B Prove the velocity of a moving object is absolute in one IRF?

[ESponge2000]

TL;DR Summary

Or is this also not absolute?

If we cannot assert that the speed of light in a vacuum is isotropic without adapting synchronization of choice,

then doesn’t this not only affect that clocks at in one IRF /different locations /lack an absolute method of synchronization,
But also doesn’t this say something about the meaning of a velocity ? Any distance / time?

Let’s assume a world where it is secretly revealed that traveling West to East there is speed of light instantaneous, and in the reverse direction a c/2 velocity .

Now let’s assume this applies to an arbitrary point in space and east and west assume are linear flat

Now …. Let’s assume there’s 2 cars, one traveling east and one traveling West and they each assess to be traveling at 80% of C relative to a stationary point which is a parcel of air at rest with the grid … the grid line where light is instantaneous eastbound and c/2 westbound

Each car measures the velocity of the other and at a point they zoom past each other very fast , one moving west and one moving east

Now you are given

1. Car 1 and Car 2 originated in the same IRF but very far apart along east west line.

2. Car 1 And car 2 undergo the same level of energy release and same changes in inertia relative to each their own clocks , but moving towards each other and ultimately passing each other by


3. Using standards physics the way we do special relativity, car 1 calculates to have reached v/c = 80%

If car 2 is moving west to east then what velocity is 80% of speed of light if in that direction light travels instantly and halved the other direction?

Next, let’s assume we got tricked . The point we thought was at the origin of the differences in speeds of light was after all not correct , this wouldn’t affect the math or any observations . But wouldn’t it still interplay in calculating a true velocity of object 1 relative to object 2?

 

[berkeman]

Let’s assume a world where it is secretly revealed that traveling West to East there is speed of light instantaneous, and in the reverse direction a c/2 velocity .

https://www.physicsforums.com/insights/how-to-avoid-breaking-physics-with-your-what-if-question/

 

[ESponge2000]

The point though is what makes it possible to measure an absolute velocity of any object even in a single reference frame once the velocity is high enough for special relativistic effects to matter? Or is there no such thing in physics as a “true velocity even in a single reference frame?”

A velocity is a length over a clock time interval and conventionally where the length is measured in the same point as the location of the clock.

We have an absolute length in a single rest frame. For example 2 points at rest with each other and we are at rest with the 2 points , there is a valid length between the 2 points in this rest frame.

But now we want to measure a velocity, any velocity, not the speed of light, it can be a fast car or a fast train … we can start the clock when it passes us and then It moves at linear constant velocity … if we don’t know what the time is for us when it actually reaches another location, and only we know what time it is at the other location when it passes the other location, Then we don’t have enough information to calculate the known distance over an unknown time interval, and therefore we don’t know the object’s velocity, right? (We don’t know have a way to assign a time at our location for an event at a distant location. , so We have d / unknown time interval = velocity

Or easier suggestion, the moving object has a clock and at constant velocity relative to stationary object , stopwatch begins when passing the stationary object and stop the stopwatch when it reaches a second location a known length distance upon itself ….

I at first feel like this velocity is absolute or is it? Or does the Lorentz transformation apply to the convention of choice which itself maps differently to velocity depending on “the synchronization convention “ and again we don’t have an absolute velocity ? Because we can calculate the length contraction with absolute math , And we would be able to use the same ship’s clock , But here we would have a known velocity for a different IRF which would not tell
Us anything about the velocity from the other IRF, or would it ?

 

[ESponge2000]

The speeds scale the same, so something travelling at 0.8c as usually measured is doing 0.8 times whatever your definition of the anisotropic speed of light is in the direction it's going.

But what is 80% of infinity ? Maybe I’m very confused
Assume speed of light c/2 in one direction and infinity in the other

In the direction the speed of light is infinity , “going faster than c” would not equate going faster than the speed of light , so does this mean an object still
Can’t go faster than c? Or does this mean the object can go infinitely fast in one direction and can’t reach or exceed 93,000 miles per second in the other ?

In this scenario what is the velocity that will produce the effects that under Einstein synchronization would give us v = 80% of c?

 

[phinds]

But what is 80% of infinity ?

an amount that suggests that you have made an invalid assumption

does this mean an object still
Can’t go faster than c?

Uh ... well, it probably has to since nothing can go faster than c.

 

[weirdoguy]

I at first feel like this velocity is absolute or is it?

