# Is it possible for two instantaneous events, one predicated on the other, to happen at the exact same time?

As the title states lets say there are two events, one is essentially the product/result of the other. Both events are absolutely instantaneous. Could these events occur at the exact same time?

• Is this a physics question or a philosophy of physics question? Jul 4 '15 at 3:27
• I would definitely say it falls more into philosophy of science. Jul 4 '15 at 5:15
• You suppose that both events are "instantaneous". Is there a difference between the terms "instantaneous" and "at the same time"? (I am not an English native speaker.) Jul 4 '15 at 12:09
• the answer depends on what you mean by events occurring "at the exact same time"
– nir
Jul 5 '15 at 10:15
• Logically possible? Sure. Under gravitational action at a distance in classical mechanics one body acting on another, and the other accelerating because of it occur simultaneously (to the extent that "instantaneous events" make sense). In modern physics the question is moot because "at exact same time" makes little sense in relativity, and classical time breaks down at Planck scales because of quantum effects, so "absolutely instantaneous" makes even less sense. Jul 5 '15 at 23:30

No, both events cannot occur at the same time.

According to the Special Theory of Relativity time and space have no separate and independent existence. Instead, space and time are coordinates in 4-dimensional spacetime. Events are the points of spacetime.

The structure independent from any choice of coordinates is the light cone of each event. It is a 3-dimensional double cone. The light cone defines the domains of causal dependence:

Event 1 is located in the vertex of its light cone. Each event within the forward cone can be affected by event 1, each event within the backward cone could have effected event 1. If event 1 can affect event 2 as you suppose, then event 2 is located within the forward cone of event 1.

Now you can choose the coordinates space and time, taking the vertex as origin of the coordinate system. But the crucial point is: There is no choice of coordinates, such that an event in the forward cone has the same value of its time coordinate as the vertex, which has time = 0. And the second remarkable fact: In case event 2 is located outside the light cone of event 1 - i.e. event 1 cannot affect event 2 - then a choice of space and time is possible such that both events are simultaneous.

The above considerations derive from the Special Theory of Relativity and refer to Minkowski space. Special relativity holds in the absence of massive objects. In the General Theory of Relativity you can approximate spacetime locally by Minkowski space. But the global structure of spacetime depends on the mass distribution.

Added on request: The Special Theory of Relativity got its name from Einstein's discovery, that many physical quantities have only a relative meaning. The two most prominent are space and time: There is no absolute time difference between two events, there is no global meaning of two events being simultaneous, there is no absolute spatial distance of two events. Many quantities depend on the coordinate system which the observer chooses. On the other hand, the speed of light is always the same, independent from any coordinate system it refers to. As a consequence, it has an absolute meaning whether one event can affect another or not. Hence a unique structure of causal dependency exists.

• nice answer; only thing is, I think the second paragraph about "The object independent from any choice of coordinates..." could be expressed more clearly.
– nir
Jul 4 '15 at 17:27
• I changed the term to "structure". Does it help? Jul 4 '15 at 17:44
• I mean that I suspect that people who are not familiar with SR, will not immediately understand what you mean by something being independent from choice of coordinates, nor why the light cone is such a thing.
– nir
Jul 4 '15 at 18:29
• I added some explanation. But it cannot replace a detailed introduction from a textbook about the Special Theory of Relativity. Keywords: Light cone, Minkowski space, 4-dimensional distance, Lorentz transformation, speed of light, simultaneity. Jul 4 '15 at 21:32
• This answer does not match the generality of the question because of several presuppositions. First, that two different events can not happen at the same spacetime point (e.g. a particle collision and release of its products), or that they have to be spatiotemporally attached at all (collapse of wave function isn't). Even assuming that, general relativity allows closed timelike curves, and so separated events that are both in causal regions of each other. Answer here can not be based on specifics of a particular model like SR, especially since we know that it breaks down at small time scales. Jul 5 '15 at 23:01

If all observers agree that two events happen at the exact same time, then they must happen at the exact same point in spacetime. If they happen at the exact same point in spacetime, they are, by definition, the same event.

• this answer is spot on!
– nir
Jul 5 '15 at 18:23
• I like your answer, but I'm not sure that is logically sound. Since information travels as a constant, finite speed, how is it possible to satisfy the antecedent "all observers agree that two events happen at the exact same time" and thus justify the consequent "they happen at the exact same point in spacetime". Maybe I'm missing something?
– nwr
Jul 5 '15 at 22:24
• The antecedent states that if you and I are any two observers, and if we each wait until information about this event reaches us, and if we then each use that information to infer the time at which the event took place, we will both infer the same time. Jul 5 '15 at 23:38
• @WillO I like your answer because it's clever so +1. But I'm still going to nit-pick. Any inference observers draw about the actual time an event occurred based on our physical theories (assuming correctness) will not account for variations in the measuring devices, such as tiny differences in electrical resistance or microscopic differences in their manufacture. In such a case, if two observers infered the exact same time, then one might not necessarily draw the conclusion of a single event. Anyway, it's probably a mute point. Nice answer.
– nwr
Jul 6 '15 at 0:14
• @NickR, in SR an observer is not generally a person or a device making measurements of limited accuracy (e.g. a passenger looking out the window) but a mathematical context - "Speaking of an observer in special relativity is not specifically hypothesizing an individual person who is experiencing events, but rather it is a particular mathematical context which objects and events are to be evaluated from." - en.wikipedia.org/wiki/Observer_(special_relativity)
– nir
Jul 6 '15 at 5:49

There is a long and rich history in physics pondering this questions. It was actually a key argument between Einstein and Bohr/Heisenberg. According to special relativity the answer is clearly "no". However, quantum mechanics could potentially allow for this through a phenomenon called "entanglement".

