Universal time

Factual Questions
1

I was watching a TV show and a physics Professor said that ‘now’ didn’t have any meaning across large distances because events aren’t causally linked. So if the Sun just blew up, you couldn’t say the Sun has blown up ‘now’ because it takes 8 minutes for the information to reach us.

This seems to contravene common sense (I know, doesn’t mean it’s wrong). I could imagine synchronising the clock in my house with one on Mars (might take some clever signalling), the two times would be the same (even though they’re not causally linked), so you couldn’t you say two things happened at the same time ?

2

I’m not qualified to answer, but one of Einstein’s mentors thought the answer was No.

[QUOTE=Hermann Minkowski ]
Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.
[/QUOTE]

3

The problem is in that special relativity, “simultaneity” (i.e. the property of two events at different locations happening at the same time) is reference-frame dependent. If you set up two synchronized clocks some distance apart (using your clever signalling), another observer moving relative to you will not see those clocks as being synchronized.

In fact, for certain types of events, different observers will disagree about which one occurred earlier in time. This would lead to problems with causality if one of these events was the “cause” of the other, since some observers would see the event happen before the cause. Fortunately the speed of light limit prevents this from happening, since events that are separated from each other in such a way that a light-speed-or-slower signal from one can affect the other have a time order that is agreed upon by all observers.

4

[QUOTE=Douglas Adams]
Time is an illusion. Lunchtime, doubly so …
[/QUOTE]

The rest of my post has been adequately explained by leahcim :wink:

5

If you see anything about advanced physics and it DOESN’T contravene common sense, they’re explaining it wrong.

6

Events that seem simultaneous to one observer in one frame of reference might not seem simultaneous in another frame. However, this is not because of the time it takes light to travel from one observer to another. Saying that we experience events on the sun 8 minutes later than an observer on the sun would observe them makes the wrong point.

See this thought experiment for an example. In this case the disparity in simultaneity is due to observers in two different inertial frames, not because of their distance apart.

7

I happen to agree with the Prof.

First, the general reason: assuming that no information can travel faster than the speed of light, what would “things happening at the same time” even mean? We can only reasonable define “now” if we clarify that we mean “now, here”. What would “now” on Mars even mean? Maybe Mars has been destroyed, and we’ll only find out about it when its light cone reaches us. Maybe some event has caused Mars to change its orbit? We’ll only know for sure when the light cone gets here. We cannot know any earlier than that, because no information may travel faster than c.

Which brings me to the specific case. Let’s try to set up some clever signalling to link the two clocks. But whatever method we use, we’re going to have a delay. If we are on Earth when Earth receives the signal from Mars, we can retrofit “here, then” to kind of fit “there, then”. Other than giving us a comfortable sounding framework for relating non-causal events with each other, what does the exercise give us? Nothing really. Other frames of reference will disagree with us anyway, and we still don’t know if “here, now” is still anywhere near being “there, now”.

I wish to point out explicitely that this viewpoint relies on the idea that no information can travel faster than c. If information can travel faster than c, then potentially you could link up the clocks; although, you are going to have other problems to deal with, such as cause happening after effect.

8

The clock on Mars would run faster than the clock on Earth, however, so they wouldn’t stay in sync.

9

Not only can we not synchronize two clocks separated by distance, we also can’t synchronize two clocks, move one away and then back again, and have them stay in sync. Even if they were perfect timepieces, with zero error.

I like the “spacetime as a loaf of raisin bread” analogy that I read in “The Fabric of the Cosmos.” It’s a way to show that an unchanging objective reality, but one that looks quite different from different inertial frames. I’ll probably muff this up but let me give it a shot, and maybe the folks who really understand this can fix it. :wink:

OK, imagine a loaf of raisin bread. The long dimension on the loaf is time. If we cut the loaf in half (the way we’d slice a piece), we get a cross section. That cross section is the universe (a 2-dimensional one), at one point in time, for anyone going the same speed as me. I see a raisin in this slice – let’s say that’s me, at one point in time, at one point in space. The bread on the left of the cut represents everything prior to that point (the past); the bread on the right of the cut represents everything after that point (the future).

Now let’s glue the two halves back together, and cut again, cutting through the “me” raisin, but at an angle. That’s the universe at one moment in time for someone going at a different speed from me. (If I rotated the knife 10 degrees counterclockwise looking from above, then it’s for someone moving through space towards the real me holding the knife, not the raisin me in the loaf.)

If the guy was moving faster, the angle of the knife would rotate more. As he reaches the speed of light, the angle reaches a maximum – let’s say that’s 45 degrees. (The actual angle is arbitrary and depends on how we relate an inch of bread in the time direction to an inch of bread in the space direction.)

OK, let’s make a 45 degree slice that cuts two raisins, call them A and B. That means that light could travel between A and B. It means that A defintely preceded B, and that this would be reported by all observers. Only someone traveling at the speed of light would have both raisins in their “slice” (in one instant) – but nobody can be traveling that fast, so it doesn’t happen.

