Is time continuous?

[athon]

Time is indeed discontinous. There are several discrete 'breaks' in time, one occuring in 1998, called the Tequila break, another in 2001 called the Port break, and in recent years one occured in 2005 caused by scotch I believe.

Scientists are baffled by this. One break included the loss of a shoe which is also unaccounted for.

Athon

 

[Deetee]

Interesting concepts, but unfortunately much of it is beyond my comprehension.
I'm still stuck in Zeno territory, I'm afraid.

 

[Cuddles]

Good question for someone who knows more than me to answer. But although the universe seems to be expanding, it seems to be expanding from some point rather than all parts equally expanding away from each other. To build on another poster's example, I have a chair 2 meters away from me. 1 minute later, it's still 2 meters away from me. It's not moving away from me at the speed of light, although my understanding is that the edges of the universe themselves are expanding at that speed. But we seem to have local distance stability -I don't see the need for stretching or new Planck spaces coming into existance as necessary to explain things. Maybe at the edges of the universe it's required? Or maybe those are pre-existing Planck spaces that the universe is expanding to fill?

I don't know -I'm sure mostly because of my weaknesses on first principles regarding this question. It's a fun question to think about though.

I'm afraid it's actually exactly the other way around. The universe is not expanding away from a single point, every point in the universe is moving away from every other point. The apparent velocity increases with distance because it is due to the expansion of space itself. For example, two points a metre apart hardly move at all, while two points 100 metres apart move 100 times as fast. There is no edge to the universe, and there cannot be Planck lengths outside the universe because there is no such thing as outside. If there was anything there for it to expand into then that thing would be part of the universe and therefore it wouldn't be expanding into after all.

The question of whether the universe is stretching or increasing in number of quanta is a very interesting one, but I'm not sure it actually makes sense. The problem is that you (a generic you, not you specifically) are basically thinking of the universe as made up of lots of little cubes with sides the Planck length which allow particles to exist at their centre. The question is then whether the universe expands by stretching these cubes or making more of them. The problem is that these cubes (probably) don't exist, in the same way that a metre doesn't exist. You can measure the distance between points as a metre, but that does not mean that there are lots of disembodied metres floating around waiting to be measured. The metre only exists as a relationship between points, and so does the Planck length. Take the points away and the length no longer exists.

On the other hand, there may be a way to answer the question. The Planck length is derived from a variety of other constants. Over the short timescale we have observed, these constants appear to be constant. If this is truly the case then the Placnk length must remain exactly the same and therefore the universe must expand by adding extra cubes, or at least it would if the cubes actually existed. Recently however, there have been many questions raised that suggest some constants, such as the speed of light or the stregth of gravity, have changed over time. If this is the case then it is possible (although still not guaranteed, depending on how they have changed) for the universe to expand simply be the non-existent cubes increasing in size. Essentially, the universe would still have exactly the same volume, but it would be bigger.

 

[Just thinking]

I'm afraid it's actually exactly the other way around. The universe is not expanding away from a single point, every point in the universe is moving away from every other point. The apparent velocity increases with distance because it is due to the expansion of space itself. For example, two points a metre apart hardly move at all, while two points 100 metres apart move 100 times as fast. There is no edge to the universe, and there cannot be Planck lengths outside the universe because there is no such thing as outside. If there was anything there for it to expand into then that thing would be part of the universe and therefore it wouldn't be expanding into after all.

This brings up (to me at least) another thought ... aside from the quanta of space itself, which I appreciate your response to. Looking at the expansion of space using the surface of a balloon analogy, one can see that it is possible for two points on that surface to experience their rate of separation just at the speed of light, making anything farther away on that surface outside of their universe -- beyond the cosmic horizon, so to speak. But it's still on the surface of the balloon. Would that make these two points still in the same universe? If you say no, let me offer this ... Imagine 3 galaxies; A, B and C. Galaxy B is just within the cosmic horizons of A and C -- place it between them, if you will -- but A and C are too far away from each other to still be receding at less than the speed of light. Now, those in galaxy B see the other two galaxies as being in their universe; in fact they place all three galaxies in the same universe. But those in galaxy A or C see the other as being beyond their cosmic horizon, or not in their universe -- in fact, they cannot even know of the other's existence. But those in galaxy B know they're there for sure.

 

[Just thinking]

Interesting concepts, but unfortunately much of it is beyond my comprehension.
I'm still stuck in Zeno territory, I'm afraid.

Zeno was no idiot ... he had great intuition.