Einstein and co called out the absurdity of entanglement in their famous Einstein Podolski Rosen thought experiment. Einstein used to call it "spooky action at a distance" i.e. spukhafte Fernwirkung in German.

In the 1960s John Stuart Bell was able to reshape the controversy in a way that would allow for experimental testing using the aptly named "Bell inequalities".

In the 1990 technology had advanced enough to actually run the experiments with perhaps Alain Aspect in Paris doing the most convincing initial work.

So far the experimental data has been quite clear: Einstein was wrong and Bohr was right: quantum entanglement seems to clearly violate special relativity and what happens at point A can impact what happens at point B instanteously regardless of how far they are apart.

This indeed an absurd and bizarre notion, but it is apparently how the universe works. It is however not a direct violation of causality since its simultanoeus and it doesn't go backwards in time.

To make things worse, according to special relativity, simultaneity depends on the framework of the observer but that's different can of worms.

• Entanglement. Yes, that is an interesting example to raise - I'd have raised it myself had I thought of it - and it does indeed appear to witness simultaneity. +1 However, although the phenomenon is supported by observation, the validity of quantum theory is open to doubt. No scientific theory has stood the test of time and there are many philosophical doubts concerning the nature of reality and what constitutes an event.
– nwr
Jul 5 '15 at 4:42
• @Hilmar: Consider the standard case of an entangled system with two components. You write " what happens at point A can impact what happens at point B instanteously ": What about considering the phaenomenon as follows: Measuring one component changes the state of the whole system. And it is the whole system which affects particles A and B, the causal relation is between the whole system and each of its parts, not between component A and component B. Jul 5 '15 at 13:28

This, I think is a very good question.

In the Newtonian picture there is such a thing as absolute time and simultaneity; I can't judge whether a light-bulb switched on at Alpha Centauri is switched on at the same time as one here on Earth.

In Einsteins picture which drops both of these concepts, there is instead only Simultaniety at a place: ie if both light-bulbs were here on Earth, or for that matter on Alpha-Centauri.

(Physically, a frame tells us when we can say events are simultaneous; there is no global frame - as in Newtons picture - but there is always one locally).

The cleverness of the question, I suggest, is the introduction of causality: if A causes B, then can A happen at the same time as B? Or must it strictly come before?

Consider for example the collision of two spheres approaching each other at the same speed; at collision they both change direction and move apart.

Q. Is the event when the first ball collides simultaneous with when the second ball collides?

Yes, but this is because the event referred to is in fact the same event and not two different events - and this is because it takes two to collide (what sound does one ball make colliding...?)

Q. Is the event when the first ball changes direction simultaneous with when the second ball changes direction?

Now, the first ball changes direction because the second ball has collided with it; these are not quite the same event in the earlier question; they are conceptually distinct; but they appear to happen simultaneously.

Symmetrically, the second ball changes direction because the first ball has collided with it; and the same reasoning above follows.

Thus we see the answer to the question is yes; they are simultaneous.

This seems puzzling, because it stills as though an event ought to occur strictly before another.

And of course, the example has been chosen to reflect this: it has obvious physical symmetry (just look at it!), but it also has an obvious causal symmetry; and so in a sense we're side-stepping the problem.

Still, in the (strict) particle picture of physics, collisions is all we have...

One might argue naively as follows :

An event is marked by change and therefore an event occurs in time.

The interval of time an event occupies must be non-zero, for if no time passes then no change can occur.

Therefore, events do not occur instantaneously.

Similarly, events that depend on one another cannot occur simultaneously.

It may also be worth mentioning that there is not commonly accepted philosophical definition of event.

As the title states lets say there are two events, one is essentially the product/result of the other. Both events are absolutely instantaneous. Could these events occur at the exact same time?

I am assuming that the two events had no relation to each other before the said event took place. Therefor there could be no measurable influence before said events occur. The mere fact that both events occur absolutely instantaneously could be the very product of effect which an event is the result of.

That is to say the predestined nature of 1 event acted on the other , only for the result to become into fruition at the instantaneous point of the occurrence of both events. Both events were both results of their own . One was the fulfillment of influence , in a manner of complete independence from the other , and the other was that result of the fulfillment to the product which was its effect.

Time only plays a part in that it is becomes the measurement by which this event plays out. However this event was always going to play out, regardless of time , if one is to assume your question is true from the outset. Once you remove time from the equation the interaction from the two events are complete in a certain perfection of foreordination of fate. The causation of consequence in a relation bound only by an event. Both products of the other. This can imply that the mere inquest into whether one event has an effect on the other already produces the result of either true or false, completely at the discretion of the observer.