Velocity in Relativity: Theoretical Analysis of Multi-Dimensional Universes

[guptasuneet]

TL;DR

In Special Relativity, there is no absolute velocity (first derivative of displacement), but there is absolute acceleration (second derivative). Is a theoretical universe possible where even the first derivative is not absolute or where even second derivative is absolute?

There are several theoretical analyses of 2 dimensional or of multi-dimensional universes.

Now, we live in a special universe that follows Newton's first law (A body at rest or a body in motion shall continue to be at rest or in motion till acted upon by an external force), and consequently where there is no absolute velocity, insofar as there is no way to determine velocity of self. However, we can detect acceleration as an application of force., and an absolute acceleration can be detected and quantified.

My query is that can we have a theoretical universe where no absolute acceleration can be determined, i.e. where Newton's First Law could be paraphrased to 'A body in acceleration shall continue to accelerate unless acted upon by an external force?'

Or perhaps is it possible to have a Universe where even an absolute velocity is definable.

Has there been any theoretical analysis of such a universe, and are there any insights from the same?

 

[PeterDonis]

In Special Relativity, there is no absolute velocity (first derivative of displacement), but there is absolute acceleration (second derivative).

No. In relativity, the acceleration that is absolute (i.e., invariant) is not the second derivative of displacement with respect to time. That is coordinate acceleration, which is not absolute; it is frame-dependent in the same way that velocity is.

The acceleration that is absolute in relativity is proper acceleration, which is what an accelerometer attached to an object reads.

 

[Ibix]

The acceleration that is absolute in relativity is proper acceleration, which is what an accelerometer attached to an object reads.

Just to add - geometrically this is a measure of the curve of a worldline, which is a property of the worldline itself. Conversely, velocity is related to the angle the worldline makes with something else and position is about the distance of the worldline from something else. That's why proper acceleration is an absolute - it's defined with only the one path.

I'm not sure if anyone has ever seriously proposed a system of physics with an absolute velocity post Newton (Aristotle doesn't count!). Arguably Lorentz ether theory is one such, but the absolute velocity is undetectable and it turns out to be just relativity with extra unnecessary assumptions. I presume you could propose some system wherein physical laws depended on a velocity parameter, but how could you validate it? The world doesn't work that way, it appears.

 

[guptasuneet]

No. In relativity, the acceleration that is absolute (i.e., invariant) is not the second derivative of displacement with respect to time. That is coordinate acceleration, which is not absolute; it is frame-dependent in the same way that velocity is.

The acceleration that is absolute in relativity is proper acceleration, which is what an accelerometer attached to an object reads.

In our relativistic universe, there is no method to determine velocity of self without an external reference, which implies that there cannot be any absolute velocity. However, as you correctly point out absolute acceleration is the reading derived from an accelerometer attached to the object itself (i.e. without any external reference).

My query is that can we conceive of a theoretical universe, where it might not be possible to determine absolute acceleration, i.e. how would a universe behave in which even acceleration is relative, just like velocity is relative in our universe? Has there been any theoretical analyses of such a universe? Or is such a conception not feasible even theoretically?

 

[guptasuneet]

Just to add - geometrically this is a measure of the curve of a worldline, which is a property of the worldline itself. Conversely, velocity is related to the angle the worldline makes with something else and position is about the distance of the worldline from something else. That's why proper acceleration is an absolute - it's defined with only the one path.

I'm not sure if anyone has ever seriously proposed a system of physics with an absolute velocity post Newton (Aristotle doesn't count!). Arguably Lorentz ether theory is one such, but the absolute velocity is undetectable and it turns out to be just relativity with extra unnecessary assumptions. I presume you could propose some system wherein physical laws depended on a velocity parameter, but how could you validate it? The world doesn't work that way, it appears.

I am not claiming that our universe has any absolute velocity. That's been experimentally confirmed and validated.

I am just thinking theoretically here. Just like we can conceive of 1 and 2 dimensional universes or even multi-dimensional universes, is it possible to conceive of a universe with an absolute velocity? How would such a universe theoretically work? And yes, how would we validate the laws of such a system?

 

[PeterDonis]

Has there been any theoretical analyses of such a universe?

I'm not aware of any.

 

[Ibix]

Me neither. The only use for a non-relativistic model that I can think of is a test framework where you do something like say that $p=m\left(v+\alpha V^\beta\right)$, where $V$ is the "absolute velocity", and then estimate the constants $\alpha$ and $\beta$ from experiment. Showing that $\alpha=0$ plus or minus ten to the minus something large would be one formal way to show that we are in a relativistic universe and put limits on our certainty of that.

