Is Time Dilation Relative in Special Relativity Experiments?

[Dale]

It seems that I am dealing with a distinction between Galilean transformations and Lorentz transformations. From the Galilean perspective the notion of a relative frame can still in a relative sense arbitrate between two velocities and say of those two velocities that one is going faster or slower with respect to the observer's frame of reference. In Lorentz transformations from SR this cannot be done due to the reciprocal and symmetric effect of Lorentz transformations between any two objects (like velocity).

I don't think that this is a distinction between Galilean relativity and SR. Say you have two inertial objects in relative motion, A and B. In both SR and Galilean relativity the velocity of A and the velocity of B depend on the reference frame. In both, the velocity of A in B's frame is the opposite of the velocity of B in A's frame. In both, there are frames where A is faster than B and frames where B is faster than A. In both, once you specify the frame the velocity of A and the velocity of B is well defined. In both, if you don't specify the frame then the velocity is undefined.

The differences between SR and Galilean relativity are that in Galilean relativity the "closing speed" is the same in all frames and in SR the speed of light is the same in all frames.

 

[objecta99]

ok I'm pretty sure I sure I understand that in both cases velocity is frame dependent but I am wondering about where the difference is (if any) between how SR and Galilean relativity handle IRF's that attempt to measure (relative to itself of course) two or more inertial objects. tell me where I am wrong here though.

In Newtonian-Galilean physics a single frame of reference can say that from its IRF that two other inertial objects have different velocities (one is slower or faster than the other), relative to the original IRF. This means that there are 3 inertial objects, one of which is the frame of reference and it can meaningfully say of the other two intertial objects that one is faster then the other in a way that SR does not strictly allow.

whereas in SR it seems to me that given an IRF then it cannot say of two other intertial objects that one is faster than the other even if only relative to itself (relative to the original IRF) due to the Lorentz invariance SR math "stuff". Am I wrong in this?

 

[pervect]

ok I'm pretty sure I sure I understand that in both cases velocity is frame dependent but I am wondering about where the difference is (if any) between how SR and Galilean relativity handle IRF's that attempt to measure (relative to itself of course) two or more inertial objects. tell me where I am wrong here though.

In Newtonian-Galilean physics a single frame of reference can say that from its IRF that two other inertial objects have different velocities (one is slower or faster than the other), relative to the original IRF. This means that there are 3 inertial objects, one of which is the frame of reference and it can meaningfully say of the other two intertial objects that one is faster then the other in a way that SR does not strictly allow.

whereas in SR it seems to me that given an IRF then it cannot say of two other intertial objects that one is faster than the other even if only relative to itself (relative to the original IRF) due to the Lorentz invariance SR math "stuff". Am I wrong in this?

I'm not sure I'm following, let me restate what I think you are saying.

If you have a frame of reference, you can imagine an object at rest in that frame, you can also imagine one or more objects moving in that frame. One difference here - there's no need to call the frame itself an object, and I don't do so. Instead I call objects at rest in a frame as - objects at rest in a frame.

If you take the speed of objects (the magnitude of the velocity), then you can say some objects are faster than others , in a particular frame, by comparing their speeds.

However, this statement will be frame dependent, for instance, the fastest object in one frame can be the slowest object (at rest) in another frame.

I don't think there is any difference between Newtonian physics and Relativity so far. The difference comes in as to exactly how you mathematically handle going from one frame to another - what you call "math stuff". I'm interpreting the vagueness of the description as incomprehension of "math stuff", with perhaps a trace of math phobia (fear of math).

 

[objecta99]

I didnt want to bring up speed bc I didn't want to complicate matters for my pea sized brain. But this leads me to believe that what you are saying is that given a frame of reference then for that frame two or more objects can be said to be faster and slower with respect to each other. For example given frame of reference x it can say of two objects y and z that y is faster than z from the pov of x? Is this also true if we substitute velocity for speed in this hypothetical?My understanding is that velocity is relative under SR such that for any two non-accelerating Frames of reference they will share the exact same relative velocity between them and only disagree about which one is faster or slower by that exact same relative velocity. I believe this bc when I asked earlier 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?”

