Is Time Dilation Relative in Special Relativity Experiments?

[objecta99]

If velocity is relative and if we cannot say which is moving away from what *objectivley, how do we say that time dilation is relative as well if we can tell who experienced the time dilation, as special relativity shows - and other experiments (muon concentrations etc). For example the jets clock is proven to run slower (and not the clock on the platform, in relation to the jet), gps atomic clocks are corrected for SR effects etc---these seem to me to argue that we do know which objects are undergoing time dilation not in a relative sense. Do experiments like the jet clocks or gps statellite clocks or muon concentration experiments get around the frame change symmetry breaking explanation any better? Does the frame change symmetry break per the twin experiment account for the reason why time dilation is relative and not objective and does this "frame change reason" account for why time dilation is relative for all other experiments (jet clocks, gps, muons)? I've heard some claim that time dilation is not relative bc we Know who will age less, (even if its after the fact and initially experienced as relative) and some say the twin paradox 'frame change' is not pertinent to how we understand the jet clock time dilation, gps satellite time dilation and high muon concentrations. thoughts?

 

[PeterDonis]

the jets clock is proven to run slower (and not the clock on the platform, in relation to the jet), gps atomic clocks are corrected for SR effects etc---these seem to me to argue that we do know which objects are undergoing time dilation not in a relative sense.

The term "time dilation" is ambiguous. Sometimes it refers to a situation where there is no invariant way of telling who is "moving" and who is not--for example, if you and I are in two separate spaceships moving relative to each other, and there is no other reference object nearby. But sometimes it refers to a situation where there *is* an invariant way of telling who is "moving": for example, if the motion is periodic. And sometimes it refers to a situation where all the clocks in question are co-located at the start and end of the experiment, so their readings can be compared directly.

GPS satellites are moving in periodic orbits around the Earth, so there is an obvious way to compare their elapsed times: just compare the time it takes for the satellite to complete one orbit, according to the satellite clock and according to the Earth clock. The satellite clock shows more elapsed time than the Earth clock, and this is an invariant fact; the Earth clock and the satellite clock both agree on it.

Similarly, in the Hafele-Keating experiments, atomic clocks were flown around the world and then returned to their starting point to be compared with clocks that stayed there. So the clocks were together at both the start and end of the experiment, which again gives an obvious way to compare them. The different elapsed times of the clocks are again invariant facts in this situation; all of the clocks agree on how much time elapsed on each one between the two events at which they were together.

 

[objecta99]

That helps a lot regarding how we assess the clocks in orbit. I have a friend that has been trying to convince me that time dilation can be shown to be non-relative and doesn't need a "turn around" twin paradox type scenerio either, but is also not an orbital situation. He sets up a scenerio like the following to make his point:

We can show that time dilation is non-relative by syncing three clocks. Clocks at point A and B (planets or big rocks in space) and the clock in the "ship" clock C. If the clock in the ship is slower than the clock at point B, then it is also slower than the clock at point A (which can be verified as still synced with B). This is all without "turn-around" in the twin paradox. If both body A, body B , and spaceship C have synced clocks then when the spaceship reached body B it will have an off-clock than what A and B have - because C had a higher velocity of the 3 bodies traveling from one to the other. The spaceship that had a reference point going from body A to body B but lost all reference to those bodies "in between" still has velocity (and will still reach body B if lined up). It doesn't lose velocity once it loses the relationship (e.g. if body A gets antimatter wiped). hence we can say that the time dilation based on C's higher velocity is non-relative.