I don't know how you'd go about building such a framework (I just pulled that momentum formula out of nowhere with no justification). Perhaps one could write a Lagrangian that includes some absolute velocity term with a "strength" parameter and derive equations of motion...? Above my paygrade, I'm afraid.

 

[guptasuneet]

It was just a thought process on why the universe is the way it is. Similar to why we have 3 physically observable dimensions, or why we have 4 observed forces? But then the answer is perhaps the anthropogenic principle.

 

[PeterDonis]

It was just a thought process on why the universe is the way it is.

Without a well-defined alternative model of some other way the universe could have been, such speculations go nowhere.

 

[guptasuneet]

Without a well-defined alternative model of some other way the universe could have been, such speculations go nowhere.

I understand that. Let me try and think of some of the implications of an 'Absolute Velocity' universe (if I can).

 

[Prishon]

Summary:: In Special Relativity, there is no absolute velocity (first derivative of displacement), but there is absolute acceleration (second derivative). Is a theoretical universe possible where even the first derivative is not absolute or where even second derivative is absolute?

There are several theoretical analyses of 2 dimensional or of multi-dimensional universes.

Now, we live in a special universe that follows Newton's first law (A body at rest or a body in motion shall continue to be at rest or in motion till acted upon by an external force), and consequently where there is no absolute velocity, insofar as there is no way to determine velocity of self. However, we can detect acceleration as an application of force., and an absolute acceleration can be detected and quantified.

My query is that can we have a theoretical universe where no absolute acceleration can be determined, i.e. where Newton's First Law could be paraphrased to 'A body in acceleration shall continue to accelerate unless acted upon by an external force?'

Or perhaps is it possible to have a Universe where even an absolute velocity is definable.

Has there been any theoretical analysis of such a universe, and are there any insights from the same?

There is no absolute acceleration either. When you accelerate through empty space you might just as well at rest in a uniform gravity field in which all matter around you accelerates and you are at rest (though feeling a force). Likewise, the rotation of the Earth (considered absolute due to the centrifugal force present) can also be viewed as the rotation of ths universe.

 

[Ibix]

(though feeling a force).

...and hence undergoing proper acceleration since the four force is directly proportional to the four acceleration.

 

[Prishon]

...and hence undergoing proper acceleration since the four force is directly proportional to the four acceleration.

Indeed. But you don't get a velocity. Like you standing on Earth.

 

[Ibix]

Indeed. But you don't get a velocity. Like you standing on Earth.

That depends on how you define "at rest". An inertial body will see your velocity change, but a co-accelerating one will not. Either way you have proper acceleration, which is invariant which is a sensible interpretation of "absolute" in this context.

 

[PeterDonis]

Let me try and think of some of the implications of an 'Absolute Velocity' universe (if I can).

No. That would be personal speculation and is off topic here. If there were an actual peer-reviewed paper proposing such a model, we could possibly discuss it (but not in this forum, in either "Beyond the Standard Model" or "Other Physics Topics", depending on the model), but nobody knows of one.

 

[PeterDonis]

There is no absolute acceleration either.

Yes, there is: proper acceleration is absolute.

When you accelerate through empty space you might just as well at rest in a uniform gravity field in which all matter around you accelerates and you are at rest (though feeling a force).

Locally, yes, this is just the equivalence principle. But you cannot extend this to a global claim about the entire universe.

Likewise, the rotation of the Earth (considered absolute due to the centrifugal force present) can also be viewed as the rotation of ths universe.

No, this won't work; the equivalence principle is local, not global.

 

[Prishon]

No. That would be personal speculation and is off topic here. If there were an actual peer-reviewed paper proposing such a model, we could possibly discuss it (but not in this forum, in either "Beyond the Standard Model" or "Other Physics Topics", depending on the model), but nobody knows of one.

Doesn't every theory stems from personal speculation?

 

[PeterDonis]

Doesn't every theory stems from personal speculation?

Whether it does or not is irrelevant to the ground rules for PF discussion. The ground rules are that a model needs to be either mainstream physics, or at least a proposal that is being seriously considered by mainstream physics. What the OP was proposing clearly does not fall into either of those categories.

 

[PeterDonis]

The OP question has been answered. Thread closed.