The answer I was given was:
“No. You just need to correctly identify the frame to which the velocities are referred.”--PeterDonis

I was also told the following by Ghwellsjr:

“Every object can consider itself to be stationary and all the other objects having relative speeds toward or away from itself. So they are each assuming that the other one is going faster than itself. But there is no way to establish an absolute velocity”

I understand this to be the case between any two non-accelerating frames of reference since the relative velocity is a relationship between the two just a disagreement about who is going faster than the other . I think I understand that. My question is if the velocity is dependent on the relationship between any two frames of reference, what can be said about the velocity of a third object from the point of view of either of the two reference frames? Specifically, can either of the two reference frames say of this third object that its velocity is greater or slower then the other reference frame. Iow consider some reference frame X and Y who share some relative velocity (only a disagreement about which is going faster) can X relative to its frame say of some further object z that it is going faster or slower compared to Y and conversely can Y relative to its frame say of some object z that it is going faster or slower compared to X?

I hope that was clear enough. it might just be the case that that my intellectual failings at math are only over shadowed by my intellectual failure to pose a clear and decent question on this forum.

 

[objecta99]

I am asking this bc I am having a war in my head with how to understand what relative velocity means based on the following line of reasoning. Consider the following hypothetical:"a clock aboard the plane moving eastward, in the direction of the Earth's rotation, had a greater velocity (resulting in a relative time loss) than one that remained on the ground, while a clock aboard the plane moving westward, against the Earth's rotation, had a lower velocity than one on the ground. Obviously one of the planes has a greater velocity than the clock on the ground from the ground clocks pov" no matter what frame you are looking from, the velocity must appear "the same" from that frame to another, and that other frame back. In other words, if looking from the ground clock, the jet must be moving away or toward at X velocity. If looking from the jet, the ground/clock must be moving away or toward at the very same X velocity. We know, however, that one has a higher velocity than the other (and time distorts differently).

The frame that is "not" rotating with the Earth is the jet flying against the rotation. That's one of the two frames. There are 2 objects, the jet/clock and the ground/clock. Everything else is irrelevant. In one scenario the jet is flying with the rotation, in the other it is flying against the rotation.

It is the case that the one jet has a higher velocity and the other a lower velocity, in relation TO the ground/clock. And when they meet, the clock represents differing slow downs between the jet/clock and ground/clock.

there is no "absolute velocity" (we determine velocity through relation). However that "relative velocity" does not mean that "the appearance of the same velocity means they are the same velocity". That these are not the same thing.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

this line of reasoning is why I am asking about how to deal with the velocity of two inertial objects in one frame of reference. Now maybe the way to look at it is that given one plane going eastward and one clock on the ground its relative velocity will be greater then the relative velocity shared between the other plane and the clock on the ground. if that's the case then how do we compare two different relative velocities (the velocity shared between the clock and the eastern bound plane and the velocity shared between the clock and the western bound plane). I understand I think how to compare the velocity of two objects but how to compare two relations or two relative velocities. I am also wondering if the proceeding reasoning is faulty and why. I thought I understood why but perhaps I am wrong now that I think about it. if anyone can clarify it would be great.

 

[PeterDonis]

if looking from the ground clock, the jet must be moving away or toward at X velocity. If looking from the jet, the ground/clock must be moving away or toward at the very same X velocity.

Yes.

We know, however, that one has a higher velocity than the other (and time distorts differently) with respect to a frame that is not rotating with the Earth.

I added the bold portion to make clear the mistake you are making; you are switching frames in mid-stream, so to speak. *Whenever* you use the word "velocity", you should *always* specify which frame it is relative to. Otherwise you will only confuse yourself (not to mention make it difficult for others to understand what you're saying).

The frame that is "not" rotating with the Earth is the jet flying against the rotation.

