Why doesn't relativity of simultaneity lead to a contradiction?

[m082844]

TL;DR Summary

Why doesn't relativity of simultaneity lead to a contradiction?

Three observers can agree upon a common definition of "now", but simultaneously claim a distant event occurs before, during, and after "now". Why is this not a contradiction? If it is one, then why not throw out relativity and go back to the drawing board?

I cannot get the following out of my head. Suppose this situation. Three frames, with varying velocities, simultaneously intersect their origins at the same time and place, making this point and time x0=0 and t0=0. These frames... let's call them observers. These observers have an agreed upon definition of "now" if "now" is t0 at x0. Each will claim the other will measure a different rate of time, sure, but they all agree on the same "now".

Ok now suppose an instantaneous distant event occurs such that each observer claims something different about the time of the even in relation to "now", for example, one says the distant event occurred before "now", one claims the event occurred during "now", and the last one claims the event occurred after "now". How is this not a contradiction? I understand abandoning absolute simultaneity, in favor of relativity of simultaneity, allows each observer to make contradictory claims about the distant event relative to "now"; however, this is still a contradiction. Accepting that contradictions exist isn't the same as resolving the contradiction.

Why do I say this is a contradiction. A contradiction is a specific concept with a specific formulation, if met, is known to be impossible to exist in reality. The formulation of a contradiction is something that is and isn't at the same time in the same respect. As an example, if I say a leaf is all red and all green, it will not be a contradiction if the leaf was green in the summer and red in the fall (the time relative to the color is referenced wasn't the same). It will not be a contradiction if two observes observe the leaf at the same time but at different velocities to the leaf (the respect is different). It will be a contradiction if it's at the claims about reality referenced the same time and the same respect.

Applying this to the relativity of simultaneity example. It follows the contradiction formulation perfectly. I'll group together the observer claiming during "now", and after "now" into "not before now" to make this clearer. So, two observers together claim the event is before and not before now as the same time in the same respect.

Why do I say the time and respect are the same? It's the same time because each observer is referencing the same definition of "now", so they are making a claim about reality relative to the same time in reality. It's the same respect, despite the similarity between this example and the leaf with velocity example. Both examples involved different observers with different velocities, true, but the respect was different in the leaf example because frequency depended on velocity, and the respects are the same here because of their shared definition of "now" doesn't depend on velocity. Velocity might affect the rate of time passing for each observer relative to "now", but their definition of "now" remains invariant between observers.

It'd be one thing to say one observer says the event was 5 min into the future of "now," and the other say 6 min into the future--this could be explained by their measuring sticks being different and the respects would be different in this case, and it wouldn't be a contradiction. But that's not what's happening. To say an instantaneous event exists before, and not before "now" is a different problem entirely from using different measuring sticks. Since each observer shares the same definition of "now" their claims of other things being relative to "now" is made in the same respect. An instantaneous event cannot exist before and not before another instantaneous event.

Relativity of simultaneity leads to a clear contradiction in my mind with this explanation. If this is true, it means the relativity of simultaneity is false. Since relativity of simultaneity is a direct consequence of the speed of light postulate, it means the speed of light postulate would be false too. Since relativity (both general and special) is based on the light postulate being true, it means relativity would be false.

If relativity is true, then how is it reconciled with this contradiction, or did I make an error in identifying it as a contradiction? What's the resolution? Mine is, I cannot overcome this contradiction for relativity, so relativity must be thrown out and I went back to the drawing board for the nature of the speed of light.

 

[Ibix]

The three frames agree what "now, here" means, but not what "now, over there" means. They've picked different 3d planes in 4d spacetime to call "now", that's all, and the three planes intersect at the time and place they call the origin. It's not really more mysterious than if three people stand in a circle all of them mean different things by "directly to my right".