This may not be enough to go on, but this is pretty much the summary he gives me. I would never endorse such a scenerio but Is this correct or have u ever heard of a comparable scenereo to this that would make sense, i mean what's the glaring problem here? To me there could be many but I'm just such a physics novice that I'm to scared to say what's at work here with 3 clocks without an orbit either or twin paradox issue. I am willing to delete this thread too if its not up to par. I don't mean to ask what might seem absurd questions to experts. thanx:-)

 

[ghwellsjr]

...
We can show that time dilation is non-relative by syncing three clocks. Clocks at point A and B (planets or big rocks in space) and the clock in the "ship" clock C. If the clock in the ship is slower than the clock at point B, then it is also slower than the clock at point A (which can be verified as still synced with B). This is all without "turn-around" in the twin paradox. If both body A, body B , and spaceship C have synced clocks then when the spaceship reached body B it will have an off-clock than what A and B have - because C had a higher velocity of the 3 bodies traveling from one to the other. The spaceship that had a reference point going from body A to body B but lost all reference to those bodies "in between" still has velocity (and will still reach body B if lined up). It doesn't lose velocity once it loses the relationship (e.g. if body A gets antimatter wiped). hence we can say that the time dilation based on C's higher velocity is non-relative.

Two rocks against one ship so the rocks win, is that how it works? Well let's just even up the score and make the scenario symmetrical, not by changing anything but simply by adding a second ship behind the first one the same distance apart in their mutual rest frame that the rocks are apart in their mutual rest frame. The clocks on the ship have been synchronized. Now whatever you want to say about the two rocks, you can also say about the two ships, correct?

 

[objecta99]

ghwellsjr that sounds right to me as far as I can tell. I would say more but I better not bc I'll just end up probably saying something wrong or unimportant--I barely have the hang of twin paradox time dilation symmetry let alone 3 clocks. Yeah just to reiterate the scenario. ship C travels from rock A to B (regardless if A gets destroyed at some point during the trip), all were originally synced, once C reaches B and is shown to have a slow clock relative to B then its also slow relative to A since A and B are synced. Walla: C's time dilation is shown to be not relative. that's the 'gist'. sounds pretty bad, I am just trying to really understand exactly why its so bad--there seems to be a lot of fast and loose playing with how the reference frames are being treated. thanx

 

[PeterDonis]

We can show that time dilation is non-relative by syncing three clocks.

I'm not entirely sure I understand the scenario, but I think the intent is that clocks A and B are at rest relative to each other, and clock C is moving relative to A and B, correct? If that's the case, this scenario doesn't show that time dilation is non-relative; it just shows that two clocks at rest relative to each other stay in sync, relative to each other. Relative to clocks A and B, clock C is running slower, yes; but relative to clock C, clocks A and B are running slower.

Yes, if clock C travels from clock A to clock B, it will have less elapsed time than the difference of clock A's reading when C passes A, and clock B's reading when C passes B. But since it only passes each clock once, there's no invariant way to say which clock(s) are "really" running slow. For that, C would have to meet up with the *same* clock (A or B) twice, or C's motion would have to be periodic so that there would be a common reference from which to compare.

Your friend might object that, since clocks A and B are in sync, reading one of them is equivalent to reading the other. But that's only true for an observer that is at rest relative to both clocks; there's nothing that requires clock C, which is moving relative to A and B, to consider their readings as equivalent. For example, say that, when C passes clock A, A's reading is exactly 12 noon, and when C passes clock B, B's reading is exactly 6 pm. B will say that A was also reading 6 pm at the same instant that C passed B; but C will not. C will say, using his own convention for clock synchronization, that clock A read something *earlier* than 6 pm at the same instant that C passed B.

In other words, from clock C's point of view, clocks A and B are *not* in sync with each other. This is an illustration of relativity of simultaneity: the definition of what events happen "at the same time", which is required for clock synchronization, is frame-dependent. C's definition of what events happen "at the same time" is different from A's and B's. And since there is no common reference from which to compare them, there is no way to say that either definition of simultaneity is the "right" one. That's how A and B can say that C is running slow, while C says that A and B are running slow.

