# Absolute Time

Surely the concept of relativity of simultaneity is an illusion based on the finite speed of light?
If an observer witnesses an event (Event A) and is at distance of zero (d=0) from Event A, then that is the TRUE time the event occurred. It is irrelevant if other observers of sufficient distance record the time the event occured as different. That is only because light has a finite speed limit. Therefore, there is an absolute time when events occur ....?

Or am i wrong?

Hi goodensn,
welcome to PF.

Times are measured by individuals with clocks and there is no absolute clock that we should all synchronise with.

For simultaneity you need 2 events ( say light flashes) separated in space. Some observers will see the flashes at the same time on their clocks, and others will see 2 flashes. It depends on the setup.

You are right in that these relativistic effects are because of the finite and unchanging speed of ligh.

Hi Mentz114,

Thanks for the reply. I understand that there is no absolute clock with which we can all synchronise with, but surely every event that happens in the Universe occurs at an absolute time (even though we may all disagree on when that time was). In order for an observer to 'know' when the absolute time of an event occurred, that observer would have to be at a distance of zero from the event.
I hope that makes sense?
Thanks

Ich
I hope that makes sense?
That makes sense as long as the recorded absolute time of an event is "now". If you want to plug in numbers, you have to compare with a set of standard events, where the clocks are adjusted to 0. Which set you use depends on your velocity or on convention.

tiny-tim
Homework Helper
Hi goodensn!

Yes, welcome to PF!
… surely every event that happens in the Universe occurs at an absolute time (even though we may all disagree on when that time was)

You might as well say that every event happens at an absolute position.

Events themselves are absolute, but time and position are just measurements, and aren't absolute.

And, as Mentz114 mentioned, simultaneity requires the same observer to measure 2 events … so how would your use of "absolute time" help with that?

OK,Thanks Ich. I would love to plug numbers in, but I'm not really a scientist ;-)

I guess what I'm driving at is that there must be an absolute truth on the order of events that occur throughout the universe. The trouble is, nobody can know what that truth is because we will all be in our own personal frames of reference. For us to 'know' the truth, we would have to be everywhere at once.

Hi tiny-tim. You are right, we cannot MEASURE truly when (or where) events occur, as we are all in our own frame of reference (as per my post above). I guess it's more of a philosophical point that there IS a flow of time in terms of all universal events, we just cannot accurately measure it (unless we step outside the universe)

Ich
I guess what I'm driving at is that there must be an absolute truth on the order of events that occur throughout the universe.
As long as these events could - at least in principle - influence each other, there is an absolute truth on their ordering.
If they can't, however, their order doesn't matter, and that fact is reflected by SR.

russ_watters
Mentor
goodensn, these issues are well tested. It is quite certain that measured time differences occur because of both relativity of simultenaety and time dilation.

One of the simpler examples that avoids the relativity of simultenaety issue is GPS satellites. They fly over (roughly) the same spot every 90 minutes or so, so the distance to the ground station that synchronizes them is always about the same for every lap around the earth. Yet they still show time dilation.

Fredrik
Staff Emeritus
Gold Member
I guess what I'm driving at is that there must be an absolute truth on the order of events that occur throughout the universe.
There isn't, and even if there was, this still wouldn't be true:

For us to 'know' the truth, we would have to be everywhere at once.
It wouldn't even help to have complete knowledge about what happens at every event in all of space-time.

I am certainly not disputing SR or GR - I fully appreciate that time dilation, etc. DOES occur. What I'm struggling with is the concept that from the Big Bang to (perhaps) the Big Crunch, lots of events happen throughout the Universe, and we may all disagree on the TIMING and the ORDERING of these events....BUT...there still must be an absolute ordering of all events in the universe.
If our Sun exploded tomorrow (using my personal frame of reference) and the moon exploded 2 weeks later (also using my own personal frame of reference) then, assuming I'm not traveling at any velocity, and i am zero distance from both events when they occur, then that is the REAL ordering of these events, regardless if people in motion that may be light years away, record these events as occuring the other way around.

tiny-tim
Homework Helper
BUT...there still must be an absolute ordering of all events in the universe.
If our Sun exploded tomorrow (using my personal frame of reference) and the moon exploded 2 weeks later (also using my own personal frame of reference) then, … that is the REAL ordering of these events

Yes, but that's only because the "news" of the sun exploding would have reached the moon well before the 2 weeks!