No, it isn't; the jet flying westward is *not* at rest in a frame that is rotating with the earth. It is simply moving slower in that frame than the observer on the ground or the jet flying eastward.

That's one of the two frames.

No, if we are going to be precise, there are *four* "frames" total that are relevant to this problem: the frame that is not rotating with the Earth, the rest frame of the jet flying westward, the rest frame of the observer on the ground (rotating with the Earth), and the rest frame of the jet flying eastward.

There are 2 objects, the jet/clock and the ground/clock. Everything else is irrelevant. In one scenario the jet is flying with the rotation, in the other it is flying against the rotation.

As the experiment was actually done, it was one "scenario" with two jets in it, one flying eastward and one flying westward. I think it is clearer to just analyze it this way, including both jets.

It is the case that the one jet has a higher velocity and the other a lower velocity, in relation TO the ground/clock.

In the actual experiment, both jets had velocities that varied with time. But if we are idealizing both jets as flying with constant velocity, we can just as easily idealize both jets as flying with the *same* velocity relative to the ground clock.

However, the real point is that the velocity relative to the ground clock is *not* the velocity that matters for understanding the difference in elapsed times; the velocity that matters for that is the velocity relative to the frame that is not rotating with the Earth (which is *not* the same as the frame of the ground clock).

And when they meet, the clock represents differing slow downs between the jet/clock and ground/clock.

No, it represents one clock slowing down compared to the ground clock (the eastward-flying jet's clock), and one clock *speeding up* compared to the ground clock (the westward-flying jet's clock). This is because, once again, the velocity that matters is the velocity with respect to a frame that is not rotating with the Earth. Relative to that frame, the westward-flying jet moves slower than the ground clock, which in turn moves slower than the eastward-flying jet. That is what makes the westward-flying jet's clock run *faster* than the ground clock, and the eastward-flying jet's clock run slower.

Try re-thinking the experiment in the light of the above; hopefully it will help to clear things up.

 

[objecta99]

Thanx PeterDonis I appreciate that. I actually feel like I understand this though in a much more vague and arcane manner. Its a bad set up chain of reasoning for the reasons you point out but I am trying to make sure I know exactly why.
My question is this though, it seems ultimately. How do we compare in SR two relative velocities. Could one say that given one plane going eastward and one clock on the ground its relative velocity could be greater then the relative velocity shared between the westward plane and the clock on the ground. if that's the case then how do we compare two different relative velocities (the velocity shared between the clock and the eastern bound plane and the velocity shared between the clock and the western bound plane). I understand I think how to compare the velocity of two objects in order to find one relative velocity (frame dependent) but how does one compare two relations or two relative velocities under SR? It's like I don't know how to relate two relative velocities to some relative frame of reference without going back to ether style nonsense. its sems on my view it can't literally be done yet we know that the greater the relative velocity the greater the time dilation is. I'm going to read your response closer too. but this seems to be where I am stuck. I am sorry to for continually posting what even I agree are faulty chains of reasoning but I am just trying to make sure I understand why those chains of reasoning are faulty. thanks again for taking the time. also I don't want to annoy everyone on physicsforums with what might be amounting to a really bad thread and I assume all the responsibility for that

 

[PeterDonis]

How do we compare in SR two relative velocities. Could one say that given one plane going eastward and one clock on the ground its relative velocity could be greater then the relative velocity shared between the westward plane and the clock on the ground.

I don't know what you mean by "the relative velocity shared between the westward plane and the clock on the ground". Relative velocity is velocity of one object relative to another. Do you mean the velocity of the westward plane relative to the ground clock? If so, obviously it's possible for the velocity of the eastward plane relatlve to the ground clock to be greater than the velocity of the westward plane relative to the ground clock; it all depends on how the planes are flown.

If you mean something else than what I've just said by "compare two relative velocities", then I don't understand what you mean and you'll have to clarify. Perhaps it would help if you take a step back and explain *why* you want to "compare two relative velocities". What will that tell you? What will it accomplish?