 

[Cuddles]

This brings up (to me at least) another thought ... aside from the quanta of space itself, which I appreciate your response to. Looking at the expansion of space using the surface of a balloon analogy, one can see that it is possible for two points on that surface to experience their rate of separation just at the speed of light, making anything farther away on that surface outside of their universe -- beyond the cosmic horizon, so to speak. But it's still on the surface of the balloon. Would that make these two points still in the same universe? If you say no, let me offer this ... Imagine 3 galaxies; A, B and C. Galaxy B is just within the cosmic horizons of A and C -- place it between them, if you will -- but A and C are too far away from each other to still be receding at less than the speed of light. Now, those in galaxy B see the other two galaxies as being in their universe; in fact they place all three galaxies in the same universe. But those in galaxy A or C see the other as being beyond their cosmic horizon, or not in their universe -- in fact, they cannot even know of the other's existence. But those in galaxy B know they're there for sure.

Now this is one of the big questions about inflation. Essentially, theories about inflation say that in the very first few moments after the big bang the universe expanded massively faster than it is now. This has the effect of smoothing out any fluctuations that should have existed after the big bang, since those fluctuations will now be bigger than the observable universe and everything we can observe will not be affected by them.

Unfortunately this then brings up the problem of what happened to the rest of the universe. This question is essentially unanswerable because it is impossible for us to see outside the universal horizon so we can't see what it is like. One way to think of it is with analogy to heat transfer along a metal bar. What happens when you heat up one end? Obviously, you don't immediately feel anything at the other end. If the bar is expanding as fast, or faster, than the speed of sound in the metal, the other end will never heat up.

It is the same with the universe. It is not so much a question of knowing something is there, but being able to communicate with it. You can think of the universe as being in thermal equilibrium. Every part has had a chance to emit and recieve radiation from other parts, so the whole thing is more or less homogenous, in the same way that a short metal bar will all be the same temperature if you heat one part of it. However, parts of the universe that are further away cannot be in equilibrium because there has not been time for them to recieve any energy, or to send it to us. This is the same as a metal bar that is a different temperature at each end. A point in the middle of the bar can "see" both ends, but it is still at a different tempertaure from both of them. In the same way, galaxy A and C can sensibly be said to be in different universes, even though galaxy B can see both of them.

The main problem, as I said earlier, is that we simply can't answer this sort of question because of it's very nature. If we could see what was happening to be able to answer it then we wouldn't need to ask in the first place. There are actually various different theories about it. Some people say that each seperate area is a different universe that may follow different physical laws. Others say that there is only one universe and that, because of an argument similar to yours, the laws of physics can't differ that much and the only differences possible between various parts are things like temperature and matter/anti-matter ratios.

To summarise, it's all very interesting to think about but we actually have no idea what the answer is. Yet.

Edit : Just for the record, I personally favour the "all one universe" hypothesis. Mainly just because it sounds more sensible, but also because I haven't really heard a good explanation for how the laws of physics would have fluctuated in the early universe, rather than just things like density, temperature and particle composistion. Given that we know for sure these things can vary but we have no evidence that the laws of physics can, Occam's razor does the rest.

 

[davidsmith73]

Planck length and Planck time are the shortest intervals of space and time possible.

I'm confused. Would you say this reflects the limitation in measurement and mathematical models or reflects an objective truth about the physical world?

 

[Cuddles]

I'm confused. Would you say this reflects the limitation in measurement and mathematical models or reflects an objective truth about the physical world?

This is answered in Ziggurat's post #8. It depends quite a lot on your interpretation. Basically, either they are the absolute fundmental limits on the physical world, or they are the scale at which none of our theories can even pretend to say anything about. In either case, anything that happens below the Planck scale is irrelevant to the larger universe. However, if the latter is true then it is possible that the apparent randomness of quantum physics could be explained by sub-Planck effects.

Edit : Just to confirm, none of this has anything to do with measurement limitations, it is either all about the maths or all about the real world. Even having perfect accuracy in measurements would not make any difference.

 

[Just thinking]

... It is the same with the universe. It is not so much a question of knowing something is there, but being able to communicate with it. You can think of the universe as being in thermal equilibrium. Every part has had a chance to emit and recieve radiation from other parts, so the whole thing is more or less homogenous, in the same way that a short metal bar will all be the same temperature if you heat one part of it. However, parts of the universe that are further away cannot be in equilibrium because there has not been time for them to recieve any energy, or to send it to us. This is the same as a metal bar that is a different temperature at each end. A point in the middle of the bar can "see" both ends, but it is still at a different tempertaure from both of them. In the same way, galaxy A and C can sensibly be said to be in different universes, even though galaxy B can see both of them.

The main problem, as I said earlier, is that we simply can't answer this sort of question because of it's very nature. If we could see what was happening to be able to answer it then we wouldn't need to ask in the first place. There are actually various different theories about it. Some people say that each seperate area is a different universe that may follow different physical laws. Others say that there is only one universe and that, because of an argument similar to yours, the laws of physics can't differ that much and the only differences possible between various parts are things like temperature and matter/anti-matter ratios.