Now let’s glue the bread back together and make a different slice, at say 20 degrees, that cuts two different raisins. To someone traveling at the right speed (toward the knife holder’s edge of the table), those two events would look like they happened at the same time. But to someone traveling more slowly in the same direction (like a 10 degree slice), one raisin winds up to the left of his “slice”, or one winds up to the right, or both. To that guy, the two events don’t look like they happened at the same time.

Who is correct? Both / neither. For any two raisins that you can cut through with less than a 45 degree angle (clockwise or counterclockwise), there is no absolute truth over which happened first. What you see will depend on your speed (with respect to the direction between the two raisins).

For any two raisins that you can cut through with a slice over 45 degrees, everyone will report the same sequence of events, and a beam of light could have passed from the first to the second, so one could have caused the other.

Clearer than mud? My apologies to Mr. Greene for making a mash of his analogy.

10

Imagine you synchronized the two clocks thus:

You place a signalling device EXACTLY halfway between the Earth clock and the Mars clock. It sends out a pulse and both clocks receive the pulse and synch themselves to it. From the point of view of your signalling device, those clocks are synched perfectly. If they each send out a pulse at “noon,” the device will receive those two pulses simultaneously.

From anywhere else in the Universe (except other points equidistant from the two clocks), however, those two pulses will not arrive simultaneously, and the clocks will appear to be out of synch.

Problem 1: The Earth and Mars both move. The only way that they will continue to appear synchronized is if your signalling device also moves, staying exactly halfway between the clocks.

Problem 2: This experiment works the same way no matter where that original signalling device is, and the definition of “exactly halfway between the clocks” is somewhat fuzzy as well.

11

Good analogy, Learjeff. The only quibbles I would add are that, first, calling the “speed of light angle” 45 degrees really isn’t arbitrary, in that it’s the strictly simplest interpretation, and assigning it to any other angle is always just going to make things harder on you for no benefit. Second, there’s a completely different raisin bread analogy one might encounter in other situations, and it should be stressed that the two analogies are unrelated to each other.

12

Yep the concept of ‘now’ is a sticky wicket in modern physics. Special relativity says that each non-accelerated observer has has (or at least can be given) their own concept of ‘now’. Once you bring in accelerated observers though it gets worse as you find they don’t really have sensible concept of a global ‘now’. Introduce general relativity and things get even worse as even unaccelerated (i.e. free-falling) observers can lose their concept of a global ‘now’. However what spacetime does have is a structure that relates all events together in some way or other.

13

Even worse there’s some spacetimes that can’t be sliced into a set of nice cross sections of ‘nows’. These spacetimes are called non-‘globally hyperbolic’ (this is a reference to the relationship with hyperbolic partial differential equations rather than their geometry). A great deal of physicists though would say though that spacetimes which fail to be globally hyperbolic are non-physical (i.e. they don’t describe actual physical situations), however they’re often wheeled out for their interesting properties.

14

Good point: you get 45 degrees if 1 light year of bread in a space direction is equal to one year in the time direction.

I believe even Einstein said that C was a funny constant in the equation (or, C squared), in that, if units were defined more sensibly in retrospect, there’d be no need for a constant at all, and you’d get E = M.

BTW, the loaf of bread time-space analogy is equivalent to time-space diagrams as shown in the wiki cite above, but (perhaps confusingly) has two spatial dimensions rather than one. In my discussion I ignored the vertical dimension anyway, so it’s just a tastier way of thinking about TSDs. Still, for some odd reason, it clicked for me in a more concrete way than TSDs.

Which is that?

15

Ah well, there goes my frickin’ raisin bread.

Thanks! Now I’m gonna have to look up hyperbolic partials.

16

You don’t even have to go that far. It happens in the GPS satellites alarming quickly: Wikipedia says:

Much, much, perhaps too much more detail is at the article Error analysis for the Global Positioning System#Relativity

17

The analogy isn’t bad at all, it’s just that for some observers how you choose to slice spacetime will be arbitary. For example, when an observer is accelerated, using a ‘straight knife’ isn’t that sensible to make the slice, but in which case, how curved should the knife be? Also the concept of a ‘straight knife’ may not really exist when the cake itself is curved.

The basic idea of a globally hyperbolic manifold (though they’re usually defined in terms of causal conditions) is that you can take a slice of cake which would be equivalent to a ‘now’ (though when I use ‘now’, it’s not necessarily related to an observer) and by looking at the properties of that slice you can completely reconstruct the whole cake.

I am suddenly feeling hungry.

18

The other raisin bread analogy is for expansion of the Universe: As the loaf of raisin bread rises, all raisins move away from all other raisins, just like galaxies getting further apart. In this case, all three spatial dimensions of the bread represent spatial dimensions, and time is represented by time.

19

Aha, raisin bread as a 3D version of the balloon.

Asymptotically Fat: imitating Inigo Montoya You keep using those words. I’m not sure I know what they mean. :wink:

20

Hot Cross Bun Time is simultaneous across all frames of reference :smiley: