Lessons From the Bizzaro Universe - Comments

[Chestermiller]

Greg Bernhardt submitted a new PF Insights post

Lessons From the Bizzaro Universe

Continue reading the Original PF Insights Post.

 

[Khashishi]

Greg Egan wrote a novel (or 3 novels!) set in the Bizzaro universe, or what he calls the Riemannian universe. His website goes over physics in the Riemannian universe in some detail. (a lot of detail, actually)
http://www.gregegan.net/ORTHOGONAL/ORTHOGONAL.html

 

[Chestermiller]

Greg Egan wrote a novel (or 3 novels!) set in the Bizzaro universe, or what he calls the Riemannian universe. His website goes over physics in the Riemannian universe in some detail.
http://www.gregegan.net/ORTHOGONAL/ORTHOGONAL.html

In my understanding, Riemannian universe focuses on the curvature of space time. The Bizzaro universe I have described assumes a flat spacetime, analogous to that encountered in Special Relativity.

 

[anorlunda]

I have to spend more time to digest it completely. But in the meantime, let me congratulate you @Chestermiller on your creative way to make a physics lesson fun. I must believe that it attracts more people to study the lesson. Of course, the #1 priority of any article on any subject must be to induce readers to read it.

 

[scottdave]

That was a fun read.

 

[kith]

Have there been attempts to teach special relativity by introducing spacetime rotations like in the insight first, and only switch to hyperbolic rotations (=Lorentz transformations) afterwards?

PS: I think that this thread would be better suited to the relativity forum because the insight is about a bizarro version of special relativity.

 

[Chestermiller]

Have there been attempts to teach special relativity by introducing spacetime rotations like in the insight first, and only switch to hyperbolic rotations (=Lorentz transformations) afterwards?

You made my day. This is exactly what I was hoping someone would suggest. Thank you so much.

 

[robphy]

Have there been attempts to teach special relativity by introducing spacetime rotations like in the insight first, and only switch to hyperbolic rotations (=Lorentz transformations) afterwards?

Taylor & Wheeler's Spacetime Physics uses Euclidean surveyors of a plane (not Bizzaro Spacetime observers) then suggests the Special Relativity case by analogy.
I've been working on a variation of that idea, but including the Galilean case as an intermediate stage.
(I've considered aspects of something like the Bizarro Spacetime... but not to the extent developed by @Chestermiller . It was entertaining. )

From my reading of the Insight, the "speed of light" c functions only as a unit conversion constant... but not an invariant limiting spatial velocity for observers.
There's no causal structure in the bizarro universe.. no invariant light cones (no eigenvectors of the boost).. But it does feature the Bizarro relativity of simultaneity (since tangents to "circles" don't coincide, except in the Galilean case).

 

[nikkkom]

Greg Bernhardt submitted a new PF Insights post

Lessons From the Bizzaro Universe
View attachment 223982

Continue reading the Original PF Insights Post.

If the fourth "time" coordinate is a space-like coordinate, (that is, it enters metric with the same sign as x,y,z terms, not with the opposite one), then it's just a 4-dimensional Euclidean space. This coordinate then must be treated on the equal footing with x,y,z. It can not be "time" anymore. "The 3D beings of the Bizzaro Universe cannot see into the time direction of their own rest frame" can not be fulfilled, just like in Minkowski space you can not arbitrarily prohibit "seeing into" a space-like direction (say, z).

The very reason our time dimension is "time" is because it enters metric with a "minus" and therefore behaves differently from x,y,z. For example, no matter how hard you turn away from t direction, you cannot completely stop moving in time, whereas you _can_ stop moving in x direction if you turn hard enough towards y or z.

 

[Chestermiller]

If the fourth "time" coordinate is a space-like coordinate, (that is, it enters metric with the same sign as x,y,z terms, not with the opposite one), then it's just a 4-dimensional Euclidean space. This coordinate then must be treated on the equal footing with x,y,z. It can not be "time" anymore. "The 3D beings of the Bizzaro Universe cannot see into the time direction of their own rest frame" can not be fulfilled, just like in Minkowski space you can not arbitrarily prohibit "seeing into" a space-like direction (say, z).

The very reason our time dimension is "time" is because it enters metric with a "minus" and therefore behaves differently from x,y,z. For example, no matter how hard you turn away from t direction, you cannot completely stop moving in time, whereas you _can_ stop moving in x direction if you turn hard enough towards y or z.

I'm beginning to get the feeling that you are not happy with the way that I have constructed and set rules for my Bizzaro universe. Since I am the great and all-powerful Bizzaro GOD, I can have any set of rules I desire for my Bizzaro Universe, and the 3D Bizzaro beings within it have to accept the reality of these rules. In other words, in the Bizzaro Universe, the laws of Physics are what I say they are. If you don't like that, stay out.

Bizzaro Universe: Love it or leave it.