 

[objecta99]

yeah I guess I just need to probably drop the issue since I am just not making much sense apparently and now I seem to be spinning in circles. from my understanding the only way to determine velocity is dependent on at least two objects. when I say "the relative velocity shared between the westward plane and the clock on the ground" I mean the "velocity of the westward bound plane relative to the ground clock and vice versa". my understanding is that in order to find a velocity we must have two things to compare--the plane itself has no velocity and the ground clock has no velocity by themselves only in relation to each other and by that fact the relative velocity is reciprocal, its just both think the other is going faster.

I seem to want to say (probably because I am totally lost) that there are two different relative velocities based on two different relationships that both involve the ground clock
1) the relative velocity of the westward plane and ground clock
2) the relative velocity of the eastward plane and ground clock

now in either case we can take the plane or the clock as the rest frame.

but How do I say that relative to the ground clock the eastward plane is going faster and the westward plane is going slower within the same* clock frame of reference?

sorry if that's a dumb question, I am not very bright.

 

[PeterDonis]

from my understanding the only way to determine velocity is dependent on at least two objects.

This sounds like it means the same thing as what I said in my previous post: "Relative velocity is velocity of one object relative to another". If that's what you mean, then yes, obviously you need two objects. (Note that you need *only* two objects, no more, no less.)

when I say "the relative velocity shared between the westward plane and the clock on the ground" I mean the "velocity of the westward bound plane and the ground clock".

This doesn't make things any clearer. Is there some reason you can't just use the same form of words I used: "the velocity of the westward bound plane relative to the ground clock"? Does that somehow not express what you are trying to say?

the plane itself has no velocity and the ground clock has no velocity by themselves only in relation to each other and by that fact the relative velocity is reciprocal, its just both think the other is going faster.

This sounds ok, yes: the ground clock thinks the plane is "going faster" (because the ground clock, relative to itself, is at rest, and the plane is moving relative to the ground clock), and the plane thinks the ground clock is "going faster" (because the plane, relative to itself, is at rest, and the ground clock is moving relative to the plane). But it seems like a clumsy way to say it: obviously anything that's moving is "going faster" than something that's at rest, and everything is at rest relative to itself. Is there some particular reason you are focusing in on this?

there are two different relative velocities based on two different relationships that both involve the ground clock
1) the relative velocity of the westward plane and ground clock
2) the relative velocity of the eastward plane and ground clock

Yes, these are two different relative velocities, both involving the ground clock, and there is no reason why they must both be the same: they *can* be the same, of course, if the planes are flown appropriately, but they don't have to be.

in either case we can take the plane or the clock as the rest frame.

Yes.

How do I say that relative to the ground clock the eastward plane is going faster and the westward plane is going slower within the same* clock frame of reference?

By "going slower", do you mean that the westward plane is going slower than the eastward plane? Or do you mean that the westward plane is going slower than the ground clock?

If it's the first of the two, you can just say it--assuming it's true, of course. If, for example, the eastward plane is flying at 500 mph, relative to the ground clock, and the westward plane is flying at 400 mph, relative to the ground clock, then the westward plane is going slower than the eastward plane, relative to the ground clock.

But if you mean the second of the two, that doesn't make sense--nothing can be going slower than the ground clock, relative to the ground clock, because the ground clock is at rest--speed zero--relative to itself, and nothing can go slower than that. The only way for the westward plane to be going slower than the ground clock is to look at their speeds relative to some *other* frame of reference than the rest frame of the ground clock--for example, the rest frame of the westward plane itself.

