# What is zero time between events?

## Main Question or Discussion Point

if an event happens at the exact moment of another for a single observer, what does instantaneous mean? This stems from a question i posed about the speed at which two entangled particles collapse into one definite state when one is measured. It got m thinking what does zero time and instantaneous really mean. Can any two events truly be said to happen in an instant with zero time elapsing between them. I know we cannot measure zero time, we could only measure down to the planck scale. So do we know that events can happen with zero time between them for a single observer?

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Simon Bridge
Homework Helper
if an event happens at the exact moment of another for a single observer, what does instantaneous mean?
That is what instantanious means - in the limit as change in time approach zero. Also see "simultanious".
So do we know that events can happen with zero time between them for a single observer?
Of course - within the limits of the measurement. Is there any other kind?

ghwellsjr
Gold Member
If you are asking about quantum issues, then you are on the wrong forum since Special Relativity does not involve those kinds of details. But if you are asking about how SR handles zero time between remote events, it's all according to a previously determined synchronization process as applied to a particular Frame of Reference and can be different for each Frame of Reference.

its hard to know which forum to post in. My question is whether two events can ever be said to be simultaneous and if so how would that be proven since its not measurable.

Nugatory
Mentor
its hard to know which forum to post in. My question is whether two events can ever be said to be simultaneous and if so how would that be proven since its not measurable.
It's measurable, just not measurable with unlimited precision.

There's no deep quantum-mechanical or metaphysical magic going on here, it's just that every measurement of everything contains some uncertainty. If we were being really strictly careful with the language, we would never say "simultaneous" without adding the qualifier "to the limits of our best available clocks".

Nugatory
Mentor
So when we say that two events are "simultaneous", we're either: 1) being sloppy by not specifying the particular frame because we think it's clear which frame is intended; or 2) being devious and not specifying the frame because we're trying to sneak a "paradox" through; or 3) demonstrating misunderstanding by thinking that it doesn't matter.
(Are there any other reasons not to specify the reference frame?)

And then, even after we've correctly said "simultaneous as observed by this observer" we STILL have to add the qualification about the limits of precision. But as long as we've been through all that, if two events have time coordinates in one reference frame that are equal, to the limits of precision of our time time measurement... That's what we mean by simultaneous.

i think the question is answered by the continuous use of the phrase "within precision limits". Therefore it is untestable and it is not possible to say any two events to any observer in any one time frame are simultaneous where time elapsed equals zero.

LURCH
I'm not sure I agree with that. Since simultenaety is frame-dependant, two events that are simultaneous in one frame can be minutes apart in another; a difference that is easily measurable. I think scenario 1) is probably right; the events are simultaneous in the same reference frame as the events in question (specifically, the reference frame of the equipment making the measurement), and this generally "goes without saying".

Simon Bridge
Homework Helper
IRL: scenario 1: sloppy language and leaving stuff to context.

We can deal in absolutes only in models - eg. absolute simultaneity is fine in classical mechanics.

Context provides the meaning.

if I go through a set of doors at the same time as you that doesn't mean absolutely our centers of mass crossed the line at the same exact time does it?

If we synchronize watches from the same manufacturer then their ticks will probably be less than a small fraction of a second apart ... so we can say they read the same time. The context is that we are close together when we make that reading (so the time light takes from the watches to my eyes and the time it takes to get to your eyes are about the same). This is a common scenario in SR thought experiments.

We can extend this further by using a third observer - so we don't have to be close together.

The concept of "at the tame time as" is well defined in SR.

Whenever we start talking about measurement we start introducing uncertainties and statistics. While we are talking about the mathematical models - then we are fine.

yes but once you define simultaneous as zero elapsed time and not an approximation then you are stuck. You can never demonstrate this experimentally because you have no way to measure it.
So much like string theory its all works mathematically but is untestable and fails newtons grounds for being science. Working mathematically does not make it a reality.

ghwellsjr
Gold Member
i think the question is answered by the continuous use of the phrase "within precision limits". Therefore it is untestable and it is not possible to say any two events to any observer in any one time frame are simultaneous where time elapsed equals zero.
yes but once you define simultaneous as zero elapsed time and not an approximation then you are stuck. You can never demonstrate this experimentally because you have no way to measure it.
So much like string theory its all works mathematically but is untestable and fails newtons grounds for being science. Working mathematically does not make it a reality.
Where did you get the idea that "zero elapsed time" is what simultaneous means or that it requires two separately synchronized clocks with less than perfect precision?

