Existence according to reference frames

[nkpstn]

Is it possible for a particle to exist according to one reference frame and simultaneously not exist according to another?

If energy is relative, can a collision between two particles have enough energy to produce new particles according to its own reference frame but not have said amount of energy according to a 3rd particle's reference frame?

Just started reading about relativity, apologies if question is noobish and/or redundant.

 

[Dale]

Hi nkpstn, welcome to PF.

No, it is not possible for a classical particle to exist and simultaneously not exist. The relativity of simultaneity refers to disagreements about the simultaneity of spatially separated events. Since a particle is not spatially separated from itself there is no disagreement.

 

[bobc2]

Is it possible for a particle to exist according to one reference frame and simultaneously not exist according to another?

If energy is relative, can a collision between two particles have enough energy to produce new particles according to its own reference frame but not have said amount of energy according to a 3rd particle's reference frame?

Just started reading about relativity, apologies if question is noobish and/or redundant.

That's not a noobish question at all, nkpstn. I believe you may have something in mind like this. I've prepared a space-time diagram to illustrate the situation. The blue guy and the brown guy in the sketch exist simultaneously, and yet the red particle exists in the blue guy's simultaneous 3-D space but it does not exist in the brown's simultaneous 3-D space (the red particle has decayed into orange and purple particles).

 

[pervect]

For some meanings of the word "reference frame", it's possible that the reference frame does not cover all of space-time.

So you might have a situation where some particle is outside the region of space-time that the reference -frame covers. I'd argue that the particle still "exists" in some sense, it's just doesn't exist in the region covered by the reference frame in question.

An example of the sort of reference frame where this happens is an accelerated reference frame.

 

[bobc2]

For some meanings of the word "reference frame", it's possible that the reference frame does not cover all of space-time.

So you might have a situation where some particle is outside the region of space-time that the reference -frame covers. I'd argue that the particle still "exists" in some sense, it's just doesn't exist in the region covered by the reference frame in question.

An example of the sort of reference frame where this happens is an accelerated reference frame.

That's a good observation, pervect. And I don't think you don't even need an accelerated frame for that. I think the Andromeda Paradox (below sketch) presented by Roger Penrose supports the concept you are suggesting. Ruth and Bill walk past each other, and their relative velocities (even at this slow speed) result in them living in two different 3-D worlds; one 3-D existence of the Andromeda Galaxy is simultaneous with Ruth (is in Ruth's world) and a different 3-D galaxy existence is simultaneous with Bill (is in Bill's world).

In Bill's 3-D world (one cross-section of the 4-D universe) the government somewhere in the galaxy is trying to decide whether to attack earth. In Ruth's 3-D world (a different 3-D cross-section of the 4-D universe) the decision has already been made and the attack is under way.

 

[Saw]

Is it possible for a particle to exist according to one reference frame and simultaneously not exist according to another?

The issue you refer to, which is a good one (at least I enjoy it), is in the end just a semantic challenge. Some people are very crafty to choose (and omit) the right words and thus phrase the matter so that it suggests something "crazy, alarming, unbelievable…". Thus they sell more books. But if you take a little time to think of it, you realize that there is nothing abnormal here and you can also choose the right words to settle that.

Whether a particle is created or destroyed is an event. In SR all frames agree on whether an event has happened or not. (Otherwise SR would be a bad theory, because theories are created for predicting events and if they do not, if they give out contradictory versions of reality, that means that they are wrong or misinterpreted.) It is true that different observers (reference frames) attach different time labels to each event, but those labels must be interpreted by those intelligent observers (isolatedly or in conjunction with other readings of their instruments) to infer the same events through the appropriate equations.

Take this example: a moun is created when a cosmic ray hits the atmosphere. At that time, the moun itself and an observer hovering in a spacecraft (at rest with the Earth) sync their clocks. The muon keeps racing towards the ground at close to the speed of light. Finally, before disintegrating, the muon hits the ground. Just before this collision, the muon consults its clock and it is time t1 in its muon-frame. An observer at the ground does the same and it is a little later, say t1+1, in the ground-frame. Please note that the moun's half-life in ground labs is t1-1. Should the ground observer start shouting that, before landing, the muon has ceased to exist "in his frame" and refuse to believe what his instruments show? No, what he does is combining his time measurement (dt = t1+1) with the fact that in his frame the moun has traversed a distance (dx). He does it through the SR's space-time interval formula. Thus he gets the proper time of the muon, which is less than a moun's half-life. Ok, that is why the moun is here, he infers. Conclusions: relativity of simultaneity solves the problem, rather than creating it.

In Bill's 3-D world (one cross-section of the 4-D universe) the government somewhere in the galaxy is trying to decide whether to attack earth. In Ruth's 3-D world (a different 3-D cross-section of the 4-D universe) the decision has already been made and the attack is under way.

So what? What is the problem?

I think that, whenever the Andromeda "paradox" is mentioned, one should also mention that there is no problem at all, no paradox. Otherwise it is misleading.

The attack was launched or not. That is an event, so it cannot be controversial in SR.

Let us assume the attack was launched. If that is simultaneous, in Ruth's frame, with her meeting Bill, that means the two events (the meeting and the launch of the attack) are spacelike, so there is no causal influence between them. In other words, if Bill (taking advantage of the fact that in his frame the attack has not yet happened) wanted to prevent it by sending a diplomatic message, the latter would not arrive in time for that purpose, because the distance would be too long for any infra-luminal or even luminal messenger to cover it before the time when the attack would also start according to Bill.

But what determines if the attack was actually launched or not? Well, it is precisely a bunch of situations like this. A bunch of events. Focus on any other situation of this sort that you can imagine and solve it according to these rules. You will realize that the story is the same in all frames.

 

[bobc2]

So what? What is the problem?

There is not problem at all. It is just a simple example implying that the universe is 4-dimensional, allowing different 3-D worlds as different cross-sections of that 4-D universe. Once the universe structure and ingredients of special relativity are understood all of the so-called paradoxes become obvious, and there are no paradoxes at all. And the events are what they are in space-time, and all observers will agree that those events are there.

 

[pervect]

It's both true and important that one's concept of now depends on one's state of motion - this is sometimes called the Andromeda paradox. However, the remark I made was to address something different.

With inertial frames , it is still true that every point in space-time has a unique set of coordinates. One observer will give an event coordinates (t,x), another the coordinates (t',x').

The Andromeda paradox just says that t is not necessarily equal to t'.

What I'm saying is different. I'm saying that if you consider all possible values of (t', x') and compute the corresponding values of (t,x), that you won't, in general, cover all of space-time.

This is related to the Rindler Horizon, which is an event horizon very similar to that of a black hole that is seen by an accelerating observer.

There's some disucssion of the rindler horizon online at http://gregegan.customer.netspace.net.au/SCIENCE/Rindler/RindlerHorizon.html, you'll also see it in GR textbooks such as MTW's "Gravitation".