If the moon exploded 5 minutes after the sun exploded, then is NO "real ordering" … some observers will say that the moon exploded first!

Hello goodensn.

For spacelike separated evnts, that is events separated so that a ray of light (photon), and therefore of course an observer, cannot be present at both events, the time order of these events may not be the same for all observers. this does not not violate causality as neither event can have any effect on the other, that is they are not causally rellated.

So at least in the case of such spacelike separated events there is no absolute time or temporal order.

Matheinste.

Fredrik
Staff Emeritus
Gold Member
This is just to further clarify what tiny-tim and matheinste said...

Consider two events A and B, with time coordinates (in some coordinate system) tA and tB respectively. Define $\Delta t=t_A-t_B$. Do the same for the x,y and z coordinates, and consider the quantity

$$-c^2\Delta t^2 +\Delta x^2+\Delta y^2+\Delta z^2$$

The events are said to be space-like separated if this is >0. If it's <0 they're said to be time-like separated. If it's =0, they're said to be light-like or null separated.

Here's the thing: That quantity has the same value in all inertial frames, so everyone agrees about what kind of separation the two events have. If the events are space-like separated, you can always find two inertial frames such that the temporal order of the events in one of them is the opposite of what it is in the other. If the events are time-like or light-like separated, you can never do that. So everyone agrees about the temporal order of time-like and light-like events.

Thank you all for your helpful messages. I think I'm getting there...slowly! Just for the record, I am talking ONLY about spacelike separated events. I fully agree with the 2 previous posts (thanks matheinste & Fredrik).
I guess it is tempting to believe that there IS a true ordering of events even if observers disagree. Consider this: If Bill records Event A occurring before Event B and Ted records Event B occurring before Event A, both observations are equally valid in their own frames of reference. I fully accept that. But... is it naive to say that 1 of the observers is really wrong? Even though their own measurement is accurate and valid?

Hello goodensn.

Disagreements between observers with regard to temporal order of spacelike separated events arise because of the observer's motion relative to each other. As all motion is relative and therefore all observers are on an equal footing neither obserever is in a position to claim to be absolutely correct in his time ordering of spacelike separated events.

Matheinste.

Fredrik
Staff Emeritus
Gold Member
But... is it naive to say that 1 of the observers is really wrong?
Naive isn't the word I'd use. "Unscientific" is more appropriate. The theory that says that one particular observer is right and everyone else wrong makes exactly the same predictions about the outcome of experiments as the alternative theories, so no experiment can distinguish between them.

dx
Homework Helper
Gold Member
There indeed is a real ordering, and this is the causal ordering of events. If event A caused event B, then this relationship is absolute. Everyone will agree that A caused B. But there is no ordering in the sense of two events being simultaneous in the Galilean sense.

Hello dx

With spacelike separated events, by their very definition there can be no causal relationship between them.

Matheinste

dx
Homework Helper
Gold Member
Hello dx

With spacelike separated events, by their very definition there can be no causal relationship between them.

Matheinste

"Spacelike related" is also a causal relationship, just like "timelike related" and "lightlike related". And all these causal relationships are absolute.

Hello dx

Quote:-

----"Spacelike related" is also a causal relationship,----

How?

For spacelike separated events a photon cannot be present at both events. So one event cannot have any influence on the other if one assumes that c is finite.