You don't need any clocks, synchronized or not, to establish that two remote events happen at the same time, as defined by Special Relativity. All you need to do is have two light signals emitted by the two remote events and then see if they arrive simultaneously at a point midway between them as defined by a rigid inertial rod between the two events.

yes but once you define simultaneous as zero elapsed time and not an approximation then you are stuck. You can never demonstrate this experimentally because you have no way to measure it.
So much like string theory its all works mathematically but is untestable and fails newtons grounds for being science. Working mathematically does not make it a reality.
You seem to be asking for simultaneity to have some demonstrable absolute meaning. We are not stuck simply because we defined simultaneity a certain way, because we know it's only a procedural definition. To think we are somehow stuck implies that properly defined simultaneity has real meaning. We could laugh at the Chinese for pointing up and saying down, but it would make no more sense than saying simultaneity should be defined such that it is the same for everybody.

Simon Bridge
Homework Helper
yes but once you define simultaneous as zero elapsed time and not an approximation then you are stuck. You can never demonstrate this experimentally because you have no way to measure it.
You seem to think that a physical model is only demonstrated if the exact prediction from the model exactly matches the outcome of the experiment.

That is not what we do. All an experiment has to do is distinguish between different models. It does not need to be 100% accurate to do that.

If model A predicts an exact value X=5units and model B predicts an exact value X=6units ... wee need our experimental design to result in a measurement of X which is accurate enough to distinguish X=6 from X=5.

From the design of the experiment we can work out an uncertainty "e".
To find out which model, if either, is "on the right track" (note: we van never tell if a model is "True" <---<<< deliberate caps.) we have to design the experiment accordingly. eg.

Lets say the experiment got a measurement for X of 5.2 units:

If e~1 then we could say that the models appear to be on the right track even though the experiment fails to distinguish them: we cannot tell which is better. If the measurement was 100 ... this tells us that both the models are way wayy off and we need to rethink them.

If e=0.1, then the experiment lends more support to model A than to model B (model A is accepted to 95% confidence, while model B is rejected).

The uncertainty is in nature - not the model.

i.e. We only need the stopwatch button-press to be "simultaneous" with the event being timed to the extent that this distinguishes between different theories about what we are timing. The model tells us how close-a match that needs to be. The confusion you are experiencing is doe to not being precise enough about your terms.

It is this sort of attention to detail - separating the models from the reality - allows us to refine our experiments so they can tell us more detail about the phenomena under study. It lets us, also, refine our models to more closely imitate nature. It is what allows us to spot Heisenberg's uncertainty as something that has to be accounted for in the design of really fine detail experiments.

If you like to think in terms of absolutes, think of it this way: we have a model for the physics we are studying, which may be absolute if we want; and we have another model for our measurements, which has to be statistical. We have to apply both to make an experiment mean something.

However - you should read more about "empiricism": we can never actually prove a physical theory ... your observation about the impossibility of an absolute measurement boils down to this in the end. But we can disprove them.

So much like string theory its all works mathematically but is untestable and fails newtons grounds for being science. Working mathematically does not make it a reality.
The trouble with string theory is not the impossibility of measuring anything: it predicts every result of every experiment ever performed after all. The trouble is that it is difficult to come up with some result from string theory that can only be modeled by string theory. i.e. we have not come up with an experiment to distinguish string theory from any other model.

We need (re above) some value X which string theory says is 5 when everything else says it is 6 and we just happen to have not measured X accurately enough yet. IFAIK: there is no such prediction... as yet. We are able to do this in the case of special and general relativity though.

If you want to discuss string theory and why it is not just dismissed as a pseudo-science; that's a big topic: you want a new thread in another forum.

Special and General Relativity, this forum, is only a small modification of classical physics. Within the framework for S/GR, the model allows absolute measurements and provides a scheme for comparing them between different observers.

We have another model with statistics built-in to it - Quantum Mechanics.