# Is it possible to create a universal calendar/clock?

1. May 13, 2014

### Fiziqs

While contemplating the twin paradox the thought occured to me that every observer should see the universe as being the same size, and the same age. If we consider a set of twins in which one twin flies off in a spaceship at near light speed, and then returns some time later, the two brothers will have aged differently. But if upon returning the brothers should run an experiment to estimate the size and age of the universe the results for each of them should be identical. In other words the size and age of the universe should be the same for both brothers, no matter what the differences in their ages may be. Even if the difference is a billion years. Indeed if we send out a hundred spaceships at different speeds, upon returning they should all agree upon the size and age of the universe. Thus shouldn't the size and age of the universe be the same for all observers?

If this weren't true then two observers standing side by side could see the universe as being of two different sizes, and two different ages. Which should be impossible. But if all observers see the universe as being the same age, then shouldn't we be able to set up a universal calendar upon which every observer could agree? In which case one twin when departing in his spaceship could tell his brother that he would be back on such and such a date, and they would be in complete agreement as to when that date is, simply by using the universe as a calendar. They may not know what age they would personally be on that date, but they would agree on when that date is.

Do all observers see the universe as being the same size, and the same age? And can't this fact be used to create a universal calendar/clock?

2. May 13, 2014

### haael

The age of the Universe does depend on the observer. Some observers can see the Universe 13 billions years old, some other only 1 second old. It depends on their velocity.

Paradoxically, the "size" of the Universe does not depend on the observer. By the "size" I mean the distance to the cosmological horizon. The horizon is always at the distance that light passed since the beginning of the Universe and the speed of light doesn't depend on velocity, so it always has the shape of the sphere.

However, you can define a universal calendar in our particular Universe. It is thanks to the fact that our Universe has finite temperature. There is such an inertial frame that the sum of momenta of all particles in the visible Universe is zero. Moreover, it will always be so, according to current theories. It will never happen that some region with a nonzero net momentum surfaces from the cosmological horizon. This is called Universe homogenity and it is an observational fact. It hasn't happened since 13 billion years, so current theories hold that it will never happen. If it should happen, our calendar will loose its universality.
That said, when there is a frame where the Universe has zero net momentum, we can define the universal calendar relative to that frame. This is the frame where the best known age of the Universe is reported. All observers agree on that frame and can easily determine it based on astronomical observations.

3. May 13, 2014

### ghwellsjr

I'm having a hard time trying to figure out what the twin paradox has to do with the age/size of the universe.

Presumably, if one person performed an experiment to determine the age/size of the universe a hundred times and he always got the same answer, then a hundred people colocated with that first person performing the same experiment should all get the same answer, assuming that the experiment is performed quickly enough that the time to do the experiment is negligible compared to the age of the universe.

So if they all perform the experiment before any of them take their high-speed round trips, they will agree on the age/size of the universe, correct? Then each one plans a different high-speed trip but they all can determine ahead of time exactly how much time will have progressed for the universe or for a person that stayed behind, so they add that to the time that the age of the universe will increase when the each individually repeat the experiment upon returning.

Are you thinking that because a traveling twin comes back at a younger age than the stay-at-home twin, he thinks the stay-at-home twin should be the same age as he is?

4. May 13, 2014

### Staff: Mentor

You are asking whether if you measure the size and age of the universe, and I measure the size and age of the universe at the same time, we will get the same answer. But how are we to determine whether we're making our measurements at the same time?

It's easy if we're both at the same position and at rest relative to one another. That's how the departing twin can, before his departure, say that he'll be back on a given date and then do exactly that. But this isn't constructing a universal calendar in the sense that you mean; it's just an agreement to use the stay-at-home twin's frame. A distant observer moving relative to stay-at-home can measure the age and size of the universe - but how is he to decide which measurement was the one that he made at the same time that the traveller left/returned? If he doesn't know this, then his measurements aren't telling him anything about when either of these events happened.

No, because it isn't a fact. The best we can do is for each observer to create their own calendar/clock based on the state of the universe that they observe. There's no unique way of connecting the dates/times provided by the different calendars.

5. May 13, 2014

### epovo

I am trying to rephrase the question with the OP's permission :)
Suppose that we had the technology to measure the age of the universe very accurately. So, if we measured the age of the universe 1 year ago and we got T, then measuring today would give us T + 1 year. So, our two twins (while both are still living on earth), take their measurement on the age of the universe and get T. Then our travelling twin does what he usually does (going for a very fast round trip). According to his clock only one year has elapsed when he's back, so he deduces that the age of the universe should now be T+1. His stay at home twin as aged 10 years, so he reckons the universe must now be T+10. So they decide to measure the age of the universe again. Who wins?

6. May 13, 2014

### Staff: Mentor

The age of the universe is essentially a parameter in the lambda CDM metric which is set by observation. That parameter increases at the same rate as proper time only for an observer which is at rest relative to the CMB radiation. For all other observers it increases faster than proper time.

7. May 13, 2014

### epovo

Yes, that's what I thought. Thank you Dalespam.

8. May 13, 2014

### Fiziqs

The twins paradox applies because it led me to realize that every observer sees the universe as being the same age and size regardless of their past or current motions. And it illustrates the problem quite well.

