Two spaceships in opposite direction at near c

[stu dent]

if you have 2 spaceships and they depart in exactly the opposite direction from a starting point, say a space station, and they accelerate to speeds nearing the speed of light, then what is the relative speed of each spaceship, using one of them as a reference frame.

it would seem to me, that the space station would be moving at a speed nearing c, and then the other spaceship would need to be traveling at double that.

but that can't be right.

 

[PeterDonis]

if you have 2 spaceships and they depart in exactly the opposite direction from a starting point, say a space station, and they accelerate to speeds nearing the speed of light, then what is the relative speed of each spaceship, using one of them as a reference frame.

it would seem to me, that the space station would be moving at a speed nearing c, and then the other spaceship would need to be traveling at double that.

but that can't be right.

Yes, it can't be right, and it isn't. The correct formula for adding velocities in SR is:

w' = \frac{v + w}{1 + vw / c^2}

where w is some object's velocity in one frame, and w' is the same object's velocity in a second frame moving at v relative to the first.

In your scenario, say spaceship A moves off to the left from the space station, with speed w, and spaceship B moves off to the right with speed v. In spaceship B's frame, the velocity of spaceship A is then w', as given by the above formula. It should be evident that if w < c and v < c, then w' < c also.

Picking some concrete numbers for an example, if v = .99c (to the right) and w = .99c (to the left), then

w&#039; = \frac{.99 + .99}{1 + .99 * .99} c = .99995 c

So spaceship A will be moving at .99995c relative to spaceship B.

 

[stu dent]

Yes, it can't be right, and it isn't. The correct formula for adding velocities in SR is:

w&#039; = \frac{v + w}{1 + vw / c^2}

where w is some object's velocity in one frame, and w' is the same object's velocity in a second frame moving at v relative to the first.

In your scenario, say spaceship A moves off to the left from the space station, with speed w, and spaceship B moves off to the right with speed v. In spaceship B's frame, the velocity of spaceship A is then w', as given by the above formula. It should be evident that if w < c and v < c, then w' < c also.

Picking some concrete numbers for an example, if v = .99c (to the right) and w = .99c (to the left), then

w&#039; = \frac{.99 + .99}{1 + .99 * .99} c = .99995 c

So spaceship A will be moving at .99995c relative to spaceship B.

i see. thx, but by what mechanism does this relationship exist? meaning, what is it in the real world is this formula explaining, or, where does it come from?

 

[arindamsinha]

i see. thx, but by what mechanism does this relationship exist? meaning, what is it in the real world is this formula explaining, or, where does it come from?

Special Theory of Relativity.

 

[PeterDonis]

i see. thx, but by what mechanism does this relationship exist? meaning, what is it in the real world is this formula explaining, or, where does it come from?

The formula I gave is the relativistic velocity addition law, which is a consequence of the Lorentz transformation formulas. See the Usenet Physics FAQ for a good (if brief) discussion:

http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html

 

[bobc2]

i see. thx, but by what mechanism does this relationship exist? meaning, what is it in the real world is this formula explaining, or, where does it come from?

stu dent, one way to get a physical feel for what's going on is to develop an understanding of your problem in the context of a 4-dimensional universe. I'll give you a quick picture and a link for further details just in the event you might be interested in this approach. I and others here can provide more information on this if you wish. One key element of the picture below is a strange and mysterious aspect of nature resulting in different cross-section views of the universe for observers moving at different speeds. This, in large measure, accounts for the strange things going on with special relativity theory and why velocities do not add the way you might have thought. The slant of the X4 axes for the red and blue rockets relate to speeds--but we have red, blue and black frames of reference here, and the X1 axes (worlds the different observers "live in") cut across the universe at different angles as well.

You might begin by looking at the picture illustrating the different times for the red and blue observers (time dilation) as shown below. When the blue guy is at position 9 along his X4 axis (time axis) his world includes the red rocket located at red's frame position 8. But when red is at his position 9, the blue rocket is at the blue position 7. Keep in mind each is viewing 3-D cross-sections of 4-dimensional rockets.

