Why is Time Relative? - Understand the Concept

[JesseM]

Remember Rach3 this discussion was triggered by your statement that:

Simultaneity does not exist. Two events may seem simultaneous in one inertial frame, and not simultaneous in other; in fact observers will not generally agree on the order of events, depending on their relative motions.

Do you disagree with Rach3's statement here? It's true that in the special case of two events at the same point in spacetime, all frames will agree that they are simultaneous, but Rach3 said that "Two events may seem simultaneous in one inertial frame, and not simultaneous in other" and "observers will not generally agree on the order of events". Both these statements would be true if you pick any two events that do not occur at the same point in spacetime, so as general statements they are correct, even if there is a special case where all frames agree on simultaneity.

Analogously, if I said "a clock that is running slower than another clock in one inertial frame may be running faster in another inertial frame", or "observers will not generally agree on which of two clocks is running slower", these statements would be correct as well, even though in the special case where the two clocks are at rest with respect to each other, all inertial frames would say they both tick at the same rate.

 

[Rach3]

Well it seems what is trivial for one is of great significance for an other.

It is trivial! It's a logical tautology! An event is simultaneous with itself, because it is itself, what is so amazing about this?

In fact all particle interactions are nothing more than a crossing of wordlines, in other words, events.

How do you think this is relevant to simultaneity of two events?

 

[MeJennifer]

Do you disagree with Rach3's statement here?

Yes, two colliding particles is simultaneity!

If you and I meet at the same time and at the same Starbucks for a coffee tomorrow then we have simultaneity. We are both at the same time and at the same place.

"Two events may seem simultaneous in one inertial frame, and not simultaneous in other" and "observers will not generally agree on the order of events". Both these statements would be true if you pick any two events that do not occur at the same point in spacetime, so as general statements they are correct, even if there is a special case where all frames agree on simultaneity.

The whole concept of simultaneity for spacelike events is a rather mute point, pretty meaningless, since there is no causal relationship possible.

So what that the spacelike "3D plane of simultaneity" or the "tilt of space" for a wordline is different from frame to frame? That's why it is called relativity.

Analogously, if I said "a clock that is running slower than another clock in one inertial frame may be running faster in another inertial frame", or "observers will not generally agree on which of two clocks is running slower", these statements would be correct as well, even though in the special case where the two clocks are at rest with respect to each other, all inertial frames would say they both tick at the same rate.

Well, in my opinion, the whole idea of "clocks running slower" and "rods getting smaller" is really a misconception of what is happening.
Clocks and rods don't change just because someone else measures them from another frame!

For object A and B in relative and constant motion with each other, nothing factually happens whatsoever with their clocks and rods, nothing! It is simply due to the fact that they are in relative motion with each other which causes them to travel through a tilted space.
For an accelerated frame versus an inertial frame it is the case that the object in the accelerated frame acquires less time than the object in the inertial frame.

 

[JesseM]

Yes, two colliding particles is simultaneity!

It is a single event, which like all single events is simultaneous with itself. But two separate events with a spacelike separation that have the same time-coordinate in a given frame is also an example of simultaneity, and it is this sort of example, not a single-event example, that you will invariably find in any physics textbook which discusses the issue of simultaneity--do you disagree?

The whole concept of simultaneity for spacelike events is a rather mute point, pretty meaningless, since there is no causal relationship possible.

But this is what physicists mean when they use the word simultaneity! You can't just make up your own definitions of words that have an accepted meaning in physics! If you think the concept is pointless, that's your opinion, but the fact is that that's what the word is understood to mean. If you want to invent a new term to deal exclusively with events that happen at a single point in spacetime, then go right ahead, but don't call it "simultaneity", that term is already taken.

Well, in my opinion, the whole idea of "clocks running slower" and "rods getting smaller" is really a misconception of what is happening.
Clocks and rods don't change just because someone else measures them from another frame!

Of course not, but the phrase "clocks running slower" does not imply they do. All it means is that the number of clock-ticks per coordinate time is smaller for a clock with a higher velocity in that coordinate system. It's a coordinate-dependent concept, just like velocity itself.

Do you have a problem with any discussion of coordinate-dependent concepts? Would you also reject the statement "the speed of light is the same for all observers", for example, since speed itself is a completely coordinate-dependent notion?

 

[Rach3]

It is really frustrating that you persist in using your own, non-standard terminology to the confusion of everyone else including yourself.

Yes, two colliding particles is simultaneity!

If you and I meet at the same time and at the same Starbucks for a coffee tomorrow then we have simultaneity. We are both at the same time and at the same place.

No, you're several meters apart over a very extended time interval measured in minutes or hours. You're trying to force colloquial usage of words over their exact, well-defined physics usage.

 

[MeJennifer]

Do you have a problem with any discussion of coordinate-dependent concepts?

Not at all.

But take for instance the 3D plane of simultanuity. What is the use, really, it is afteral spacelike separated!