I don't know the best way of measuring the age of the universe, so let's just say that we use the background temperature as our gauge for the age of the universe. Our universal clocks would really be just universal thermometers. Given a sufficiently standardized methodology for taking that temperature, every observers' thermometer should give the same reading.

If one twin takes off in his spaceship at near light speed, and then returns at some later date, they may not agree on how much time has passed, but they will agree on the current temperature/age of the universe. Both before leaving, and upon returning, the twins' temperature readings for the universe should be the same. The same would be true at any point during the traveling twin's trip. Their readings as to the temperature of the universe will always be the same, and they can use that temperature as a calendar.

The same would be true for all observers, everywhere. The temperature of the universe tells them how "long" it has been since the big bang. Thus the universe has a built in calendar/clock.

Last edited: May 13, 2014
9. May 13, 2014

### Staff: Mentor

It tells you how long it has been for the observer (or collection of observers who are at rest relative to one another) making the measurement.

That's a fine clock for that observer, but no one has ever suggested that there is any problem with doing that. Pick any interesting event, whether it's the big bang or the tragic encounter between a mouse and my neighbor's cat this morning, and watch any time-dependent phenomenon, whether it's the cooling of the universe or the cooling of the mouse's corpse, and you have a built-in calendar/clock.

However, both of these "clocks" (and any other imaginable clock) share the same weakness. If I use this clock to assign a time to some event distant from me, and you use this clock to assign a time to that event, and you are moving relative to me... We will assign different times. You have a fine useful clock, and I have a fine useful clock, but we don't have a sharable synchronized clock, which is what I think you meant by "universal".

10. May 13, 2014

### ghwellsjr

No it doesn't. In order for multiple observers to agree on time, they have to be colocated. That's what I said in my first post. But observers that are mutually in motion will not agree on time. So while the twin is traveling, he will measure a different age for the universe than he did before he left. How is he to know which measurement is correct? And then if he continues traveling inertially and the other twin travels even more rapidly to catch up to him and then becomes colocated with him, and they both make the same measurement of the age of the universe, they will get the same answer but it will be different than the measurement they made before they separated.

Let's pretend that there were a bunch of clocks set to zero near the beginning of the universe and all these clocks traveled inertially at different speeds with respect to each other. Which one do we consider to be measuring the age of the universe? The one that happens to be wherever we are? Why not all the others? Just from a simple analysis using Special Relativity, we know that all those other clocks are ticking at a slower rate than "ours" according to the inertial frame in which "ours" is at rest and so we would have to say that other parts of the universe are younger than our part right now. But we would also have to say that according to the inertial reference frame of any of those other clocks, they would be older than "ours" is right now.

That's true.

That's not true or if it is true, then the measured temperature of the universe cannot be a valid measurement of its age.

You would only make statements like those if you don't understand the basics of Special Relativity.

The problem you are addressing is one of understanding the difference between Proper Time and Coordinate Time. All clocks keep track of Proper Time. The Coordinate Time of an inertial reference can be set to the Proper Time of an inertial clock at rest in that frame but the Proper Times displayed on all the other inertial clocks moving according to that frame will not agree with the Coordinate Time. There is no confusion about the differences between the Proper Times and the Coordinate Times. The problem is deciding which Coordinate Time applies to the age of the universe. If we transform to the rest frame of any one of the other clocks, the Coordinate Time for our clock right now gets larger. In other words, the age of the universe doesn't have a single answer.

That's why I ask what the problem has to do with the Twin Paradox.

11. May 13, 2014

### Fiziqs

Let's go back to our twins again, but this time let's assume that both of them are going on a trip. They agree to rendezvous back at earth at a future "universal" time. Or in other words, they agree to rendezvous back at earth when the universe reaches a specific temperature. Regardless of any other onboard clocks/calendars that they might have, their "universal temperature clocks" will allow them to know exactly "when" to be back on earth. Whether this means that it will be one week later for one twin, and ten years later for the other, doesn't matter. A clock based upon the temperature of the universe will enable them both to end up in the same place at the same "time".

As for distant events we should be able to agree upon when those events occurred as well. If I see a distant event, I should be able to estimate what the temperature of the universe was at the time the event occurred. Likewise you viewing the event from a different perspective should be able to estimate the same temperature, and thus the same moment in "universal" time. Again, you might say that the event occurred one week ago, while I may say that it occurred ten years ago, but the date that it occurred on our respective "universal" calendars should be the same.

Therefore we can maintain a coherent universal calendar, separate from our own personal calendars, that are consistent for every observer, everywhere.

12. May 13, 2014

### Fiziqs

We do appear to be talking past each other. What I am simply proposing is that we use the temperature of the universe (or some other parameter) as a universal clock. Our own personal clocks become irrelevant. We no longer refer to our own relative concepts of time, but refer instead to a universal concept of time based upon a gauge common to everyone, the temperature of the universe. We could then refer to any specific universal date as corresponding to a specific temperature.

