Is Time Dilation Relative in Special Relativity Experiments?

[ghwellsjr]

I'm not 'trying' to learn anything new in the 'scientific' sense I am trying to understand something 'theoretically' or philosophically. frankly despite my appreciation of how generous folks on physicsforums are, this consistent retort always annoys me and makes me want to actually study physics so I can reach philosophers and the general public a bit more succinctly.

"Relative velocity is the speed of one object in the rest frame of another object" how is this relative velocity as opposed to relative speed? I don't understand. However even though I ask this I am starting to get a sense why most physicists approach velocity (speed and direction) as a very composite entity such that certain questions are not really wanted in the manner that I ask them.

Sorry, I should have said "Relative velocity is the velocity of one object in the rest frame of another object" as the wikipedia link says.

Speed is the magnitude of velocity. Between non-inline objects, you need to describe the relative velocity which includes the magnitude of the speed and its direction. For inline objects, you already know the direction (by definition) so you can talk just about the speed.

 

[objecta99]

Its like in quantum mechanics where you cannot define speed and position simultaneously?? My point is that when I asked this question on these forum in this thread: "basically what I am wondering is can two velocities relative to each other have different velocities under SR and relative to each other" I was told:

"No."

So while I understand that speed is a magnitude that can be compared between two objects in a single reference frame and between two objects traveling in the same direction especially as necessary to define their relative velocity, what does that explicitly say about how we understand velocity simpliciter or velocity in itself where this is a relation not analogous to speed. I find it to be different from either direction alone as in the case of two speeds moving away on the same axis or between two directions with different speeds. velocity is of a different sort on my hunches.

 

[PeterDonis]

Its like in quantum mechanics where you cannot define speed and position simultaneously??

No.

speed is a magnitude that can be compared between two objects in a single reference frame and between two objects traveling in the same direction especially as necessary to define their relative velocity, what does that explicitly say about how we understand velocity simpliciter or velocity in itself where this is a relation not analogous to speed. I find it to be different from either direction alone as in the case of two speeds moving away on the same axis or between two directions with different speeds. velocity is of a different sort on my hunches.

Velocity is just a speed in a particular direction. It can be any direction; a fully defined reference frame, which allows you to describe any relative velocity, includes all directions, not just one. I'm not sure what else there is to say about it.

 

[objecta99]

yeah its like we are talking past one another. let me rephrase. you cite the Doppler effect to hold potentially between any two objects such that for example there could be a 1 to 3 relation in speed, I am asking can their be a 1 to 3 relation with relative velocity between two objects--or how is that question undefined. "Velocity is just a speed in a particular direction" that's the definition of a velocity, obviously. moving on, how am I restraining direction to a single direction? I am not, I specifically addressed the speed and direction inputs required for relative velocity but then I asked how we are to define velocity that doesn't simply define it relative to a speed or relative to a direction (if we are limited in this respect then the whole freakin point I am making about relative velocity is correct) but relates from a single reference frame (and within a scenario of three potential refrence frames) other objects with respect to their comparative velocity in a single reference frame. I should do stand up where I annoy physicists with obtuse questions perhaps but it just seems like you should be able to say something more direct to what I am explicitly asking. Also if the issue with the uncertainty principle is that we cannot know position and speed, how is that not analogous (at least) with relative velocities difficulty in getting beyond a relation between direction and speed? you are saying there is no analogy? I am not talking causation.

 

[A.T.]

you are saying there is no analogy?

When two things have nothing in common, is that something they have in common?

 

[objecta99]

the word analogy comes from the greek meaning proportion. the logically strongest sense of analogy is, what's been known since the ancient Greeks, called an "identity of relations"--this is the form of analogy that shows up on your SAT and IQ test: A is to B and C is to D. Per my analogy, In qm "position is to speed" as in SR "direction is to speed" in how we define an electron or a velocity. I don't think I need say much more for my analogy to obtain sans you demonstrating why there is no such commonality with some margin of charity given to my position. saying that there is no analogy is not a reason why there is no analogy.

 

[ghwellsjr]

yeah its like we are talking past one another. let me rephrase. you cite the Doppler effect to hold potentially between any two objects such that for example there could be a 1 to 3 relation in speed,

It's a 1 to 3 relation in tick rate, not speed.

I am asking can their be a 1 to 3 relation with relative velocity between two objects--or how is that question undefined.

It's not a 1 to 3 relation. One object is at rest with 0 velocity. The other object is not 3 times faster or any other value. You could call it a fraction of the speed but not a speed that is some multiple of the other object because its speed is zero. Is this where all the confusion lies? Are you trying to compare the speed of one object as a factor of the speed of the other object?

 

[objecta99]

Yeah so speed is relative such that tick rate can be fractional but how can we say that relative velocity is so fractional and not one to negative one type relation sort of speak. I am not trying to solve a problem in a textbook I am asking a more philosophical question about how we understand relative velocity in itself and not as a problem where speed is known but direction isn't or between a relation of 3 different 'velocities'. I am asking, Can an Inertial Reference Frame X compare the velocities of objects Y and Z, relative to X's frame of reference, such that either Y's velocity is greater then Z or Z's velocity is greater than Y's? this is not a question about how to measure but how we are defining the notion of velocity hypothetically but from your perspective it might seem trivial and by the definition of velocity undefined or nonsense. the derivative on velocity is acceleration and that does not tell us anything per say about the meta-question on velocity.

 

[Nugatory]

This is not a question about how to measure but how we are defining the notion of velocity hypothetically but from your perspective it might seem trivial and by the definition of velocity undefined or nonsense. the derivative on velocity is acceleration and that does not tell use anything per say about the meta-question on velocity.

Velocity is easy to define. Write the position coordinates of the object as a function of time, and the velocity is defined as the derivative of position with respect to time. Different frames may use different coordinates, and when they do the derivatives will also be different - which is why it makes no sense to speak of a velocity without specifying the frame in which it applies.

You should be in the habit of never speaking of any speed or velocity without also specifying what it is relative to - this specification is equivalent to specifying the origin of the coordinate system of a frame and is required for the velocity you're speaking of to be meaningful.

 

[PeterDonis]

I am asking can their be a 1 to 3 relation with relative velocity between two objects--or how is that question undefined.

It's undefined because, other than comparing their magnitudes (i.e., speeds), there is no way to compare velocities in different directions. So there is no such thing as "a 1 to 3 relation" between velocities in different directions, if you're not just comparing their speeds.

how am I restraining direction to a single direction?

You're not. But you're trying to compare velocities in different directions, and you've insisted that you don't just mean comparing their speeds. And as I noted above, that can't be done.

if the issue with the uncertainty principle is that we cannot know position and speed

It isn't; we're talking about classical SR here, no quantum effects.

(Btw, it would really help if you would use paragraphs. Your posts are almost unreadable.)

 

[Dale]

Can an Inertial Reference Frame X compare the velocities of objects Y and Z, relative to X's frame of reference, such that either Y's velocity is greater then Z or Z's velocity is greater than Y's?

Velocity is a vector and vector spaces are not ordered sets so they don't have a "greater than" operation. Speed is a positive real number which is an ordered set so it does have a "greater than" operation. So no, you cannot compare velocity that way, but yes, you can compare speed that way.

 

[objecta99]

Thanx Dalespam, that's a very clear way of understanding it. Thanx PeterDonis, sorry for the lack of paragraphs. Thanx Nugatory. I may have succeeded in asking one of the lamest questions (repeatedly) on this forum. Glad to see that it was a nonsensical question by the definition of relative velocity. 'twas a Poor question in one sense, but it had some pedagogical value for me.