 

[objecta99]

that was awesome, you read the scenario correct. C travels from rock A to rock B and all three are "originally" synced, when spaceship C reaches rock B and C is slow compared to B then its slow compared to A bc A and B are synced or at rest together. You guys summed this up well. I won't try to add anything I just wanted to at least convey the scenario best I could and let those who really know what they are talking about help clarify the scenario. thank you very much

 

[ghwellsjr]

...
We can show that time dilation is non-relative by syncing three clocks. Clocks at point A and B (planets or big rocks in space) and the clock in the "ship" clock C. If the clock in the ship is slower than the clock at point B, then it is also slower than the clock at point A (which can be verified as still synced with B). This is all without "turn-around" in the twin paradox. If both body A, body B , and spaceship C have synced clocks then when the spaceship reached body B it will have an off-clock than what A and B have - because C had a higher velocity of the 3 bodies traveling from one to the other. The spaceship that had a reference point going from body A to body B but lost all reference to those bodies "in between" still has velocity (and will still reach body B if lined up). It doesn't lose velocity once it loses the relationship (e.g. if body A gets antimatter wiped). hence we can say that the time dilation based on C's higher velocity is non-relative...

Time for some more spacetime diagrams to show you that Time Dilation is relative just like Velocity is relative to an Inertial Reference Frame (IRF). In this spacetime diagram, rock A is shown in blue, rock B is shown in black and ship C is shown in red traveling at 0.6c from blue A to black B. Since in this frame, C is traveling at 0.6c, its clock is Time Dilated by the factor 1.25 which means the dots marking off one-year increments of time are spaced 1.25 years of Coordinate Time:

As you can see, during the time that red ship C is traveling from blue rock A to black rock B, five years has transpired for A and B but only four years has transpired for ship C. But that's only true in the mutual rest frame of A and B. In other frames, the speeds of all objects can change and with them the Time Dilation factors.

To see this, we transform to the rest frame of the red ship C:

As you can see, the red ship C is not Time Dilated but the two rocks are Time Dilated.

As I suggested in post #4, you can make the scenario symmetrical by adding another ship D shown in green behind ship C and spaced the same distance apart in their mutual rest frame as rocks A and B are separated in their mutual rest frame:

If we ignore rock B, this looks just like a mirror image of the first IRF. We see blue rock A traveling from stationary red ship C to stationary green ship D in four years whereas both ships ticked off five years.

Can you see that Time Dilation is relative to your chosen IRF just like velocity is?

For completeness sake, we transform this frame back to the original IRF:

You commented that ship C had a higher velocity of the three bodies and I have already shown you that this is not true in the last two diagrams but now I want to show you that we can pick a frame in which all the bodies are traveling at the same speed (0.333c) and all of them are subject to the same Time Dilation:

For both red ship B and black rock A, it takes them each four years to reach their respective destinations, a completely symmetrical scenario.

Any more challenges for the notion that Time Dilation is not relative?

 

[objecta99]

ok here's some more challenge.

If we have a train car with a photon going up and down between two mirrors at the speed of light - the faster that train car is moving, the farther these photons are traveling to get from mirror to mirror. And since they cannot travel faster than the speed of light, time slows down in compensation.

On the platform, however, the distance is not elongated. It only appears elongated from inside of the train car. So from the perspective of each time is slowing down, but in reality, the clock in the train will have less ticks once the train stops and the count is reflected. If the platform was moving at the same speed (away from the train), the ticks would show as the same (as time would equally slow down).

How come I cannot say that as a consequence of relativity that the sun is rotating around the Earth just as much as the Earth is rotating around the sun, even though we know that the Earths orbit is due to the gravitation of the Sun and the direction and speed in which the Earth is traveling that compensates for the gravity so it does not just drop into it. From our perspective the Sun is rotating around the Earth, and from the Sun's perspective the Earth is rotating around the sun.

 

[Dale]

How come I cannot say that as a consequence of relativity that the sun is rotating around the Earth just as much as the Earth is rotating around the sun.

Certainly you can do this. You can use any coordinate system you like, but of course the math will be simpler in a well chosen coordinate system.