The time that your clock measures becomes irrelevant. The universe becomes the clock and it is the same for every observer. Every observer, everywhere, will agree as to the current temperature of the universe. Thus we all agree as to what the universal date is, making the universe a "universal" calendar.

13. May 13, 2014

### Staff: Mentor

Sure, there is nothing wrong with adopting such a convention. As I said before, the age of the universe is essentially a parameter in the lambda CDM metric which is set by observation. That parameter increases at the same rate as proper time only for an observer which is at rest relative to the CMB radiation, but there is no reason that you couldn't adopt the convention to use that coordinate time for other observers also.

14. May 13, 2014

### ghwellsjr

Let's stipulate that each observer's observation of the age of the universe based on temperature matches the Proper Time on an inertial clock that has elapsed since about the beginning of the universe and colocated with that observer. Is that something we can agree on?

Maybe some spacetime diagrams will help to show what the problem is. Let's just consider two clocks that end up colocated with widely separated solar systems but which have been traveling away from each other at 0.6c. Let's also say that both clocks have accumulated 14 billion years, Ours is shown in blue and the distant one is shown in red:

Since we measure the age of the universe (according to our stipulation, assuming you have agreed with it) to be 14 billion years by measuring the temperature of the universe, we have to ask what an observer at the other solar system will measure at the same time. Isn't that what a universal calendar is? As you can see, he will measure 11.2 billion years.

But what if we go to his rest frame:

Now we will say that he will measure 17.5 billion years when we measure 14 billion years. Now maybe you will object that since the universe "really" is only 14 billion years old that I should not have extended the length of the other worldline out to 18 billion years, and that now for him should "really" be limited to 14 billion years. And I would rebut by saying how can you say that the other solar system even exists right now? When we look at it right now we see it at 7 billion years old as this spacetime diagram indicates:

So the issue that I am trying to get you to address is that even if the measured temperature of the universe correlates to its age, you still have to find an agreement on which reference frame to use and which Coordinate Time in that coordinate system you are going to apply to the age of the universe so that you can call it a universal calendar. I don't know what you mean by universal calendar if it doesn't yield the same answer for all observers "at the same". If you are saying that it simply yields the correct answer for all observers at different times, then I don't know why you are calling it a universal calendar.

And I still don't know what any of this has to do with the Twin Paradox.

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15. May 13, 2014

### WannabeNewton

You do realize temperature is not a Lorentz-invariant right? If I'm in the CMB mean rest frame I will write down the usual blackbody distribution for the photon gas $\eta = \frac{1}{e^{hv/T_0} - 1}$ but an observer in a frame moving relative to the CMB will write down the blackbody distribution $\eta = \frac{1}{e^{hv'/T} -1}$ where $T = \frac{\sqrt{1-v^2}}{1 - v\cos\theta}$, $\theta$ being the angle at which the observer points their telescope at the sky, measured relative to the $x$-axis of the CMB mean rest frame. So the observer ascribes to the photon gas an effective equilibrium temperature different from that in the CMB mean rest frame and in fact one that is to a good approximation a dipole distribution. It is rather $\eta$, the mean occupation number, that is a Lorentz-invariant.

So your use of temperature is about as close to a "universal" clock as the use of ideal atomic clocks i.e. it isn't close even in the slightest.

16. May 13, 2014

### ghwellsjr

Fine. No one is disagreeing with this. Which is why I keep asking what does this have to do with the Twin Paradox?

But you haven't addressed my question of what happens if the two twins take a trip and end up colocated at a different speed (and place) from where they started (according to their original mutual rest frame):
I just drew you a spacetime diagram of people on earth observing a distant event. Since the age of the universe was only 7 billion years at the time of that event and assuming we could see how an observer there measures the temperature of the universe at that time and place to yield a 7 billion year old universe, then in what sense are we talking about a universal calendar? Are you saying that different parts of the universe vary in age according to their distances from us (based on our reference frame)? That doesn't sound like "every observer should see the universe as being the same size, and the same age" as you stated in your OP.

Until you satisfactorily address my concerns, I don't see how you can come to this conclusion.

Last edited: May 13, 2014
17. May 13, 2014

### pervect

Staff Emeritus
I don't understand why you think that.

If we imagine different observers, certainly the proper time they've measured since the big bang won't be the same.

To try to be more specific, if we take two observers in the same spot at the same time, each of which is carrying a clock, and we imagine looking backwards in time, the time reading for "the big bang" on each observer's clock will be different.

18. May 14, 2014

### ghwellsjr

You mean, if the two observers have a mutual speed between them, correct?

19. May 14, 2014

### Staff: Mentor

No.
All observers who are at rest relative to one another will agree, but observers moving relative to one another will not agree.

You were able to use this "universal clock" to reunite the traveling twin with his stay-at-home twin only because you had the traveler stop at the end of his return journey, so he and stay-at-home were at rest relative to one another. If traveler had continued moving, his temperature-of-universe clock would not have agreed with stay-at-home's.

20. May 14, 2014

### pervect

Staff Emeritus
Yes, sorry, two observers moving relative to each other which happen to be in the same spot at the same time. I was also considering each observer to have no 4-acceleration (i.e. an accelerometer carried by either observer would always read zero), which implies that they were both following geodesics.