 

[stevendaryl]

I'm beginning to get the feeling that you are not happy with the way that I have constructed and set rules for my Bizzaro universe. Since I am the great and all-powerful Bizzaro GOD, I can have any set of rules I desire for my Bizzaro Universe, and the 3D Bizzaro beings within it have to accept the reality of these rules. In other words, in the Bizzaro Universe, the laws of Physics are what I say they are. If you don't like that, stay out.

Bizzaro Universe: Love it or leave it.

An analogy that comes to mind is a special comic book with exactly one drawing per page. It's a three-dimensional object. There is a "time axis" that is the direction from the first page toward the last page. Characters move around in a two-dimensional world as function of the time coordinate (page number).

Where the analogy becomes difficult is that you want Euclidean distance to correspond to proper time. So you have a cast of comic characters on each page, and let's say that each character is drawn with a watch showing his or her own proper time. Then the writer/illustrator has a tough assignment:

1. Each character's 2-D location within a page must vary continuously as a function of page number (or approximately continuously, since you can't have a continuous function of a discrete coordinate).
2. For a character that is "at rest" (the same place on the page from one page to the next), the time on the watch increases linearly with the page number. Let the amount of increase from one page to the next be $\Delta t$.
3. For a character that is "moving", you compute the change on their wristwatch as follows: $\Delta t' = \Delta t \sqrt{1+(\frac{D}{d})^2}$ where $d$ is the thickness of a page, and $D$ is the distance the character moves from one page to the next.

I think that's a model of the Bizarro Universe.

 

[Chestermiller]

An analogy that comes to mind is a special comic book with exactly one drawing per page. It's a three-dimensional object. There is a "time axis" that is the direction from the first page toward the last page. Characters move around in a two-dimensional world as function of the time coordinate (page number).

Where the analogy becomes difficult is that you want Euclidean distance to correspond to proper time. So you have a cast of comic characters on each page, and let's say that each character is drawn with a watch showing his or her own proper time. Then the writer/illustrator has a tough assignment:

1. Each character's 2-D location within a page must vary continuously as a function of page number (or approximately continuously, since you can't have a continuous function of a discrete coordinate).
2. For a character that is "at rest" (the same place on the page from one page to the next), the time on the watch increases linearly with the page number. Let the amount of increase from one page to the next be $\Delta t$.
3. For a character that is "moving", you compute the change on their wristwatch as follows: $\Delta t' = \Delta t \sqrt{1+(\frac{D}{d})^2}$ where $d$ is the thickness of a page, and $D$ is the distance the character moves from one page to the next.

I think that's a model of the Bizarro Universe.

I don't follow this all in detail, but in the Bizzaro Universe, each 3D rest frame has its own private time direction in which the frame of reference is moving (relative to 4D Bizzaro space-time) at the velocity c. Differences in velocity perceived by 3D beings are the result of differences in the time directions (i.e., the directions of the 4D velocity vectors) of the various rest frames. If this is captured by the analogy that you have described, that would be great. So, in item 3, it seems that you have derived the equation for "time contraction" in the Bizzaro Universe (which should tell us something about the Bizzaro twin paradox).

I was hoping that other members would get interested, as you have done, in investigating other features of the Bizzaro Universe, like "length expansion," frame dependence of the speed of light, and acceleration trajectory shape. Anyone out there interested?

 

[nikkkom]

Since I am the great and all-powerful Bizzaro GOD, I can have any set of rules I desire for my Bizzaro Universe, and the 3D Bizzaro beings within it have to accept the reality of these rules.

If the rules (axioms) are not mathematically consistent, you can't derive meaningful theorems from them.

Your "time" coordinate is simply space-like. This completely determines how coordinates transform under rotations. There is no freedom to insert any additional rules. Your space is isomorphic to 4D Euclidean space.

 

[Chestermiller]

If the rules (axioms) are not mathematically consistent, you can't derive meaningful theorems from them.

Your "time" coordinate is simply space-like. This completely determines how coordinates transform under rotations. There is no freedom to insert any additional rules. Your space is isomorphic to 4D Euclidean space.

This does not prevent me from saying each 3D rest frame within my 4D Euclidean space has its own private time axis that is perpendicular to the other three Cartesian coordinates for that rest frame, and, unbeknownst to the 3D beings within that rest frame, the frame is traveling at the speed c through 4D Euclidean space; the 3D beings are somehow (by their biological makeup) unable to see into that 4th time dimension. The only way that the time direction (in 4D Euclidean space) of a body can change is if a force is applied to body to cause its time direction (and attached rest frame) to rotate.

 

[nikkkom]

This does not prevent me from saying each 3D rest frame within my 4D Euclidean space has its own private time axis that is perpendicular to the other three Cartesian coordinates

Why do you call this axis "time axis", if mathematically it enters metric symmetrically with other, "space" axes?
To be a time coordinate, its term has to enter metric with a different sign.

 

[Chestermiller]

Why do you call this axis "time axis", if mathematically it enters metric symmetrically with other, "space" axes?
To be a time coordinate, its term has to enter metric with a different sign.