 

[objecta99]

thanx Dale. Yeah I am having a real time debate back and forth with someone who wants to argue with me that time dilation and velocity are non-relative. so I am outsourcing for the heck of it to get any help I can. This guy (friend whos becoming more my enemy after every passing hour lol) takes the view that given the train platform hypothetical that there really is a time dilation on the trains clock but not for the platform clock though we see both as time dilated. I know its the old basic debates lol. My last comment was a little hubristic which was intentional lol. I don't hold the positions that I am playing devils advocate for and I have also learned a lot from the help and diagrams I have been given on here just in the last 24 hours so I don't want to sound like an entitled naïve twit. so far I feel solid about how to symmetrically account for time dilation in a frame dependent manner but the train platform scenario has tripped me up somewhat, I wonder if its a consequence of the two never actually meeting but only theoretically meeting or what?? appreciate all the help iv'e been given.

 

[ghwellsjr]

ok here's some more challenge.

Are these your challenges or do they come from your friend?

If we have a train car with a photon going up and down between two mirrors at the speed of light - the faster that train car is moving, the farther these photons are traveling to get from mirror to mirror. And since they cannot travel faster than the speed of light, time slows down in compensation.

When you make statements like this, you should make it clear which frame they apply to. It is obvious that it's the frame of the railroad tracks for which your scenario is being described.

On the platform, however, the distance is not elongated. It only appears elongated from inside of the train car.

What distance are you talking about, the distance between the mirrors or the distance the train travels between successive reflections of the photon off of one mirror?

So from the perspective of each time is slowing down, but in reality, the clock in the train will have less ticks once the train stops and the count is reflected.

Less ticks than what? You have to be very clear when you are setting up a scenario.

If the platform was moving at the same speed (away from the train), the ticks would show as the same (as time would equally slow down).

The same as what? Are you forgetting what I have already told you? Pick an Inertial Reference Frame, any thing that is moving according to that IRF is Time Dilated compared to the Coordinate Time of that frame.

How come I cannot say that as a consequence of relativity that the sun is rotating around the Earth just as much as the Earth is rotating around the sun, even though we know that the Earths orbit is due to the gravitation of the Sun and the direction and speed in which the Earth is traveling that compensates for the gravity so it does not just drop into it. From our perspective the Sun is rotating around the Earth, and from the Sun's perspective the Earth is rotating around the sun.

The Sun's rest frame is inertial, the Earth's is not. It's far easier to describe and analyze everything from the Sun's IRF. That would show us that the moving clocks on the Earth run slower than the Coordinate Time of the Sun's IRF and stationary clocks on the Sun run at the same rate as the Coordinate Time (neglecting any gravity influences). You cannot say the same thing about the Earth's frame because it is not inertial.

 

[acegikmoqsuwy]

\displaystyle \Delta t = \frac {\Delta t_0} {\sqrt{1-\left(\frac {v} {c}\right)^2}}

Why does it say \displaystyle t' = \gamma \left(t-\frac{vx} {c^2}\right)? Clearly t' = \gamma t

Unless of course, v = 0 or x = 0

ok here's some more challenge.

If we have a train car with a photon going up and down between two mirrors at the speed of light - the faster that train car is moving, the farther these photons are traveling to get from mirror to mirror. And since they cannot travel faster than the speed of light, time slows down in compensation.

On the platform, however, the distance is not elongated. It only appears elongated from inside of the train car. So from the perspective of each time is slowing down, but in reality, the clock in the train will have less ticks once the train stops and the count is reflected. If the platform was moving at the same speed (away from the train), the ticks would show as the same (as time would equally slow down).

Even though the distance of the platform doesn't change, the length of the train car does to keep the speed of light constant, and time dilation, in effect, backs this up.

How come I cannot say that as a consequence of relativity that the sun is rotating around the Earth just as much as the Earth is rotating around the sun, even though we know that the Earths orbit is due to the gravitation of the Sun and the direction and speed in which the Earth is traveling that compensates for the gravity so it does not just drop into it. From our perspective the Sun is rotating around the Earth, and from the Sun's perspective the Earth is rotating around the sun.

You can say this, and in a certain perspective, the geocentric model was correct since in our perspective that is how the universe is. The reason why the other model is what we use, however, is because it simplifies everything down.