 

[FactChecker]

Three frames, with varying velocities, simultaneously intersect their origins at the same time and place, making this point and time x0=0 and t0=0. These frames... let's call them observers. These observers have an agreed upon definition of "now" if "now" is t0 at x0. Each will claim the other will measure a different rate of time, sure, but they all agree on the same "now". Ok now suppose an instantaneous distant event occurs such that each observer claims something different about the time of the even in relation to "now", for example, one says the distant event occurred before "now", one claims the event occurred during "now", and the last one claims the event occurred after "now". How is this not a contradiction?

Exactly what fact is in contradiction? They are all in agreement about time in one spot, ##x_0##, at one time, ##t_0##. They disagree about time in other places, but that does not contradict their agreement about the time in the original spot, ##x_0##, at time ##t_0##.

 

[PeterDonis]

These observers have an agreed upon definition of "now" if "now" is t0 at x0.

That's not just "now". It's "here and now". All three observers are co-located at this event. But "now" involves not just that event, but other events, and if we pick some other event (with nonzero x) for which one observer assigns the time t0, the others will assign different times to that event. Or if we pick an event where the observers are not co-located, say observer #1 is still at x0 but at time t1 by his clock, the other observers will assign both different times and different x coordinates to that event.

 

[Dale]

These observers have an agreed upon definition of "now" if "now" is t0 at x0.

They don’t agree on “now”. That is what the relativity of simultaneity means. In the Lorentz transform $$t’= \gamma(t-vx/c^2)$$ So $$t’\rvert_{t=0}=-\gamma v x/c^2 \ne 0. $$ Meaning they do not agree on “now”.

As others mentioned, the most they can agree on is “here and now”.

This is not a contradiction, it is just something that is challenging for students to learn. We don’t accept or throw out scientific theories on the basis of whether they are difficult to learn. We accept or throw them out on the basis of how well they match experimental evidence. Relativity is accepted on that basis.

 

[ersmith]

Also note that the amount by which observers can disagree about the time between events depends on the distance between those events. For events that are close together in space and relatively far apart in time, all observers will agree on the order of the events: there can be no contradiction in causality. Such events are called "timelike" separated.

Only for events that are far apart in space and relatively close in time ("spacelike" separated events) can the observers disagree about the order of events. For such events nothing, not even light, can go between the events, and so it literally cannot matter which event came first -- neither one can influence the other. Thus no contradications can arise in practice, as long as the speed of light is the maximum rate for transmission of information (which both theory and many, many experiments indicate).

 

[m082844]

The three frames agree what "now, here" means, but not what "now, over there" means. They've picked different 3d planes in 4d spacetime to call "now", that's all, and the three planes intersect at the time and place they call the origin. It's not really more mysterious than if three people stand in a circle all of them mean different things by "directly to my right".

I don’t find this convincing unfortunately. It amounts to accepting contradictions exist.

I agree with you, using the relativity light model, they disagree as to the “now” over there… I believe this is the essence of relativity of simultaneity. It’s one thing if all agreed that the “now” over there were before “now” over here, but disagreed as to the degree—for example 6 min vs 10 min before now. In that case, it could be said the respect were different since the measuring sticks used were different. But the fact they disagree about whether “now” over there comes before and not before “now” over here is a strait up contradiction. “Now” over there cannot come before and not before “now” over here.

It’s not the same at all to everyone in a circle facing center (standing right side up) saying directly to my right means different things. Having the same definition of “now” means they have the same definition of after “now” and before “now”. Everyone in the circle has a different definition of “right”.

 

[PeterDonis]

I don’t find this convincing unfortunately.

Unfortunately, relativity has been confirmed by many, many experimental tests. So relativity is reality, and reality is not going to change. So your only option is to change your understanding.

It amounts to accepting contradictions exist.

It does no such thing. The mathematical model used in SR is perfectly consistent. It just isn't what you appear to think it is.

What actual math involved with SR have you encountered?

the relativity light model

What do you mean by the "relativity light model"?

the fact they disagree about whether “now” over there comes before and not before “now” over here is a strait up contradiction. “Now” over there cannot come before and not before “now” over here.

This is wrong. One of the consequences of SR is that the time ordering of spacelike separated events is frame dependent. Again, the mathematical model that shows this is perfectly self-consistent.