I can call it whatever I want. It is the private direction assigned to each 3D rest frame moving through 4D Euclidean space at velocity c. If you don't like the word "time, " I'll call it the "shmime" direction. But changes in the shmimes exhibited on the watches of the beings in a given rest frame $\Delta \tau$ correspond directly to distances traveled by the rest frame through 4D Euclidean space, according to the equation $\Delta s=c\Delta \tau$.

 

[nikkkom]

I can call it whatever I want.

I'm not talking your right to call it however you want. I ask why do you treat it differently. Since this coordinate enters metric symmetrically with space-like coordinates, there is no logical reason to distinguish it.

 

[Chestermiller]

I'm not talking your right to call it however you want. I ask why do you treat it differently. Since this coordinate enters metric symmetrically with space-like coordinates, there is no logical reason to distinguish it.

I distinguish it by saying that each rest frame of reference has its own private time direction through 4D Euclidean space, and each object and frame of reference is always traveling at the velocity magnitude c in that direction (although the direction of a body in 4D Euclidean space changes when the body is accelerated). The magnitude can never change.

 

[Arthur Mitchell]

If objects such as galaxy's seen through telescopes (or naked eye) are measured, quantified, etc., isn't it conceivable that due to space/time, that the mass calculated may no longer exist?

 

[Chestermiller]

If objects such as galaxy's seen through telescopes (or naked eye) are measured, quantified, etc., isn't it conceivable that due to space/time, that the mass calculated may no longer exist?

Are you asking this about the Bizzaro Universe or about the actual universe? If you are asking this about the actual universe, it might be better to start a new thread on this question.

 

[Arthur Mitchell]

My question about the actual universe.Because of space/time, isn't it reasonable to assume that the objects we see such as galaxy's, no longer exist as such, and have been replaced by other matter, forming other galaxies?

 

[dagmar]

Well, I have made use of this model myself 25 years ago in my efforts to grasp SR. You are not first to think of this model.

But, what is this speed of light you are talking about? Have you realized that there is no such thing as speed of light in this model, yours and mine?

Here is a 2D example: an observer is moving with proper time the y-axis: He shines a beam of light, makes an angle θ = 45 degrees to horizontal x-axis, call this c=1. Now set him to travel himself at c=1. By yours and mine Borentz transformations the speed of light he is now emitting from his frame transforms to θ = 0 degrees to the horizontal = infinite speed, as measured again by an observer with proper time the y-axis. Completely analogous to the Lorentz addition of velocities ( rotations of axes, only speed of light remains constant there.)

So, no observer could ever decide which is the right speed of light since the light which is emitted by a moving frame varies in speed according to the velocity of this very moving frame each time. I doubt if light could ever exist in a universe with such properties.

Cheers, be good.

 

[Chestermiller]

Well, I have made use of this model myself 25 years ago in my efforts to grasp SR. You are not first to think of this model.

But, what is this speed of light you are talking about? Have you realized that there is no such thing as speed of light in this model, yours and mine?

Here is a 2D example: an observer is moving with proper time the y-axis: He shines a beam of light, makes an angle θ = 45 degrees to horizontal x-axis, call this c=1. Now set him to travel himself at c=1. By yours and mine Borentz transformations the speed of light he is now emitting from his frame transforms to θ = 0 degrees to the horizontal = infinite speed, as measured again by an observer with proper time the y-axis. Completely analogous to the Lorentz addition of velocities ( rotations of axes, only speed of light remains constant there.)

So, no observer could ever decide which is the right speed of light since the light which is emitted by a moving frame varies in speed according to the velocity of this very moving frame each time. I doubt if light could ever exist in a universe with such properties.

Cheers, be good.

Thanks Dagmar. I'm glad to see that I am not the only one to think of and play with this model. I thought there would be other interesting opportunities for interpretations, but no other members seemed to be interested in pursuing this. One particular situation I was interested in was "what would the kinematics of constant acceleration look like in terms of the trajectories of particles in the x-t plane?"

I did realize that there would be issues with the speed of light for this universe. I was just using the symbol c for a characteristic velocity of the system. I was more interested in other physical aspects of the Bizzaro Universe.

 

[dagmar]

"what would the kinematics of constant acceleration look like in terms of the trajectories of particles in the x-t plane?"

Well, the lines of constant acceleration in this model are just circles, like the lines of constant acceleration in the Minkowski plane are hyperbolas. I said like, because the radius of curvature of those hyperbolas in the Minkowski plane is constant, and constant acceleration is constant curvature so to speak.

Another analogy with 2D-Minkowski plane, is the law of addition of velocities: It is the old familiar $tan(θ+φ)=\frac{tanθ+tanφ}{1-tanθ tanφ}$, where $u=tanθ$, $v=tanφ$ play the role of velocities (θ and φ are the angles the worldlines make with the t-axis) with further analogies in 4 dimensions.

Well, for anyone who is not familiar with Lorentzian manfolds, your model is an excellent substitute to study the rotations of the plane ( boosts ) at an intuitive level which is the direct Geometric inspection and interpretation of our everyday world.

Of course there are some drawbacks with the inconstancy of the speed of light, and the backwards in time travel which pops out everywhere, but otherwise is an excellent model.