It's all just perspective. Anything can seem like anything else. The reason why certain things are accepted is because they work in all the perspectives. One exception, however, is the statement that we are the center of the universe. This appears to be true no matter where you stand in the universe, but that's because everything is moving away from everything else.

 

[objecta99]

these are a rephrasing of the general arguments posed to me by said friend that I have had the hardest time contending with. I hope it doesn't matter too much bc regardless if I supported the *correct interpretation of relativity or not, on my view what counts is that such support or contention involves qualitative understanding (that's probably something more appreciated in philosophy than science meh?) even if a qualitative understanding entailed a certain view rather than some other view on the matter.

Yeah I set that train platform scenario up poorly. Its just the usual question as to whether if we could compare the two clocks, the train clock would be slower when held side by side to the latter (or however that's achieved hypothetically via speed of light video transmission) and from this we could say that the time dilation was non-symmetrical (it only appears symmetrical) and non-relative. I am not endorsing this view but that is the argument made by some (maybe not here). I understand to the level I do, that an IRF must be chosen in order to assess relative time dilation, I have no disagreement there. Some ppl still want to poo-poo that and say that there is only one frame or clock where this is an "actual" time dilation taking place. I'm sure you are much more aware of the nuances in this debate than I am and have encountered such a challenge, but there it is. sorry, my response was hubristic in tone and I was going to respond with " I pity the fool that claims time dilation is non-relative" lol?

 

[Dale]

objecta99, it would be helpful if you would stop talking so much about your friend. Since we are not privy to your conversations with him/her we cannot realistically be expected to contribute to the conversation. Simply ask the questions that *you* have as directly as possible.

One thing that may help is to understand that in the theory of relativity not everything is relative. Even pre-relativity there was a long list of things which were relative (velocity, kinetic energy, momentum, etc.) and a list of things which were not relative (duration, length, mass, etc.), so the fact that some things are relative and others are not is nothing new.

All relativity did was expand the "relative list" to include duration, length, and simultaneity and also expand the "non-relative list" to include new concepts which were not discovered before (spacetime interval, proper acceleration, etc.).

To simply use the name of the theory to broadly claim that "everything is relative" is pure ignorance. Certain specific quantities (length) are relative, other specific quantities (invariant mass) are invariant, and the theory is completely silent on other concepts (moral/ethical values).

 

[objecta99]

Pls no one get mad at me, i just want to rephrase what seems to be the biggest sticking point for "me". I am not disagreeing with any points raised by any of you folks i just am trying to rephrase the issue to make sure i am not missing anything. Pls do not think i am not getting what is being told me, if anyone wants to respond with a simple "i already explained this" or "go back to my former post" i will gladly and graciously accept such without qualms. Heres my line of questioning:

Just bc we need a relative frame to compare velocity does this mean that if one object has velocity then the other object relative to it has the same velocity and mirrors its velocity per relative velocity. can we have two objects with different velocities, and yet they are still relative to each other in that we cannot compare without the frames of reference.

consider the simplisitic hypothetical stated as such, i realize that it does potentially beg the usual "we need a IRF" :
"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."

There are two frames of reference. The clock on the jet, and the clock on the ground.

1) Does the clock in one have greater velocity as experimentally shown?
2) Does the clock in one slow more than the other as experimentally shown?

basically what I am wondering is can two velocities relative to each other have different velocities under SR and relative to each other?
Back to the 'train platform' scenerio, do the implications of SR entail that the platform would need to carry the same velocity as the train just bc velocity is relative. If so does this mean that nothing could have more velocity than anything else, and all objects would be traveling the same velocity as the object they are referenced with relatively? Time slows the faster the velocity for the object traveling such (which as shown is not necessarily both objects - if it was then a clock on a plane does not have greater or lesser velocity than a clock on the ground). IOW how do I understand that there can be two different velocities (even when they are relative to each other) if relative velocity means that time dilation and velocity are symmetrical in intertial frames--does this symmetry mean that they are equal in velocity? or just share the same factor for Lorentz transforms--and what is the difference. Pls guys I know I am testing some patience perhaps its not my intent, I am just really trying to make sure I fully understand and in order to do this I have to repeat a bit. thank you

 

[PeterDonis]

"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."

