen from the 'observation deck' of B particles as the situation is symmetrical.
My question then becomes, how to reconcile these two notions of time?

Just a note about the boundaries containing A and B. I would like to suggest that not only do they not need to be physical containers, but they need not be considered as reference frames either.

* I cannot understate the importance of the assumption of 'external time'. Nearly everyone I speak to about it struggles with accepting that it is an assumption and not a fundamental fact about our universe. I'm trying to recall who could corroborate this and John Barrow comes to mind but I can't seem to find where I read it.

PeterDonis

qbit, you appear to be jumbling together a number of different concepts, and I don't think it's helping. I would advise stepping back and taking things slower.

What does "frozen" mean? Does it just mean that an object stays in the same place all the time?

Try thinking of things in spacetime, rather than "change" in "time". In other words, there is a 4-dimensional arena, time + 3 space dimensions, and every object is just a curve in this 4-dimensional arena, the object's worldline. If an object is at rest in the particular reference frame we're using, it's worldline is just a "vertical" line--its x, y, z coordinates stay the same for all values of t. Is that what you mean by "frozen"? Or do you mean something else? If so, can you describe what you mean in terms of what a "frozen" object's worldline looks like? If you can't, then you should consider the possibliity that your idea of "frozen" is not well defined.

If we draw A's worldline in spacetime, we don't need a second object, B, to determine how "time passes" for A. We just compute the proper time along A's worldline. In other words, in relativity, we *assume* that every object carries its own "internal clock" along with it, and the time elapsed on this clock is given by the proper time calculated from the metric along the object's worldline.

If we go down to the quantum level, any object is made of quantum particles that have frequencies associated with them, so the assumption that every object carries its own internal clock seems to be well justified. So basically *every* object is a "system in a state of change".

Now you're talking about extended objects or systems, which wouldn't be described by just a single worldline in spacetime; each one would correspond to a whole *region* of spacetime, with a boundary between the two regions. (Btw, I'm confused by the fact that later on you say the boundaries don't need to be physical containers or reference frames. How do you know where the boundaries are?) Talking about extended objects brings in a whole new set of complications, which to me seems premature when you haven't even got the basics of pointlike objects down yet.

Now you are confusing "speed" with "rate of change"; "rate of change" as you have been using the term means something different. Let me try to describe the sort of scenario I think you are talking about, but in what seem to me to be correct relativistic terms.

Suppose I construct a "clock" consisting of a beam of light bouncing between two mirrors that are at rest relative to each other. (This is called a "light clock" and is often used in relativity thought experiments.) I designate one mirror as the "home" mirror; and a "tick" of the clock occurs each time the light beam reflects off the "home" mirror. The light clock can then measure "rates of change" in terms of "ticks"--how many "ticks" elapse between any pair of events of interest.

It is easy to show that each "tick" of the clock takes up the same amount of proper time of the mirrors, regardless of the speed of the clock relative to us observing its motion. In other words, "rate of change" relative to the light clock is *different* from "speed" as in "speed of the light clock".

Also, of course, I can *change* how much proper time of the mirrors elapses for each "tick" of the light clock by simply changing the distance between the mirrors. So even though the clock uses a light beam, which always travels at the same speed, its "tick rate" can be adjusted to whatever we want. So "rate of change" relative to the light clock is also different from "speed" as in "speed of the particle used inside the clock".

They can't unless A's "particles" are photons; but the concept of "passage of time" doesn't make sense to begin with for photons. Nor does the notion of "reference frame" make sense for photons; you can't have a reference frame in which a photon, or any other object moving at c, is "at rest".

No, it doesn't--see above.

Now you're confusing "rate of change" with average energy per particle, which is what "temperature" is. This is another set of complications that I don't think is helpful at this point. For one thing, there is no "maximum possible temperature"--the average energy per particle can increase without bound. If the object is made of particles with nonzero rest mass, their average velocity will approach c more and more closely but never reach it as the temperature increases without bound. (If the "object" is made of photons, such as a "photon gas", the average energy per photon, or temperature of the photon gas, can also increase without bound, even though photons always move at c; the photons' frequency increases without bound while their speed stays the same.)