Here is a link for more details (see post #19):
https://www.physicsforums.com/showthread.php?p=4138850#post4138850

 

[bobc2]

If you were able to follow the space-time diagrams in the previous post and link, then you can easily see in the sketch below how it is that the velocities add. In the previous post we had red and blue frames moving in opposite directions at the same speed with respect to the black frame. Now we look at the speeds of the red and black frames with respect to the blue frame. The black frame moves at 1/2 the speed of light with respect to the blue frame (moving in blue's negative X1 direction). The red frame is moving at 1/2 the speed of light with respect to the black frame (moving in black's negative X1 direction).

But, now you see clearly that (1/2)c + (1/2)c does not give you 1 x c for the red frame with respect to the blue frame. Red is moving at relativistic speed in the blue negative X1 direction, but certainly not at the speed of light.

 

[harrylin]

Special Theory of Relativity.

In addition: SR does not give a "mechanism", as it is based on logical (mathematical) deduction of phenomenological principles. Historically there have been different explanations of "what is really going on". If Bob's 4D reality makes sense to you, then that is nice; alternatively you could go for Lorentz's "ether" concept or Harvey's "physical relativity" or ...

 

[stu dent]

Special Theory of Relativity.

no offense, but you may as well have said: because i said so. Which will never be satisfactory for me, even if it is einstein that said so.

i mean, not that i doubt einstein is correct, but i want to know why he must be correct. why it is necessary for it to be that way.

i mean, i realize it must be many steps of logic building upon each other in order to arrive at this conclusion, but there are steps that provide certainty and conclude this fact.

if i am in a space ship, and i travel in one direction at nearly the speed of light, and another does so in the opposite direction, then i don't see how i influence that other space ship. i don't understand how my velocity, can hold implications for the velocity of another object. it makes perfect sense to me that an energy with mass cannot reach the speed of light. i get that.

but i don't fully get why or how it can be that my velocity relative to another object that has mass can't reach or exceed the speed of light.

what I'm thinkign now, that i will ponder further also, is that it nearly seems as though the quantity of energy required to accelerate an object would then be different depending on your reference frame.

or, since this seems not to make a lick of sense, the relative velocity of (let's call it spaceship A and B and then Earth) of A relative to earth, is the equivalent to A relative to B.

or no, wait, A relative to light in Earth frame, is equivalent to A relative to light in B frame, which may or may not be different, which i also need to think about, and also, a curious thing would seem to me, that the closer that B approaches the speed of light then, regardless of the velocity of A, the more similar A's velocity is to Earth's in B's reference frame.

which intuitively feels to me, like the opposite of time dilation effect, because it is like putting the universe on pause, while you continue to age.

 

[stu dent]

thanks for all the replies, i will explore these links and posts, but may not get to reply until later.

 

[PeterDonis]

if i am in a space ship, and i travel in one direction at nearly the speed of light, and another does so in the opposite direction, then i don't see how i influence that other space ship. i don't understand how my velocity, can hold implications for the velocity of another object.

It doesn't. That's not the issue. The issue is, how do you *measure* the velocity of an object that is spatially distant from you? You can't observe it directly, so you have to somehow translate the direct observations you can make into a value for the distant object's velocity. Any such translation is not just dependent on your motion, or on the motion of the distant object; it's also dependent on the properties of spacetime itself, since the information about the distant object's motion has to travel to you through spacetime. And it's the properties of spacetime that give rise to the relativistic velocity addition formula.