There are two frames of reference. The clock on the jet, and the clock on the ground.

No, there is also a third one: a frame that is *not* rotating with the Earth. This is the frame with respect to which the velocity is given in what you quoted. The plane moving westward has a lower velocity relative to this frame because it is moving in the opposite direction to the Earth's rotation, so with respect to a non-rotating frame it is moving slower.

basically what I am wondering is can two velocities relative to each other have different velocities under SR and relative to each other?

No. You just need to correctly identify the frame to which the velocities are referred.

 

[ghwellsjr]

Just bc we need a relative frame to compare velocity does this mean that if one object has velocity then the other object relative to it has the same velocity and mirrors its velocity per relative velocity. can we have two objects with different velocities, and yet they are still relative to each other in that we cannot compare without the frames of reference.

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. One such method uses Doppler shifts, measuring the rate of the other object's clock compared to its own. Then it is easy to calculate the relative velocity. Both objects will determine that the other one is moving away or toward at the same speed (in opposite directions).

However, if you establish a reference frame, you can transform the worldlines of the objects to other frames that will increase the speed of the objects to much higher degrees, all the way to just under the speed of light.

Is that what you're wondering about?

 

[objecta99]

yes and I am both glad you posted this and not glad for other reasons due to what I thought I understood. DOH! I have to ask for my own sanity and understanding that if that's the case then in that instance how come I can say that between two objects "traveling along the same line at any arbitrary speeds and they are interial" that they can make some agreed upon calculations about who's speed has greater magnitude without regard to any reference frame, and still claim that velocity is always relative. It seem that the relative velocity is addressing the problem of giving an absolute position and velocity etc but that doesn't mean that we can't in some cases tell and agree who is going faster than who. am I right here? is this a speed vs velocity thing or am I not understanding that relative velocity and in some cases velocity can be separated meaningfully.

can the arbitrary speeds not be the same, can they be assumed to be at least possibly different in these comparative and agreed upon cases of whos traveling faster.??

I hope I have missed your point bc if the preceding is more or less right then I got checkmated potentially.

 

[objecta99]

This is what I am trying to understand:
Is the following true or false: It is not the case that in all cases where two objects are moving at different proper times, in both reference frames there will not be an agreement about who is traveling faster then the other.

 

[ghwellsjr]

yes and I am both glad you posted this and not glad for other reasons due to what I thought I understood. DOH! I have to ask for my own sanity and understanding that if that's the case then in that instance how come I can say that between two objects "traveling along the same line at any arbitrary speeds and they are interial" that they can make some agreed upon calculations about who's speed has greater magnitude without regard to any reference frame, and still claim that velocity is always relative.

I said they will each measure the other one to be traveling at the same speed, exactly.

It seem that the relative velocity is addressing the problem of giving an absolute position and velocity etc but that doesn't mean that we can't in some cases tell and agree who is going faster than who. am I right here? is this a speed vs velocity thing or am I not understanding that relative velocity and in some cases velocity can be separated meaningfully.

The equal speeds are in opposite directions so in that sense you could say that the velocities are the negative of each other.

can the arbitrary speeds not be the same, can they be assumed to be at least possibly different in these comparative and agreed upon cases of whos traveling faster.??

I hope I have missed your point bc if the preceding is more or less right then I got checkmated potentially.

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.

 

[ghwellsjr]

This is what I am trying to understand:
Is the following true or false: It is not the case that in all cases where two objects are moving at different proper times, in both reference frames there will not be an agreement about who is traveling faster then the other.

You have made a very convoluted statement and I don't know what "moving at different proper times" means.

Let me see if this statement will make it clear for you:

For any two inertial objects traveling at any arbitrary speeds along a line according to an Inertial Reference Frame, you can always transform to the rest frame of one of them which will produce a speed for the other one, and then you can transform to the rest frame of the other one which will produce the same speed in the opposite direction for the first one.