Two "reference frames" can't move at c relative to each other. See above.

qbit

PeterDonis,

Thank you for such a detailed reply. I am familiar with the coordinate system used in physics and have read the textbooks. Your comments are an accurate reproduction of what I have learnt from these books. But judging from your comments, my post has completely failed to convey the central tenet of the problem.
Essentially what I'm asking is 1. that we put aside our conventional physics looking glass for a minute and agree on what are observable facts and 2. pick up the conventional model again and compare it with what we found. Putting aside what I'm calling the Conventional Model, which is the Standard Model and the Classic Model (which includes relativity), is difficult because they are, to misquote, “unreasonably effective” in describing our universe (no, I haven't read Eugene Wigner's book yet).
Let's take another look at the first step. A 4D coordinate system is an artefact. The is no Cosmic Sign post pointing out three spatial dimensions and there is no Cosmic Clock marking out time. It doesn't exist in reality. Humans invented it to help explain and describe our universe. It has done an exceptional job of doing so, but there must be limits to what it can explain and describe. I am curious to know the descriptive limits. In order to explore an aspect of this, we need to appreciate that for time to progress, stuff must change. If it does not (zero point energy excluded) no time could be said to elapse. This is what I mean by frozen. This about it for a minute and we can see why we also need to consider the state of the observer.
Classical physics, Newtonian and Relativistic, both treat time as another dimension with the latter describing (accurately) interdependencies between space and time. Relativity was built upon Newtonian physics, where time is like a line and 'now' is a point on it. Material objects change physically and chemically in a causal manner and the faster they do so the greater their rate of change. Time in this model is independent and fundamental to the universe. This is the Cosmic Clock. So for instance, this gave rise to the convention that (leaving vectors aside) a change in distance divided by a change in time equals speed: s = d/t (I've omitted the delta symbols).
But what if speed (or if we're insisting on a vector, velocity) were defined as s = t/d ? I'm not being flippant here. I've tried to devise thought experiments (read first post in this thread and the post you responded to) where an observer could not tell the difference. I'm asking, what would happen if you now process this with Special Relativity? Can Relativity decide if t/d is really different to d/t? Is it simply convention? I'm not challenging Relativity here: I'm expecting distances to contract and time to dilate. These are observable phenomena.
I apologise for my last post. I should have been more descriptive with system A and B and used massive particles with relative speeds close to c. I could have used photons but then I suppose I'd also need to also describe the medium which slowed B's photons to a stand still. This would appear to A as 'frozen'. Think I need to post an illustration.

harrylin

Please specify precisely:
s =
t =
d =

qbit

harrylin,

s = speed in metres per second (or seconds per metre is my conjecture)
t = time in seconds
d = distance in metres (scalar - direction not specified or needed here)

qbit

I've had another think about the problem and I think I have a scenario that is much clearer. I also have a result that might be of interest.

Imagine we're in a cinema watching a short film where a ball rolls from left to right across a surface marked with a metre. The ball takes half of one second to cover this metre. Conventionally, we would calculate that the ball's speed as 1.0m / 0.5s or two metres per second (2m/s) in the film. But it's not wrong to say that the ball took 0.5s / 1.0m = 0.5s/m. However, not only is it unconventional, it's weird to think of things changing their time per unit distance. It's a bit like saying there is only a standard distance and each object in motion has its own time.

After this short film, the projectionist greets you, apologises and explains, "I had the film showing at twice the speed it should have been shown. In reality, that ball was filmed moving at one metre per second." We could not have known this by just watching the film. It's entirely possible that balls can be filmed at 2m/s. But on reshowing, we see the ball taking one second to move over the very same one one metre. We could say 1s/m and that description would not be incorrect. In terms of movement, speed, velocity or Rate it makes no difference. What I've tried to demonstrate in previous posts is that Rate is more fundamental than distance or time (!).