 

[stu dent]

In addition: SR does not give a "mechanism", as it is based on logical (mathematical) deduction of phenomenological principles. Historically there have been different explanations of "what is really going on". If Bob's 4D reality makes sense to you, then that is nice; alternatively you could go for Lorentz's "ether" concept or Harvey's "physical relativity" or ...

i think maybe mechanism was not the best word, what i was trying to convey was a hard thing to say. i meant like, why it must be.

math is all very nice. but math is not enough. it is not a proper explanation.

for example, we could plot 4 dimensional equations in a 2d altitude map kind of way, but for 4d, and we'd get some confusing drawings. the understanding would be lost on us. we could do operations as well, and mathematical deduce the results of these things, and try to draw more kind of maps again as well.

but still, we would know nothing.

but call the 4th dimension time, and suddenly everything changes. the realisation, which is not mathematical, makes everything apparent. it allows it to make sense. it provides a real world understanding. we were plotting a moving object in time frames.

i was getting at something like that. i want to understand how it can be possible, and why it must be possible, and what exactly is happening.

the formula should be telling for this, but i am uncertain how it got discovered, why it must be that way.

the formula is precise directions of how. it does not show why, nor does it show why it is certain that is how.

 

[stu dent]

how did lorentz figure out lorentz transformations, and why they were necessary?

 

[Warp]

how did lorentz figure out lorentz transformations, and why they were necessary?

The lorentz transformation can actually be derived by simply starting with the assumption that the speed of light in vacuum is the same for all observers (which, in fact, is an observed and measured phenomenon, rather than being a mere hypothesis). It isn't even all that complicated to understand how it's derived from there.

The factor that Lorentz came up with was simply a description of how relative lengths contract in different frames of reference (and, as said, is derived directly from assuming that c is the same in all frames of reference.) It described the results of the Michelson-Morley experiment as well as a bunch of others.

(This was technically speaking a hypothesis at first, because there was only a limited amount of measurement data available. However, with time it has been proven quite accurate in quite many different situations.)

 

[harrylin]

how did lorentz figure out lorentz transformations, and why they were necessary?

He was developing an electrodynamics theory (electrons etc) which modeled electrodynamics relative to a stationary medium, the "ether". Following the "Galilean" transformations of classical mechanics, it should be possible in theory to detect motion relative to the ether - but such experiments failed.

In earlier discussions I gave a much simplified sketch of how he figured it out:
https://www.physicsforums.com/showthread.php?p=3756233#post3756233 (very roughly the same approach as Einstein)
https://www.physicsforums.com/showthread.php?p=3887942#post3887942 [/url] (simplified and incomplete derivation; and see the correction in the there following post).

 

[robinpike]

no offense, but you may as well have said: because i said so. Which will never be satisfactory for me, even if it is einstein that said so.

i mean, not that i doubt einstein is correct, but i want to know why he must be correct. why it is necessary for it to be that way.

i mean, i realize it must be many steps of logic building upon each other in order to arrive at this conclusion, but there are steps that provide certainty and conclude this fact.

if i am in a space ship, and i travel in one direction at nearly the speed of light, and another does so in the opposite direction, then i don't see how i influence that other space ship. i don't understand how my velocity, can hold implications for the velocity of another object. it makes perfect sense to me that an energy with mass cannot reach the speed of light. i get that.

but i don't fully get why or how it can be that my velocity relative to another object that has mass can't reach or exceed the speed of light.

Student, don't give up on seeking the answer to that question - that question shows great insight.

 

[bobc2]

Student, don't give up on seeking the answer to that question - that question shows great insight.

A wonderful and refreshing response, robinpike.

 

[robinpike]

if i am in a space ship, and i travel in one direction at nearly the speed of light, and another does so in the opposite direction, then i don't see how i influence that other space ship. i don't understand how my velocity, can hold implications for the velocity of another object. it makes perfect sense to me that an energy with mass cannot reach the speed of light. i get that.

but i don't fully get why or how it can be that my velocity relative to another object that has mass can't reach or exceed the speed of light.

Here is an example of the issue:

Two space ships accelerate in opposite directions from a space station in deep space. The space station calculates the speed of each departing spaceship relative to itself by sending out light signals to the space ships, which they return straight back to the space station.

In this way, the people on the space station can calculate the speed of each spaceship relative to themselves. Eventually, the two space ships reach individual departing speeds from the space station of 3/4 the speed of light.

This suggests that the people on the space station see the two space ships recede away from each other at 1.5 times the speed of light?

And yet the two space ships can still communicate with each other by sending light signals to each other.