 

[objecta99]

"I said they will each measure the other one to be traveling at the same speed, exactly."

ok that gives me some relief. I am about to have a panic attack bc I am trying to defend the position that velocity in SR is always relative (frame dependent--saying who is going faster is always based on a IRF) and an interlocutor (old friend) is claiming things like the following:

"Most think (in the field of SR) that you can have two objects with different velocities, and yet they are still relative in that we cannot compare without the frames of reference."

He is claiming that my view of strict relative velocity in all scenarios of two moving objects entails that as he puts it:

"In what seems your position, the platform would need to carry the same velocity. In fact nothing could have more velocity than anything else, so all SR goes out the window in your view. All objects would be traveling the same velocity as the object they are referenced with. That means there would never be any time dilation, as all clocks would travel the same velocity in relation to every other clock. It's simply not what relativity suggests, but it is the implication of your seeming misunderstandings around this topic. "

this is a philosopher working on publishing his third book in a trilogy who is saying this to me bc I am trying to defend the stict notion that velocity is strictly frame dependent and relative to a chosen IRF. He is saying that this forces me into the view that between any two objects, relative to each other, they must be traveling at the same speed and furthermore that this is a problem to my view of SR. I have tried to argue against this person for the sake of reppin' what I take to be the implications of SR. AM I wrong best u can tell here? I take solace in the quote that u mention but I still feel insecure on the matter. I wish I could defend what I take to be the correct SR understanding better. I am doing my best, this is not a homework exersize its realpolitik and I am just a minion trying to do my duty to physics sir.

 

[objecta99]

Let me see if this statement will make it clear for you:

For any two inertial objects traveling at any arbitrary speeds along a line according to an Inertial Reference Frame, you can always transform to the rest frame of one of them which will produce a speed for the other one, and then you can transform to the rest frame of the other one which will produce the same speed in the opposite direction for the first one.

I am glad you say this and that I was not reading u right.

 

[objecta99]

"proper time" meaning ones own clock in ones own path. I might have used that term technically incorrect but I mean how I clarified/equivocated here. the statement u refer to though convoluted (double negation) is done for modal reasons and that's just how such statements tend to come off sounding; convoluted.

 

[A.T.]

I am trying to defend the stict notion that velocity is strictly frame dependent and relative to a chosen IRF.

That is correct.

He is saying that this forces me into the view that between any two objects, relative to each other, they must be traveling at the same speed

This is also correct. The speed of the other object is the same across the two rest frames of the objects.

 

[objecta99]

A.T. thanks for the help sir. when I say that "he is saying this forces me into the position..." I am not disagreeing that I hold that view--I am claiming that is the right way to look at things and he is saying it is not hence I am "forced" to that position due to my bad understanding of SR on his view. He claims that such a "forced position' is wrong on the correct SR interpretation while I am endorsing the view that the speed is the same across two rest frames. just for clarity. I hope I am not bringing down the gods of physicsforums upon me for my queer postings. I am dealing with a friend who's ultimate goal is promoting not just antinatalism (humans should stop breeding morally), and bad physics (on my view), but also efilism which is the view that we should end all sentient life on Earth including animals for objective moral reason--hence his extreme objective view of relative velocity (its consistent at least). you might see now my ego investment on proving this particular writer wrong;)

 

[A.T.]

He claims that such a "forced position' is wrong on the correct SR interpretation

His claim:

"That means there would never be any time dilation, as all clocks would travel the same velocity in relation to every other clock."

is nonsense, and doesn't follow from the symmetry of relative speeds. In each clock's rest frame you have two clocks at two different speeds (one at 0, the other at v > 0) that are ticking at different rates.

 

[objecta99]

Ok, I think I have gotten to the problem (I think). mind you your dealing with an amateur and it goes without saying that what will be obvious to you folks is not so with me. 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). some say that at certain speeds that Lorentz relativity can be reduced to Galilean relativity but others claim that this is nonsense. Does this make sense to anyone, or am I understanding wrong here?

 

[Dale]

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.

 

[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.