It only becomes practical when a bunch of photons from an object that is X million light years away, reaches your eye. Before that, and here is a coordinate dependent concept for you, it simply does not exist!
But when the photon worldlines and the worldlines of your eyes cross then we have something we can measure, then we have a space-time event.

Would you also reject the statement "the speed of light is the same for all observers", for example, since speed itself is a completely coordinate-dependent notion?

Actually it is worse with speed, rapidity would be much more suitable in coordinate dependent concepts.

 

[MeJennifer]

It is really frustrating that you persist in using your own, non-standard terminology to the confusion of everyone else including yourself.
No, you're several meters apart over a very extended time interval measured in minutes or hours. You're trying to force colloquial usage of words over their exact, well-defined physics usage.

I am sure you know what I mean, it was meant to explain something.
And talking about persisting in using one's own standards, you claimed that simultaneity did not exist remember?

Again, I have no problem whatsoever from the perspective of space-time to consider the crossing of two or more worldlines a simultaneity.

Anyway, no problem, I am wrong, and you guys are right.
Sorry to have frustrated you!

 

[JesseM]

But take for instance the 3D plane of simultanuity. What is the use, really, it is afteral spacelike separated!

It only becomes practical when a bunch of photons from an object that is X million light years away, reaches your eye. Before that, and here is a coordinate dependent concept for you, it simply does not exist!

As a practical matter at that moment, sure. But retroactively you can assign coordinates to events once the light from them has reached you...it would be very difficult to calculate anything physical in relativity without using some coordinate system, and for a given observer the coordinates of distant events can only be assigned in retrospect. Do you know of a way to restate the theories of SR and/or GR in a way that doesn't use a coordinate system at all, and only refers to the times that light from distant events reaches your worldline, yet still has all the same predictive power as the usual coordinate-dependent formulations of these theories? Maybe such a thing would be possible, but mathematically I imagine it would be a lot more complicated.

In any case, you didn't tell me if you agree or disagree with my earlier statement:

But two separate events with a spacelike separation that have the same time-coordinate in a given frame is also an example of simultaneity, and it is this sort of example, not a single-event example, that you will invariably find in any physics textbook which discusses the issue of simultaneity--do you disagree?

Assuming you agree that the accepted definition of simultaneity in physics does indeed deal with events that have a spacelike separation, would you also agree that when having a discussion about physics, it is best to use the accepted definitions of scientific terms rather than one's own idiosyncratic definitions, regardless of whether or not the standard definition appeals to your sense of aesthetics or utility?

 

[MeJennifer]

So do you think these two statement can both be true:

"...two separate events with a spacelike separation that have the same time-coordinate in a given frame is also an example of simultaneity, and it is this sort of example, not a single-event example, that you will invariably find in any physics textbook which discusses the issue of simultaneity "

"Simultaneity does not exist. Two events may seem simultaneous in one inertial frame, and not simultaneous in other; in fact observers will not generally agree on the order of events, depending on their relative motions."

They both make sense?

Anyway I am prepared to surrender to both of you.

 

[JesseM]

They both make sense?

Sure, provided you interpret the sentence "simultaneity does not exist" to mean "absolute simultaneity does not exist". With that understanding, do you think there are any other inconsistencies between the two quotes?

 

[MeJennifer]

Sure, provided you interpret the sentence "simultaneity does not exist" to mean "absolute simultaneity does not exist". With that understanding, do you think there are any other inconsistencies between the two quotes?

Well seems we are back to square one
I think that absolute simultaneity does exist.
They are crossing wordlines in space-time! For instance when two particles collide we have an absolute simultaneity in space-time.
They meet, at the same time and at the same place!

The other simultaneity, e.g. the spacetime separated 3D plane of simultaneity is not physical, it is a (re)construction. useful for calculations, but again not physical! It is spacetime separated!

 

[Rach3]

Well seems we are back to square one, because I think that absolute simultaneity does exist.
They are crossing wordlines in space-time! For instance when two particles collide we have an absolute simultaneity in space-time.

But that is meaningless! A collision is a single event, there's nothing to be simultaneous about!

 

[JesseM]

Well seems we are back to square one, because I think that absolute simultaneity does exist.
They are crossing wordlines in space-time! For instance when two particles collide we have an absolute simultaneity in space-time.
They meet, at the same time and at the same place!

That is indeed a particular example where all frames agree on simultaneity. But the phrase "absolute simultaneity" is understood to refer to an objective general notion of simultaneity that can be used to decide if an arbitrary pair of events are simultaneous or not. Again, the accepted definition of simultaneity is that it deals with arbitrary pairs of events, not solely with events at a single point in spacetime. Do you agree that this is the standard meaning?

 

[JesseM]

But that is meaningless! A collision is a single event, there's nothing to be simultaneous about!

A collision is a single event, but there are cases where you could talk about two events happening at the same point in spacetime--for example, if you have two clocks that meet at a single point, and at the moment they meet the first clock reads 2:00 while the second reads 3:00, then the separate events of "the first clock reads 2:00" and "the second clock reads 3:00" occur at the same point in spacetime.