 

[objecta99]

"when I say "the relative velocity shared between the westward plane and the clock on the ground" I mean the "velocity of the westward bound plane and the ground clock"".--objecta99

"This doesn't make things any clearer. Is there some reason you can't just use the same form of words I used: "the velocity of the westward bound plane relative to the ground clock"? Does that somehow not express what you are trying to say?"

sorry yes I edited to mean what u say, I messed up there. I meant what you said."If it's the first of the two, you can just say it--assuming it's true, of course. If, for example, the eastward plane is flying at 500 mph, relative to the ground clock, and the westward plane is flying at 400 mph, relative to the ground clock, then the westward plane is going slower than the eastward plane, relative to the ground clock"

yes I meant the first one and that makes sense as far as speed, what about velocity though, how can I say (if I can), that relative to the ground clock the eastward plane has greater velocity compared to the velocity of the westward plane within the same clock frame of reference. idk why I said speed, that was a mistake on my part again--I meant to say velocity. sorry about that.

 

[PeterDonis]

I meant what you said.

Ok, good.

yes I meant the first one and that makes sense as far as speed

Good.

how can I say (if I can), that relative to the ground clock the eastward plane has greater velocity compared to the velocity of the westward plane within the same clock frame of reference.

In general, velocities can't be compared this way, because velocity includes direction as well as speed. If I'm going north at 20 mph and you're going west at 30 mph, which one of us has the "greater" velocity, as opposed to the greater speed?

Even if you just restrict to one spatial axis, east-west in this case, it doesn't really seem right to say that one velocity is greater or less than another, as opposed to speed. For example, suppose one plane is flying west at 500 mph, relative to the ground clock, and the other is flying east at 500 mph, relative to the ground clock. They both have the same speed (500 mph), but if we include direction, the westbound plane has velocity - 500 mph and the eastbound plane has velocity + 500 mph. Do we want to say the eastbound plane "has greater velocity" because + 500 is greater than - 500?

Once again, I think it might help to take a step back and ask: *why* do you think it's important to be able to say that one plane has greater velocity (as opposed to speed) than the other? What does that accomplish?

 

[objecta99]

thank you this has been very helpful and I appreciate you taking the time to help a novice on these matters. I intend to commit some time to study physics and I won't be continually asking questions like I have here. its only fair that I put in some work myself and not just rely on the generosity of others who have studied the matter with some depth. I'm glad that you say this about velocity and that I understood at least that much lol. I don't personally want to say that one plane has greater velocity than another, I just wanted to make sure that unlike speed, saying such about velocity is not the correct way to understand SR. As for the reason why I wanted to know this, its bc I have been engaged in some conversations with ppl that tried to challenge the view that velocity is relative in this respect and I wanted to make sure I knew what the correct SR view was. the conversation i was engaged in is admittedly a philosophical one about what we mean by relativity in all cases where that word is used including morality, ontology and physics. I'd hate to be another armchair philosopher who was too lazy or ignorant to not even represent the correct understanding of relative velocity in SR. this has helped me and hopefully primed me for a more sure footed endeavor when I crack upon a physics 101 textbook lol. thanks again

 

[objecta99]

one more quick question though, is the relativity of velocity (that we cannot compare two different velocities in one rest frame) true in Newtonian--Galilean relativity or is it only in SR that we accepted that velocity was relative in this way?

 

[PeterDonis]

is the relativity of velocity (that we cannot compare two different velocities in one rest frame) true in Newtonian--Galilean relativity or is it only in SR that we accepted that velocity was relative in this way?

There's no difference between Newtonian physics and SR in this respect. There's a difference in how velocities get transformed when you change reference frames, but that's a separate issue.

Glad this discussion helped!

 

[ghwellsjr]

If two objects are traveling along the same line at any arbitrary speeds and they are inertial, then they can make some measurements to determine the velocity of the other object relative to itself without regard to any reference frame.

No, a velocity is always with regard to some reference frame. You cannot have a velocity without a reference frame. At most the reference frame may be implicit or otherwise understood.

I think you know that, but the OP may be confused by that.

Doesn't my statement "relative to itself" cover that requirement?

What I meant by "without regard to any reference frame" is that since Doppler is invariant, the first object does not need to be concerned about establishing a coordinate system, that is, synchronizing any clocks or sending out any radar signals. Instead, a passive Doppler measurement can be used by an inertial object to determine the velocity of another inline inertial object relative to itself.