Matheinste

If a beam of light is sent from a certain time/place (t_0,x_0), and intercepted at a different time/place (t_1,x_1), , all inertial observers in the universe will agree that the light was sent before it was received. Does this not follow from the Lorentz transformation -

$$t'_1 - t'_0 = \gamma( t_1 - t_0 ) - \gamma\beta(x_1 - x_0)$$

so if $$t_1 - t_0 > 0$$ then $$t'_1 - t'_0 > 0$$ ?

Tentative proof - because (x_1 - x_0)/(t_1 - t_0 ) = 1, we can get

$$\frac{t'_1 - t'_0}{t_1 - t_0 } = \gamma( 1-\beta)$$

The RHS is always positive so the numerator and denominator on the left must have the same signs. So causality is always preserved in this scenario.

QED

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dx
Homework Helper
Gold Member
By causal relationship I don't mean literally that one caused the other. Spacelike, timelike and lightlike relationships are causal relationships in the sense that that they determine the causal structure of spacetime.

Hello Mentz114

You are of course correct in that sense.

I was thinking of two unrelated events rather than the transmission and reception of the same photon. Would what i have said be true in this sense. That if the events were the emission of two photons at spcelike sperated (points)events, i.e. each outside the other's light cone, then observers in certain relative motions could disagree on the temporal order of these events (emissions). They are in each other's absolute "elsewhere".

Thanks Matheinste

Matheinste, I got carried away with my little proof, but it's not the issue. You are completely right about causaly separated events.

M

Hello Mentz114.

Thanks.

Matheinste.

Another thought on the equation I wrote. For causally disconnected points,

$$\frac{x_1 - x_0}{t_1 - t_0} = v > 1$$ and we can see

$$\frac{t'_1 - t'_0}{t_1 - t_0 } = \gamma( 1-v\beta)$$

and now the sign of the RHS can flip, and priority be reversed.

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tiny-tim
Homework Helper
Just for the record, I am talking ONLY about spacelike separated events.

I guess it is tempting to believe that there IS a true ordering of events even if observers disagree. Consider this: If Bill records Event A occurring before Event B and Ted records Event B occurring before Event A, both observations are equally valid in their own frames of reference. I fully accept that. But... is it naive to say that 1 of the observers is really wrong? Even though their own measurement is accurate and valid?

Hi goodensn!

I think you accept that a pair of events on its own has no ordering.

But you are wondering whether a pair of events in the context of belonging to the time-line of two observers can be given an ordering.

If the excellent Bill and Ted are inertial observers, then it seems sensible to choose an observer whose velocity is the average of their velocities (so that they have equal and opposite velocities wiht respect to him), and then let him decide which of Bill's and Ted's clocks is earlier.

But for that definition of ordering of inertial observers' clocks ("B < T") to be a "real" ordering, it would need to be well-ordered, in the sense that:
if B < T and T < U, then B < U.​

I suspect that's not valid in two or more dimensions … would someone like to work it out?

haha i use this argument on my cousin all the time goodensn... you cant say either are wrong... its all "relative" hence the reason why its called the theory of relativity... it is all based on observation relative to the observer... einstein said that at high velocities there could be time dialation... everything is up for interpretation as long as the conclusion is consistent!

Fredrik
Staff Emeritus
Gold Member
But you are wondering whether a pair of events in the context of belonging to the time-line of two observers can be given an ordering.

If the excellent Bill and Ted are inertial observers, then it seems sensible to choose an observer whose velocity is the average of their velocities (so that they have equal and opposite velocities wiht respect to him), and then let him decide which of Bill's and Ted's clocks is earlier.

But for that definition of ordering of inertial observers' clocks ("B < T") to be a "real" ordering, it would need to be well-ordered, in the sense that:
if B < T and T < U, then B < U.​

I suspect that's not valid in two or more dimensions … would someone like to work it out?
It's easy to transform the 3+1-dimensional problem into the 1+1-dimensional problem, but I really don't understand what you're trying to do in the 1+1-dimensional case.