OK ... fine. I actually understand your points and arguments -- I actually like the metal bar analogy. Now consider this ... Those in galaxy B consider Galaxies A and C to be in their same universe; so let's have those in Galaxy A send a signal to those in B. (Or just have those in B take a photo of Galaxy A ... that way there's no need to wait for signal time.) They then send that information to Galaxy C ... giving them in effect information of something that is outside of their universe, proving that existence lies beyond their universe. Galaxy C now has information from beyond their universe ... no?

 

[davidsmith73]

This is answered in Ziggurat's post #8. It depends quite a lot on your interpretation. Basically, either they are the absolute fundmental limits on the physical world, or they are the scale at which none of our theories can even pretend to say anything about. In either case, anything that happens below the Planck scale is irrelevant to the larger universe. However, if the latter is true then it is possible that the apparent randomness of quantum physics could be explained by sub-Planck effects.

Edit : Just to confirm, none of this has anything to do with measurement limitations, it is either all about the maths or all about the real world. Even having perfect accuracy in measurements would not make any difference.

How could we, in principle, find out which interpretation is correct?

I read Ziggurat's post #8 and it seems to me (I'm no mathematician) that the Planck scale is a result of an interface problem between QM and general relativity. Doesn't this suggest that we are dealing with a mathematical construct which serves to bridge these two theories rather than explain an observation?

 

[joesixpack]

Is time continuous?
It has generally appeared so to date, though there seem to be some gaps in the early 1980s.

I feel better now. I thought I was the only one who noticed all those time-gaps in the early '80s.

If you do find any artifacts from those time-gaps (eg. photographs, videotape, &c.) they would probably violate Herr Heisenberg's uncertainty principle by showing both where I was and what I was doing. In the interest of physics, they should be burned.

 

[Bodhi Dharma Zen]

Zeno of Elea... anyone?

 

[e-sabbath]

Correct me if I'm wrong, but if space and time are the same thing, and everything is made up of superstrings, then isn't the smallest possible unit of time the length of a superstring? At least, I remember reading something of that nature.

 

[Yllanes]

Correct me if I'm wrong, but if space and time are the same thing, and everything is made up of superstrings, then isn't the smallest possible unit of time the length of a superstring? At least, I remember reading something of that nature.

That is not exactly the approach of this thread. We are talking about the fact that when you combine general relativity and quantum mechanics (in particular, c finite and constant + uncertainty principle + equivalence principle), you arrive at the seemingly inescapable conclusion that spacetime is quantised. This is a conclusion we can reach just by combining naively our two current physical theories.

This is model-independent, it is present whether we use path integral quantum gravity, quantum cosmology, loop quantum gravity, string theory, etc. Of course, each of this models explains the reasons for this quantisation in a different way. But all of them coincide in the basic idea, which is a pretty strong indication in favour of a discrete spacetime.

However, they may all be wrong. As you no doubt know, none of them have any empirical validation.

 

[e-sabbath]

Of course, you're correct in that regard. I was wondering something that seemed to follow from superstring theory, but I hadn't seen specifically mentioned.

 

[Dave1001]

Is there a way we can reconcile our ability to conceptualize continuity and infinities with a universe that is completely quantized, discrete, and finite?

Also, according to the theories of a finite, quantized universe, shouldn't we be able to determine an exact number of planck space-time units in the universe? What are they? How does this work in the context of a big bang/expanding universe? We concetualize the universe as expanding in volume over time, but that doesn't seem to work in the context of space time?

I suspect a lot of my conceptual limitations here are due to the lack of our models being intuitively accessible.

Any one care to break this stuff down further?

 

[Yllanes]

Is there a way we can reconcile our ability to conceptualize continuity and infinities with a universe that is completely quantized, discrete, and finite?

Yes, but it is very difficult. For a taste, check the loop quantum gravity page in Wikipedia.

Also, according to the theories of a finite, quantized universe, shouldn't we be able to determine an exact number of planck space-time units in the universe? What are they?

I don't understand this question. In the current continuous picture the universe may be finite or infinite. If it is finite, then we can give a value for its total volume. If it isn't we can't. Something similar should happen with a discrete universe.

We concetualize the universe as expanding in volume over time, but that doesn't seem to work in the context of space time?

It does work. The trick is that in cosmology we can separate the spatial and temporal parts (we can divide spacetime in slices of constant t), so we can talk in these terms. Cosmology is a part of General Relativity, so it has to work in the context of spacetime.

 

[Cuddles]

OK ... fine. I actually understand your points and arguments -- I actually like the metal bar analogy. Now consider this ... Those in galaxy B consider Galaxies A and C to be in their same universe; so let's have those in Galaxy A send a signal to those in B. (Or just have those in B take a photo of Galaxy A ... that way there's no need to wait for signal time.) They then send that information to Galaxy C ... giving them in effect information of something that is outside of their universe, proving that existence lies beyond their universe. Galaxy C now has information from beyond their universe ... no?

The problem you have here is that signal time is always relevant. In fact, signal time is the source of the problem to start with. The reason galaxy A cannot see or communicate with galaxy C is that there has not been enough time for anything, including light, to pass between them. Taking a photo of a galaxy is no different from them sending a signal, it is all just light passing between them.

Interestingly, this problem would not be solved even with faster than light communication. As long as information can only travel at a finite speed there will always be a horizon beyond which nothing can reach us. The only way this could change would be with instantaneous communication.

How could we, in principle, find out which interpretation is correct?

I read Ziggurat's post #8 and it seems to me (I'm no mathematician) that the Planck scale is a result of an interface problem between QM and general relativity. Doesn't this suggest that we are dealing with a mathematical construct which serves to bridge these two theories rather than explain an observation?

No, if those theories are correct then space-time really is quantised. As Yllanes says

when you combine general relativity and quantum mechanics (in particular, c finite and constant + uncertainty principle + equivalence principle), you arrive at the seemingly inescapable conclusion that spacetime is quantised. This is a conclusion we can reach just by combining naively our two current physical theories.

The trouble is that we are fairly sure that both relativity and quantum physics are flawed, since they do not explain everything, hence the search for a theory of everything. Like I said, either space-time really is quantised, which is what our current theories seem to say, or we simply don't have theories capable of saying anything meaningful about this scale.

The main problem is that the Planck length is so small that we cannot obseve anything on that scale and are unlikely to be able to do so in the near future. It is pretty much impossible to investigate these ideas and so all the speculation about this is likely to remain such for quite a while yet.

Edit : Possibly I'm not explaining this very well. There are basically two possibilities. The first is that our theories are wrong and quantisation of space-time is simply an artifact created by trying to apply theories somewhere where they are not relevant. I suppose you could call this a mathematical construct, but it would be more accurate to simply call it an error. Since we know that both the theories are not complete, this is entirely possible. On the other hand, these theories are the best we have so far, so it is also reasonable to say that any new theory that replaces them will also predict a similar thing, but will do so in a more complete way. Both views are equally valid and at the moment we have no way of telling which is correct.

 

[Ziggurat]

How could we, in principle, find out which interpretation is correct?

I read Ziggurat's post #8 and it seems to me (I'm no mathematician) that the Planck scale is a result of an interface problem between QM and general relativity. Doesn't this suggest that we are dealing with a mathematical construct which serves to bridge these two theories rather than explain an observation?

I'd answer differently than Cuddles: namely, we don't know yet whether these scales represent just a mathematical artifact of where two incomplete theories intersect, or whether there's really something fundamental about them (like quantization). The intersection tells us that at least this is where current theories break down badly, even if nothing like quantization emerges. But the only way to really test the difference is to do experiments at energy densities approaching the planck scales (namely with particle accelerators), but we're not close to those energy densities yet, and without any tests, new theories like what Yllanes alludes to remain basically idle speculation.

 

[Just thinking]

The problem you have here is that signal time is always relevant. In fact, signal time is the source of the problem to start with. The reason galaxy A cannot see or communicate with galaxy C is that there has not been enough time for anything, including light, to pass between them. Taking a photo of a galaxy is no different from them sending a signal, it is all just light passing between them.

Interestingly, this problem would not be solved even with faster than light communication. As long as information can only travel at a finite speed there will always be a horizon beyond which nothing can reach us. The only way this could change would be with instantaneous communication.

I actually thought about my scenario more and realized there is what may be a major flaw in it ... there is no universal 'now' to the universe. Let me put it this way ... even if a far off galaxy was somehow still within our inertial reference frame (that is, not moving at all with respect to us), it would be erroneous (if not flat out nonsensical) to ask, "what are the occupants of that galaxy doing right now?" Space-Time not only makes any two objects separated by space to be spatially distant/different, but different in time as well. (Our 'now' is not their 'now' -- even though our clocks would run at the exact same rate.) Therefore, the occupants in the middle galaxy could not be thought of as sending us a photo of the more distant galaxy when we think of them doing so, they would have had to have sent it far earlier in our past. So far back in time that it would exceed the age of the universe -- hence, we never get it. (After all, they must wait for the distant galaxy's light to reach them first before sending a photo to us; and since they are on our cosmic horizon, that means that the age of the universe, to us, is too little for both signals to complete their journeys.)