 

[ghwellsjr]

I was also told the following by Ghwellsjr:

“Every object can consider itself to be stationary and all the other objects having relative speeds toward or away from itself. So they are each assuming that the other one is going faster than itself. But there is no way to establish an absolute velocity”

I understand this to be the case between any two non-accelerating frames of reference since the relative velocity is a relationship between the two just a disagreement about who is going faster than the other . I think I understand that. My question is if the velocity is dependent on the relationship between any two frames of reference, what can be said about the velocity of a third object from the point of view of either of the two reference frames? Specifically, can either of the two reference frames say of this third object that its velocity is greater or slower then the other reference frame. Iow consider some reference frame X and Y who share some relative velocity (only a disagreement about which is going faster) can X relative to its frame say of some further object z that it is going faster or slower compared to Y and conversely can Y relative to its frame say of some object z that it is going faster or slower compared to X?

I think your fundamental problem is that you keep wanting to associate a reference frame with an object at rest in that reference frame. You need to understand that all reference frames are equally valid, even those for which nothing is at rest.

For example, consider an Inertial Reference Frame in which there are two inertial observers both starting out at the origin of the IRF and traveling at half the speed of light in opposite directions. There is no other observer nor any object at rest in this IRF. Does that make perfect sense to you?

To illustrate, here is a spacetime diagram depicting that scenario:

Note that the Time Dilation (the spacing of the dots) is the same for both observers because they are traveling at the same speed in this IRF.

To illustrate how each observer can use Doppler to determine the speed that the other one is moving relative to himself, I have drawn in a couple light signals showing how the blue observer is comparing the red observer's clock to his own:

As you can see, the blue observer sees the red observer's clock ticking at 1/3 the rate of his own. If we call the Doppler factor "D", then he can plug it into the following formula to determine the velocity "v" (as a fraction of c) of the red observer relative to himself:

v = (1-D²)/(1+D²) = (1-0.3333²)/(1+0.3333²) = (1-0.1111)/(1+0.1111) = 0.8888/1.111 = 0.8

Now if we transform to the IRF in which the blue observer is at rest, we see this diagram:

And sure enough, the red observer is traveling at 0.8c in the rest frame of the blue observer. Note that the Doppler factor is the same in this IRF as it is in any IRF but the Time Dilations for the two observers are different. It's 1 for the blue observer and 1.667 for the red observer.

The red observer can also do the same thing observing that the blue observer's clock is running at 1/3 the rate of his own and calculating that the blue observer is traveling 0.8c with respect to himself:

And in the red observer's rest frame, the blue observer is traveling at 0.8c:

Here's one more spacetime diagram the same as the previous one but with the Doppler signals that the blue observer sees of the red observer's clock added in:

Note how the Doppler factor is the same for both observers even though the Time Dilation is different.

Does this help?

 

[objecta99]

thanx a lot Gh, this was very helpful. I am asking a very simple question and this actually was very helpful in my understanding actually incredibly so about factors which relate time dilation in relative sense. However my question is a bit more direct and simple. 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? If so, how do you understand the distinction if any, between relative velocity and velocity? the standard answer from a physicist will be along the following lines:

The velocity of an object is always relative to a frame of reference. In that sense there is no distinction between relative velocity and velocity. If you say "X has velocity V," I will ask, "in what frame?'

In frame X object Y may move faster than object Z. But there will be a frame W in which Z moves faster than Y. So there is no absolute sense in which one moves faster than the other. It was once thought that there was an "ultimate" frame of reference that could be determined physically. That this was not the case is what led to Relativity.

