# The relativity of time and defining the age of the universe

1. Dec 7, 2011

### smotpoker

The relativity of time and defining the "age" of the universe

I have been doing searches on the relativity of time and its relation to the "age of the universe," among other things. I have come across some insightful Q&A, but I have yet to really see a "solid" response to my innate question (or questions, as it were). I apologize if one has been given on another post; I am new here and haven't had the "time" (pun) to look thru them all yet. So, here are my questions for anyone who might be able to shed some light:

1) From what I have learned/read/seen, time is relative. The passage of time for observer A who is travelling at speed D within space-time (say someone on Earth travelling around the Sun) is different than the passage of time for observer B who is, say, travelling in a spacecraft at 99% the speed of light (.99c, I'll call it D1) within space-time. In essence, the passage of time for A from the perspective of B is faster, while the passage of time for B from the perspective of A is slower; the person travelling really fast (B) seems to be moving through time slower than the person just sitting on Earth (A) from A's perspective, and the other way around. However, the passage of time for each of them with respect to themselves ("personal time"?) seems normal from their own frame of reference (not compared to each other's frame of reference).

If I am correct in my explanation here (which I certainly may not be), then my question is this: how can we assign an age to the universe, e.g. how can we say the Big Bang happened so and so many years ago?

If the passage of time is relative based on the speed through which you travel through space-time, then how can we even contemplate assigning an age to the "beginning" of it? It would seem to me that it's an arbitrary point; our assignment of the age would be based only on our tiny little perspective (frame of reference) as forced on us by our being on Earth. Maybe I can explain my question better with a hypothetical situation building off my first example.

Let's say observer A from above is the same - a person on Earth right now. But now let's say observer B is a person who is still travelling at 99% the speed of light, but they started travelling at that speed 1 second after the Big Bang and have been ever since (throw out biology). Now, right away I see that my question is in and of itself a paradox because I am assigning a time value (1 second) to a question about time, but let's avoid that for now. Would it not mean that the "age" of the universe to B, were he to stop suddenly and land on Earth right now, be much lower than the 13.7 billion years that A seems to think has elapsed since the Big Bang? Wouldn't he have perceived that passage of time to be like maybe only 1 billion years since his passage of time is slower relative to ours since he was moving much faster?

I just can't get my head around that concept. And that leads to my second question.

2) I have read that interstellar space travel is possible based solely on the relativity of time (not using "warps" or "wormholes" or anything like that) because if you could travel close to the speed of light, you could traverse say, 40 light years, in like maybe 1 year. Is that true? Again, I just can't get my head around it. Is that because the "40 light years" we assign as a distance to another star system is relative since it is based on a unit of time, and even though light does technically take 40 of "our" years to reach us from there, if we were travelling on the light beam, the passage of time from our new perspective would be much smaller? In essence, if we could travel on a beam of light, would we be able to pretty much go anywhere a limitless amount of times because, from our perspective on the light beam, time essentially slowed to a halt?

Sorry if these questions got too convoluted or in-depth; I have just been doing a lot of research lately and my brain is fumbling for some semblance of an explanation to things I'm having trouble grasping.

Thanks.

2. Dec 7, 2011

### lalbatros

Re: The relativity of time and defining the "age" of the universe

Have a look at this wiki page about comoving distance.
There is also a definition for comoving time:

Relativity is about the possibility to use any system of coordinates to describe the laws of physics. However, when communicating about time we need to agree on a common system of coordinate. The comoving time and distance system of coordinate is clearly defined and easy to understand. We can easily imagine a co-moving clock.

Of course, "practically" no real clock could be able to survive from the big bang till now!
Or is that true?
After all, the universe itself is a clock.

3. Dec 7, 2011

### Matterwave

Re: The relativity of time and defining the "age" of the universe

To add to the above response, a "comoving" object is simply an object which sees the universe as isotropic, i.e. an object which "free falls" according to the overall expansion of the universe and has no "peculiar velocity" due to other forces (including gravity of local objects). We sometimes also call these objects "substratum particles". The geodesics of the set of all possible such objects fill the space-time manifold (our universe) and are orthogonal to a set of Cauchy surfaces which foilate the space-time manifold. Thus, we can use the proper time along these geodesics as a "global time coordinate", and it is this time with respect to which we make such statements as "the age of the universe is XXX years".

Of course this proper-time would be infinite if the Universe did not begin in a singularity. We cannot extend our geodesics past some previous proper time (~13.7 billion years before today) and therefore we call our space-time "geodesically incomplete", and know that a singularity existed at the big-bang.

4. Dec 7, 2011

### PatrickPowers

Re: The relativity of time and defining the "age" of the universe

Yes that is true. The more energy you put into accelerating a clock towards a star, the sooner the clock arrives there. Twice as much energy, half the time. There is no limit to this.

The way this works is that if you shot the clock out of a cannon that suddenly accelerated it to .99c relative to the star then the star suddenly seems much closer as far as the clock is concerned. Everything tells it that the star is 1/7th as far away as it was before the cannon fire, and the journey time it measures is 1% more than that. Strange!

As to "why," this is what has to happen so that the laws of physics compatible with a finite speed of light. (This is sort of a tautology: if an equation does not survive these weird "distortions" then it isn't a law of physics.) This is a good thing, since our bodies rely on the laws of physics for proper operation, so it is nice that they always apply.

And yes the proper time of a beam of light is always zero. Light does not age, so we can see things from 13 billion years ago. As to what if anything "time" means to a photon, that we don't know. The photons haven't told us.

5. Dec 7, 2011

### PatrickPowers

Re: The relativity of time and defining the "age" of the universe

Yes that is true. The more energy you put into accelerating a clock towards a star, the sooner the clock arrives there. Twice as much energy, half the time. There is no limit to this.

The way this works is that if you shot the clock out of a cannon that suddenly accelerated it to .99c relative to the star then the star suddenly seems much closer as far as the clock is concerned. Everything tells it that the star is 1/7th as far away as it was before the cannon fire, and the journey time it measures is 1% more than that. Strange!

As to "why," this is what has to happen so that the laws of physics are compatible with a finite speed of light. (This is sort of a tautology: if an equation does not survive these weird "distortions" then it isn't a law of physics.) This is a good thing, since our bodies rely on the laws of physics for proper operation, so it is nice that they always apply.

And yes the proper time of a beam of light is always zero. Light does not age, so we can see things from 13 billion years ago. As to what if anything "time" means to a photon, that we don't know. The photons haven't told us.

Last edited: Dec 7, 2011
6. Dec 7, 2011

### Elroch

Re: The relativity of time and defining the "age" of the universe

An interesting point has just occurred to me about the definition of the age of the Universe. The correct point was made that different observers that have been around since the start of the Universe would be different ages because of their different motion and exposure to gravitational time dilation. While it is true that there is a common time for co-moving observers, this is a rather rough definition, as the distribution and movement of galaxies has a lot of randomness.

But there may be a unique definition from the physics. There are many paths from the big bang to any space-time point in the Universe. Each of these paths has a different proper time. The maximum of these proper times seems a good definition of the age of the Universe at a point.