Frame of Reference & Time: Defining Time Without a Ref.

[icantevenn]

Hello,
I wish to know what is the relationship between a frame of reference and time. Specifically,without a frame of reference, what would be a hypothetical state of time. Professor Witten predicts that an ultimate physical theory will dissolve space-time as we know it. I would like to discuss how is time defined without a frame of reference.

 

[PeterDonis]

I would like to discuss how is time defined without a frame of reference.

The kind of "time" that is associated with a frame of reference (a better term would be "choice of coordinates") is more properly referred to as "coordinate time". A given coordinate chart assigns a "time" coordinate to every event in spacetime. But this assignment, of itself, has no physical meaning.

There is also "proper time", which is the time actually measured by a clock traveling along a particular worldline. This kind of time is independent of any choice of coordinates. Whenever you see an actual time measurement quoted--something like "1 year elapsed on observer A's clock between his departing from Earth and arriving at Alpha Centauri"--it is a proper time.

The distinction between proper time and coordinate time is often obfuscated by the fact that, for many problems, the most convenient choice of coordinates assigns a "time" coordinate to certain events that happens to be the same as the reading on a clock carried by a particular reference observer at those events. It's hard to be more precise unless you can give a specific scenario that illustrates whatever issue you are concerned about.

 

[icantevenn]

It's hard to be more precise unless you can give a specific scenario that illustrates whatever issue you are concerned about.

Suppose, for instance, that I wish to understand what exactly time is and wish to understand it by questioning beyond my surroundings. I imagine a space which is a vacuum, as much empty as possible. There are no objects, and for a moment I wish to remove my body's gravity from this thought experiment. What I am trying to understand is how time comes into existence.

 

[Ibix]

You can define a concept called "proper time" easily enough - it's what your watch shows. No need to define a set of coordinates (a frame of reference) or anything. The problem is that you can't generalise that to work out "what time it is over there". It only tells you what time it is where you are.

You could set up a system of measurement of time at any point based entirely off people's watches and the speeds they were travelling, as long as you filled space with people and their watches traveling in all directions. But I think that, if you do that systematically, you end up defining a frame of reference.

You can handle specific problems without reference to a coordinate system - for example the twin paradox can be resolved simply using proper time and relative velocity. I am not sure about a general definition of time. I rather suspect any definition of "now, over there" implies a choice of frame.

Edit: Must type faster...

 

[icantevenn]

But I think that, if you do that systematically, you end up defining a frame of reference.

Yes, you put it perfectly. This is what would happen in almost all explanations.
I would like to ask you, based on everything that has been discovered in physics so far, how would you answer if I ask: how time comes into existence? For instance, gravity was action at a distance for Newton, but Einstein explained its source. Has there been any physical theory about time that says something similar?
I am not a physicist so my reading is limited. Thanks

 

[PeterDonis]

any definition of "now, over there" implies a choice of frame.

Yes, it does.

 

[PeterDonis]

how time comes into existence?

Why do you think time must "come into existence"?

gravity was action at a distance for Newton, but Einstein explained its source. Has there been any physical theory about time that says something similar?

No, unless you consider relativity, which considers "time" to be just one particular aspect of spacetime, to be such a theory.

 

[icantevenn]

Why do you think time must "come into existence"?

A number of physicists have expressed ideas that suggest that time sort of comes into existence at the Big Bang

 

[Ibix]

Yes, you put it perfectly. This is what would happen in almost all explanations.
I would like to ask you, based on everything that has been discovered in physics so far, how would you answer if I ask: how time comes into existence? For instance, gravity was action at a distance for Newton, but Einstein explained its source. Has there been any physical theory about time that says something similar?
I am not a physicist so my reading is limited. Thanks

It depends what you mean. In relativity, time is a dimension just like the three spatial dimensions. The only real difference between time and the spatial dimensions is that time has the opposite sign in the metric (i.e., Pythagoras' Theorem for space-time is $\Delta s^2=\Delta x^2+\Delta y^2+\Delta z^2-(c\Delta t)^2$). That turns out to have a whole host of implications - notably that c is a speed limit for causation (which gets rid of all the "simultaneous causality" problems), and our very different experience of time versus space.

But, why four dimensions, not three or five? And why only one time-like dimension? As far as I'm aware we don't have a definitive answer to questions like this. I think that physicists largely assume that a future theory of quantum gravity will provide some kind of an explanation, but we're still working on that one.

 

[PeterDonis]

A number of physicists have expressed ideas that suggest that time sort of comes into existence at the Big Bang

Pop science articles, which is where I strongly suspect you read these ideas, are not science, and are not appropriate sources for discussion on PF. If you can find something in the peer-reviewed literature that discusses this idea, that would be within bounds.

 

[Ibix]

A number of physicists have expressed ideas that suggest that time sort of comes into existence at the Big Bang

Time is a part of space-time, which came into existence at the Big Bang as far as we're aware. What happens "outside the universe" or "before the universe" isn't something we have the tools to discuss, even assuming the concept makes any sense at all.

Edit: In fact, the Big Bang itself is a singularity, which means that relativity doesn't describe it - only shrugs its shoulders and says "you need a better theory to discuss what happens then". So it's another thing that we don't have an answer to.

 

[icantevenn]

It depends what you mean. In relativity, time is a dimension just like the three spatial dimensions. The only real difference between time and the spatial dimensions is that time has the opposite sign in the metric (i.e., Pythagoras' Theorem for space-time is $\Delta s^2=\Delta x^2+\Delta y^2+\Delta z^2-(c\Delta t)^2$). That turns out to have a whole host of implications - notably that c is a speed limit for causation (which gets rid of all the "simultaneous causality" problems), and our very different experience of time versus space.

But, why four dimensions, not three or five? And why only one time-like dimension? As far as I'm aware we don't have a definitive answer to questions like this. I think that physicists largely assume that a future theory of quantum gravity will provide some kind of an explanation, but we're still working on that one.

Thank you so much. This was very helpful.