Just to get a little more familiar with this, some other common values such as the speed of sound: 340m/s becomes 0.00294s/m and light in a vacuum: 2.998x10E8m/s becomes 3.336x10E-9s/m.
As we can see, very high speeds approach zero. Now something interesting happens if we examine an instantaneous event where time taken = 0. Conventionally, any distance divided by zero is mathematically undefined (d/0 = nd). Using the unconventional notation, we have zero divided by some distance which gives us zero (0/d = 0). And zero, is a number!

So what? Well, maybe phenomena such as quantum entanglement where the collapse of the superposition of one particle to a certain state dictates that the second, entangled particle collapses instantaneously, might be better described by a number rather than a 'not defined'. I really don't know. Would someone like to share their understanding of this?

As for Relativity, I'm going to take a guess at my own question and say that it doesn't dictate which way around we should measure speed: d/t or t/d. The theory itself brings into question what is meant by 'now' anyway. But, as I said, I'm guess and not smart enough to do the math. Can anyone help?

Thanks.

PeterDonis

qbit, I've read your posts #10 and #13 and I'm having real trouble figuring out what specific question or questions you are really asking. Your posts seem to be a jumble of various thoughts but there's nothing there I can really grab onto. I would recommend, as I said before, stepping back and taking things slower. Try to find one specific question about one specific thing, and frame it in a way that, as you say, focuses on observable quantities instead of coordinates or abstractions (a focus with which I agree).

PeterDonis

qbit, in addition to the general comments in my last post, I do have some specific comments on posts #10 and #13:

Can you give an actual example? You said you want to focus on observables; every object we've actually observed changes. We've never observed anything that doesn't change.

I'm not sure this is an accurate description of relativity, unless you restrict attention solely to a single object and its worldline. As soon as you have multiple objects in relative motion, there is no single "universal time" that applies to all of them. That's a key difference between Newtonian physics and relativity.

I don't see the point of this entire thread of thought; it looks to me like you're changing the numbers describing observable quantities, without changing the relationships between the observable quantities themselves at all.

You could if the film had time stamps in it as well as the "distance stamp" provided by the meter stick. Most camcorders nowadays will do that for you automatically. All you're really showing here is that any measurement of distance or time must involve a comparison between some "standard length" or "standard time interval" and the length or time interval you're interested in. Which is true, but hardly sensational.

In relativity, yes, you can view things this way. In fact, since the speed of light provides a universal standard for "rate", and nothing can go faster than light, you can view "speed" as a pure number between 0 and 1. (Which makes it clear why we normally use distance/time and not time/distance--the latter would make "rate" a number from 1 to infinity, much more difficult to deal with, at least for most purposes--I suppose one could contrive a scenario where it would be easier.) But of course "speed" defined this way is frame-dependent, just as distances and times are, so it's still not the best thing to focus on.

This is a separate question and should probably be posted in the quantum mechanics forum rather than here.

qbit

PeterDonis,

Thanks again for replying. Your comments make clear that nothing I have posted makes any sense. And yes, I admit...

...that I have struggled with formulating the question. Your comment:

...is accurate. A time/distance relationship has no conceptual advantage. The more I think about it the more ridiculous it is. I really should have stuck to the adage, "Think it through before posting." I'm not sure it's a prolonged lapse of reason or just stupidity. I'm glad 'qbit' is not my real name.

Proton decay? No one has observed a proton decay. It may stay unchanged indefinitely. But that has no use here.

Thanks again for your time.

PeterDonis

It may stay a proton indefinitely, but that doesn't mean it's "unchanged". All sorts of things about the proton may be changing. Even if it's just sitting inside an atomic nucleus, its quantum wave function is changing.