If you dig into the unexamined assumptions behind your claims quoted just above, you will find that at least one of them is not valid in SR. One of the most common stumbling blocks for people trying to understand SR is to not realize how many unexamined assumptions underlie the intuitions on which they are relying.

Having the same definition of “now” means they have the same definition of after “now” and before “now”.

Yes, but different inertial frames in relative motion in SR do not have the same definition of "now".

Again, the mathematical model that says this is perfectly self-consistent, and has a perfectly clear definition of what "now" means and how different inertial frames have different definitions of it.

Everyone in the circle has a different definition of “right”.

This is not a good analogy. A better one is that people facing in different directions have different definitions of "in front of me" and "in back of me"; their spatial coordinate axes are rotated relative to each other. Different inertial frames in SR have both their "space" and their "time" axes rotated in spacetime; their different definitions of "before now" and "after now" correspond to the people facing in different directions with different definitions of "in front" and "in back".

 

[robphy]

TL;DR Summary: Why doesn't relativity of simultaneity lead to a contradiction?

Three observers can agree upon a common definition of "now", but simultaneously claim a distant event occurs before, during, and after "now". Why is this not a contradiction? If it is one, then why not throw out relativity and go back to the drawing board?

Relativity of simultaneity leads to a clear contradiction in my mind with this explanation. If this is true, it means the relativity of simultaneity is false. Since relativity of simultaneity is a direct consequence of the speed of light postulate, it means the speed of light postulate would be false too. Since relativity (both general and special) is based on the light postulate being true, it means relativity would be false.

If relativity is true, then how is it reconciled with this contradiction, or did I make an error in identifying it as a contradiction? What's the resolution? Mine is, I cannot overcome this contradiction for relativity, so relativity must be thrown out and I went back to the drawing board for the nature of the speed of light.

In the spirit of Minkowski's "spacetime geometry" reformulation of special relativity,
consider the Euclidean analogue of your question.

Consider a family of concentric circles with three radial surveyors meeting at its center.
When a surveyor meets a circle, consider that surveyor's tangent line.
A surveyor assigns coordinates (t,y),
where t is the radius of that circle
and y is the distance along that tangent line from the surveyor,
using a long ruler that the surveyor carries tangent to the circles.

From the diagram below, the three surveyors assign different t-values for the black point.
When GREEN assigns t = 1,
then RED assigns t < 1
and BLUE assigns t > 1.

Is this a contradiction? Should one reject Euclidean geometry?

The Minkowski version of this situation addresses relative simultaneity in special relativity.
While special relativity has a lot of non-intuitive features,
its predictions agree quite well with experimental results,
compared to predictions based on Galilean physics.

 

[Dale]

But the fact they disagree about whether “now” over there comes before and not before “now” over here is a strait up contradiction. “Now” over there cannot come before and not before “now” over here

And yet, nature is relativistic, as confirmed by many experiments. So since nature is relativistic and you (wrongly) believe that relativity is contradictory, then your conclusion must be that nature is contradictory.

What is actually happening is that your idea of “now” is simply not part of nature. Nature cares about cause and effect, not about simultaneity. Causes must precede effects, nature enforces that. But nature simply does not enforce the human concept of “now”.

 

[m082844]

Unfortunately, relativity has been confirmed by many, many experimental tests. So relativity is reality, and reality is not going to change.

I wasn’t trying to be snarky I was trying to be empathetic, you’re being rude and pompous. Please tone it down if you want to continue conversing.

The available evidence supports both special relativity and Lorentz ether theory, and relativity is based on an unverified assumption that might be wrong (its light postulate). The one-way speed of light has never been measured.

It does no such thing. The mathematical model used in SR is perfectly consistent.

Even a perfectly consistent model that produces contradictions cannot be true.

What do you mean by the "relativity light model"?

The constancy of the speed of light in all inertial frames.