How many threads repeating this claim, and people refuting it, are you going to post? You've been told the answer repeatedly, on many occasions. That's very disrespectful for everyone who tried to help you.

 

[Ibix]

But what is 80% of infinity ?

In that case one of your "spatial" axes is actually null and I don't think you can really define "speed" in that coordinate system. You'd need to think carefully about how most physical quantities were expressed in that system - it's already full of subtlety just by picking an anisotropic form, but it gets worse if you pick an anisotropic form with one null and one timelike coordinate.

 

[ESponge2000]

an amount that suggests that you have made an invalid assumption

Uh ... well, it probably has to since nothing can go faster than c.

But is it that nothing can travel faster than the speed of causality, or is it that nothing can travel faster than 186,000 miles per second ?

 

[Ibix]

But is it that nothing can travel faster than the speed of causality, o

Nothing can leave the future light cone of any event on its past worldline, would be the formal statement that generalises to curved spacetime as well.

 

[Ibix]

Or "nothing can overtake a light ray (edit: in vacuum), no matter how you screw around with the maths".

 

[ESponge2000]

Nothing can leave the future light cone of any event on its past worldline, would be the formal statement that generalises to curved spacetime as well.

So maybe let’s make this simpler. Let’s adopt a convention of choice that all of the time it takes a light beam to travel round trip is in just one direction and not the other …. Using special relativity math under this alternative model of how the universe works , What velocity in miles per second would be obtained such that the Lorentz factor is 1/0.6 ?

 

[pbuk]

A velocity is a length over a clock time interval and conventionally where the length is measured in the same point as the location of the clock.

Here lies the origin of your misunderstanding: velocity does not involve any length or time interval.

Velocity is the rate of change of position with respect to time: to understand the significance of this you need to learn calculus.

The 'velocity' you are talking about (distance divided by time) is actually average speed and is not a very useful thing in the context of special relativity.

 

[Ibix]

Using special relativity math under this alternative model of how the universe works , What velocity in miles per second would be obtained such that the Lorentz factor is 1/0.6 ?

As I already said, that's got a null coordinate and I don't think you can even define speed in that system.

 

[ESponge2000]

Here lies the origin of your misunderstanding: velocity does not involve any length or time interval.

Velocity is the rate of change of position with respect to time: to understand the significance of this you need to learn calculus.

The 'velocity' you are talking about (distance divided by time) is actually average speed and is not a very useful thing in the context of special relativity.

This is helpful ! There we go

 

[ESponge2000]

As I already said, that's got a null coordinate and I don't think you can even define speed in that system.

I thought SR is compatible with any convention that allows for roundtrip average speed in all IRF to be 186,000 miles per second though. And the same acceleration effects for instance would have the same consequences.

An object traveling a certain velocity from earth will age 3 years traveling an apparent distance from earth perspective to be 4 light years. Of the be object does the trip in the reverse direction (towards earth), the same length and the same passage of time for ship …. But if we don’t assume isotopic speeds of causality we don’t have a proper velocity measurement being the same for each leg of the trip… we do have that the same level of acceleration and being shoved against the back of the ship due to extreme changes in speed would be the same no matter what direction we travel the same length , but velocity seems to have no meaning

 

[Ibix]

I thought SR is compatible with any convention that allows for roundtrip average speed in all IRF to be 186,000 miles per second though.

SR is compatible with much more outré coordinate systems than the one you're considering. But that does not mean that you can take coordinate differences and divide them (which is what you're doing to get a speed here) and get a meaningful answer.

More generally, we almost always use orthogonal coordinates (if we can) because the interpretation of components of vectors is straightforward. You're tripping over the extra mathematical complexity here because you really need to use the full tensor formalism in non-orthogonal coordinate systems, and you aren't.

 

[Ibix]

but velocity seems to have no meaning

You can define velocity; it just isn't plausible to define it as a ratio of vector components any more when you're using null coordinates.

 

[pbuk]

@ESponge2000 you seem to have posted many threads which indicate that you have started to think about special relativity. This is a good thing, as it introduces you to a fascinating subject, but before you can start asking meaningful questions about any aspect of physics you need to understand the mathematics involved and use it to express your thoughts mathematically.

Just throwing words like like "proper velocity" and "Lorentz factor" around is not physics, and it is not helping you understand anything.