And I will ask again:

I realize that z or y may move faster (speed) in frame x. What I am wondering is can their velocities (z compared with y) be compared in the same frame x. This gives us three potential frames of reference. It seemed to me that in a single frame of reference you cannot compare the VELOCITIES of two other objects bc in order to establish a relative velocity it must be between exactly two 'objects' where one will see the other as going faster than the other and vice versa. Does vector addition allow us to compare the two objects velocities in a single reference frame in the most general cases? It would seem to me it only allows us to compare the velocities in different reference frames not the same reference frame. It only allow us to know the relative velocity of say A to C when we have the velocities of A to B and B to C, but it doesn't tell us how to compare the velocities of B and C from the frame of A--this would cause a kind of 'absolute velocity' it seems which is nonsense. Is that right or how am I wrong.

You mention the Doppler effect being different by a factor which yields different magnitudes is that true of the values for relative velocity? I was under the impression that the difference between any two objects with respect to their relative velocity, where there is a reciprocal relation given by the Lorentz tansforms, is one of a + and - distinction ONLY? two objects define a frame dependent relative velocity such that not only the factor but also the absolute numerical value/ratio is the same for both. that's my view, how is this not the case, where am I wrong here? If such is not the case then my general philosophical context for how I understand relative velocity would not obtain.

 

[ghwellsjr]

thanx a lot Gh, this was very helpful. I am asking a very simple question and this actually was very helpful in my understanding actually incredibly so about factors which relate time dilation in relative sense. However my question is a bit more direct and simple. 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? If so, how do you understand the distinction if any, between relative velocity and velocity? the standard answer from a physicist will be along the following lines:

The velocity of an object is always relative to a frame of reference. In that sense there is no distinction between relative velocity and velocity. If you say "X has velocity V," I will ask, "in what frame?'

In frame X object Y may move faster than object Z. But there will be a frame W in which Z moves faster than Y. So there is no absolute sense in which one moves faster than the other. It was once thought that there was an "ultimate" frame of reference that could be determined physically. That this was not the case is what led to Relativity.

And I will ask again:

I realize that z or y may move faster (speed) in frame x. What I am wondering is can their velocities (z compared with y) be compared in the same frame x. This gives us three potential frames of reference. It seemed to me that in a single frame of reference you cannot compare the VELOCITIES of two other objects bc in order to establish a relative velocity it must be between exactly two 'objects' where one will see the other as going faster than the other and vice versa. Does vector addition allow us to compare the two objects velocities in a single reference frame in the most general cases? It would seem to me it only allows us to compare the velocities in different reference frames not the same reference frame. It only allow us to know the relative velocity of say A to C when we have the velocities of A to B and B to C, but it doesn't tell us how to compare the velocities of B and C from the frame of A--this would cause a kind of 'absolute velocity' it seems which is nonsense. Is that right or how am I wrong.

You mention the Doppler effect being different by a factor which yields different magnitudes is that true of the values for relative velocity? I was under the impression that the difference between any two objects with respect to their relative velocity, where there is a reciprocal relation given by the Lorentz tansforms, is one of a + and - distinction ONLY? how could two objects define a frame dependent relative velocity such that not only the factor but also the absolute numerical value/ratio was the same for both. If such is not the case then my general philosophical context for how I understand relative velocity would not obtain.

I don't have time to give a thorough answer to all you specific questions but it appears to me that you are grasping most of the concepts. Remember, I have been talking specifically about inertial inline objects where we can use shortcuts.

One shortcut is when we have two objects both with speed that can be different according to a particular Inertial Reference Frame. Then we can use the velocity addition formula to calculate their relative speed.

Relative velocity is the speed of one object in the rest frame of another object.

But in general, it's better to understand the bigger picture that permits non-inertial and/or non-inline objects. Then there will not be a single number that is the relative velocity. Instead, it will be a function of time and it gets very complicated if you want to deviate from the standard way of doing things in Special Relativity which is to use an IRF and not worry about relative velocity. If you do insist on determining the velocity of one such object with respect to another such object, then it is up to you to define the non-inertial frame and to work out all the math.

And the point is, you won't have learned anything new about the scenario, it's just another arbitrary way of presenting the information but there won't be any new information. All reference frames are equally valid and equivalent in terms of their information content.

 

[objecta99]

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.

 

[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.)