This is wrong. One of the consequences of SR is that the time ordering of spacelike separated events is frame dependent. Again, the mathematical model that shows this is perfectly self-consistent.

If you dig into the unexamined assumptions behind your claims quoted just above, you will find that at least one of them is not valid in SR. One of the most common stumbling blocks for people trying to understand SR is to not realize how many unexamined assumptions underlie the intuitions on which they are relying.


Yes, but different inertial frames in relative motion in SR do not have the same definition of "now".

Sure they do, whenever they are at the same time and place. Perhaps you don’t like my use of the word “now” to represent this case. Let’s make it the origin and call this time t0 instead. Different observers claim an instantaneous distant event comes before during and after t0, a clear contradiction as it is a claim that something is and isn’t at the same time in the same respect.

 

[ersmith]

But the fact they disagree about whether “now” over there comes before and not before “now” over here is a strait up contradiction. “Now” over there cannot come before and not before “now” over here.

I think you may want to step back and think carefully about what, exactly, "now" means. It's not some mystical thing: it's simply a set of events with the same time coordinate. What relativity teaches us is that the time coordinate is very much like the three spatial coordinates (and indeed related to them, albeit in a slightly complicated way expressed by the Lorentz transformation).

There's nothing special about the spacetime plane x=0, I'm sure you'd agree: there's no particular contradiction if one observer assigns coordinates such that an event has x > 0 and another assigns them such that x' < 0. We're entirely comfortable with the fact that "here" is observer dependent, and means different things on a "moving" train and on a "stationary" platform.

The fact is that in the universe we live in, "now" also means different things on the train and on the platform. Again, this is just a statement about coordinates. What contradiction do you think arises by the observers assigning different coordinates? What's so special about time, in your view? If you think very carefully about this, you'll find that you're implicitly assuming that if different observers have different nows then they will disagree about causality. But that's not true in relativity: everyone will agree about actual causes and effects, and only disagree about the order of events that cannot affect one another.

 

[m082844]

And yet, nature is relativistic, as confirmed by many experiments. So since nature is relativistic and you (wrongly) believe that relativity is contradictory, then your conclusion must be that nature is contradictory.

What confirming experiments do you mean? I don’t think any exists that confirms special relativity over Lorentz ether theory.

What is actually happening is that your idea of “now” is simply not part of nature. Nature cares about cause and effect, not about simultaneity. Causes must precede effects, nature enforces that. But nature simply does not enforce the human concept of “now”.

It is wrong according to the relativity model of light and the belief that contradictions exist.

 

[PeterDonis]

The available evidence supports both special relativity and Lorentz ether theory

You need to read this:

https://www.physicsforums.com/insights/pfs-policy-on-lorentz-ether-theory-and-block-universe/

 

[PeterDonis]

Even a perfectly consistent model that produces contradictions cannot be true.

A perfectly consistent model cannot produce contradictions. The definition of "consistent" is that there are no contradictions.

Perhaps you don’t like my use of the word “now” to represent this case.

Both I and @Dale have already pointed out that "here and now" is the proper way to refer to what you are talking about, namely, a single point (event) in spacetime that is the spacetime origin of multiple inertial frames in relative motion.

 

[Dale]

What confirming experiments do you mean? I don’t think any exists that confirms special relativity over Lorentz ether theory.

Indeed, LET is one common interpretation of special relativity (the other being the block universe), so there can be no experimental discrimination between them. However, that doesn’t fix your issue. Different frames disagree on simultaneity in Lorentz aether theory too. You cannot avoid this specific problem with an appeal to LET. It is part of the Lorentz transform, which is the basis of LET.

It is wrong according to the relativity model of light and the belief that contradictions exist.

What are you saying here? Are you saying that you believe contradictions exist?

Relativity does not produce contradictions. If you disagree then please support your claim with a reference from the modern professional scientific literature. Personal speculation is not permitted here.

 

[PeterDonis]

Thread closed for moderation.

 

[Dale]

The OP continued to post statements with no support in the professional scientific literature. So their recent post is deleted and the thread will remain closed.