Or in other words:

You're tripping over the extra mathematical complexity here because you really need to use the full tensor formalism in non-orthogonal coordinate systems, and you aren't.

 

[Ibix]

The speeds scale the same, so something travelling at 0.8c as usually measured is doing 0.8 times whatever your definition of the anisotropic speed of light is in the direction it's going.

I got the maths wrong above. Shouldn't reply while cooking.

Consider an isotropic system. A radar pulse emitted at the origin at t=-l/c bounces off an object at x=l, t=0, and returns to the origin at t=l/c. Now consider the same thing in an anisotropic system - we simply add some $\Delta t$ to the reflection time, but the emission and return times are unaffected. So the coordinate speed of light in this system is $l/(l/c\pm\Delta t)$. As long as $|\Delta t <l/c$ x is a spacelike coordinate, but there's nothing actually wrong with a larger $|\Delta t|$ except for increasingly strange behaviour of the coordinates.

Now consider an object leaving the origin at a speed the isotropic system calls $v$. It arrives at $x=l$ at time $l/v$. In the anisotropic system it arrives at time $l/v+\Delta t$, so its coordinate speed is $l/(l/v+\Delta t)=vl/(l+v\Delta t)$, or $vl/(l-v\Delta t)$ in the opposite direction. So in the case that $\Delta t=l/c$, an arbitrary velocity $v$ in the isotropic system maps to $v/(1\pm v/c)$, with the sign depending on the direction.

 

[PeterDonis]

The very title of this thread contains a fundamental error: there is no such thing as "absolute in one IRF". The very idea makes no sense.

 

[PeterDonis]

is there no such thing in physics as a “true velocity even in a single reference frame?”

There isn't.

 

[PeterDonis]

The OP question is based on a fundamental error, which has now been corrected. Thread closed.

 

[Dale]

I thought that it might be helpful, for future reference, to show how the substance of this question could be answered using Anderson’s convention.

If we cannot assert that the speed of light in a vacuum is isotropic without adapting synchronization of choice,

then doesn’t this not only affect that clocks at in one IRF /different locations /lack an absolute method of synchronization,
But also doesn’t this say something about the meaning of a velocity ? Any distance / time?

Yes. An anisotropic speed of light convention will make all one way speeds anisotropic. Any one way speed depends on the synchronization convention.

Let’s assume a world where it is secretly revealed that traveling West to East there is speed of light instantaneous, and in the reverse direction a c/2 velocity .

There is no need for any “secretly revealed” thing. We can just choose a simultaneity convention with Anderson’s $\kappa=1$.

Now let’s assume this applies to an arbitrary point in space and east and west assume are linear flat

Now …. Let’s assume there’s 2 cars, one traveling east and one traveling West and they each assess to be traveling at 80% of C relative to a stationary point which is a parcel of air at rest with the grid … the grid line where light is instantaneous eastbound and c/2 westbound

Each car measures the velocity of the other and at a point they zoom past each other very fast , one moving west and one moving east

Now you are given

1. Car 1 and Car 2 originated in the same IRF but very far apart along east west line.

2. Car 1 And car 2 undergo the same level of energy release and same changes in inertia relative to each their own clocks , but moving towards each other and ultimately passing each other by


3. Using standards physics the way we do special relativity, car 1 calculates to have reached v/c = 80%

If car 2 is moving west to east then what velocity is 80% of speed of light if in that direction light travels instantly and halved the other direction?

The transform between an Einstein synchronized frame and an Anderson frame is: $$T=t-\kappa x/c$$$$X=x$$$$Y=y$$$$Z=z$$ where the capitalized coordinates are Anderson’s and the lower-case coordinates are Einstein’s.

From this you can calculate that $$V=\frac{dX}{dT}=v\frac{1}{1-\kappa v/c}$$ where $v=dx/dt$. So for your scenario with $\kappa=1$ and $v=\pm 0.8 c$ we get the speed in the "fast" direction is $V=4 c$ and the speed in the "slow" direction is $V=-0.444 c$.

Next, let’s assume we got tricked . The point we thought was at the origin of the differences in speeds of light was after all not correct , this wouldn’t affect the math or any observations . But wouldn’t it still interplay in calculating a true velocity of object 1 relative to object 2?

What you are describing here is not anisotropy, it is inhomogeneity. There isn’t a point where the one way speed of light changes, it is a direction.