 

[harrylin]

Here is an example of the issue:

Two space ships accelerate in opposite directions from a space station in deep space. The space station calculates the speed of each departing spaceship relative to itself by sending out light signals to the space ships, which they return straight back to the space station.

In this way, the people on the space station can calculate the speed of each spaceship relative to themselves. Eventually, the two space ships reach individual departing speeds from the space station of 3/4 the speed of light.

This suggests that the people on the space station see the two space ships recede away from each other at 1.5 times the speed of light?

And yet the two space ships can still communicate with each other by sending light signals to each other.

That is not an issue (and different from the OP), except if it is still an issue for you if your replace "light in space" by "sound in air". There is in principle no problem for two airplanes to exchange sound signals if they recede away in opposite directions at 3/4 the speed of sound.

 

[ghwellsjr]

Yes, that's because, as PeterDonis pointed out in post #2, they see each other receding away from each other at:

w' = (.75 + .75)/(1 + .75 * .75) c = .96 c

 

[jartsa]

Here is an example of the issue:

Two space ships accelerate in opposite directions from a space station in deep space. The space station calculates the speed of each departing spaceship relative to itself by sending out light signals to the space ships, which they return straight back to the space station.

In this way, the people on the space station can calculate the speed of each spaceship relative to themselves. Eventually, the two space ships reach individual departing speeds from the space station of 3/4 the speed of light.

This suggests that the people on the space station see the two space ships recede away from each other at 1.5 times the speed of light?

And yet the two space ships can still communicate with each other by sending light signals to each other.

Let us ask the question: How much can a photon's velocity change?

-300000 km/s - 300000 km/s = -600000 km/s

A photon approaching a spaceship, that is moving to the left very fast, has velocity -300000 km/s

After this photon has reflected from the spaceship it has velocity 300000 km/s

Before the reflection the photon and the spaceship had about the same velocity, then the velocity of the photon changed by 600000 km/s.

 

[bobc2]

Let us ask the question: How much can a photon's velocity change?

-300000 km/s - 300000 km/s = -600000 km/s

A photon approaching a spaceship, that is moving to the left very fast, has velocity -300000 km/s

After this photon has reflected from the spaceship it has velocity 300000 km/s

Before the reflection the photon and the spaceship had about the same velocity, then the velocity of the photon changed by 600000 km/s.

Nice idea, jartsa. But, are you sure it was the same photon?

 

[jartsa]

Nice idea, jartsa. But, are you sure it was the same photon?

Let me rephrase the idea, not using the word photon:

300000 km/s is a very important constant in physics.

600000 km/s is a somewhat useful constant:
Light sphere's diameter can increase by 600000 km/s.
Light beam's velocity can change by 600000 km/s.

 

[ghwellsjr]

Let me rephrase the idea, not using the word photon:

300000 km/s is a very important constant in physics.

600000 km/s is a somewhat useful constant:
Light sphere's diameter can increase by 600000 km/s.
Light beam's velocity can change by 600000 km/s.

I'm not sure what you're getting at here but if you're following Special Relativity, light always travels at 300000 km/s in any frame you choose. It's velocity never changes and nothing can travel faster than 300000 km/s.

 

[Drakkith]

Let us ask the question: How much can a photon's velocity change?

-300000 km/s - 300000 km/s = -600000 km/s

A photon approaching a spaceship, that is moving to the left very fast, has velocity -300000 km/s

After this photon has reflected from the spaceship it has velocity 300000 km/s

Before the reflection the photon and the spaceship had about the same velocity, then the velocity of the photon changed by 600000 km/s.

Yes, but so what? It's speed is always the same at 300,000 km/s.

 

[jartsa]

I'm not sure what you're getting at here but if you're following Special Relativity, light always travels at 300000 km/s in any frame you choose. It's velocity never changes and nothing can travel faster than 300000 km/s.

Light beam going to the left has velocity -300000 km/s.
Light beam going to the right has velocity +300000 km/s.

Is this not the normal way of talking about velocities of things?

Light beam going to the left may turn into light beam going to the right, when reflecting, right?

 

[jartsa]

Yes, but so what? It's speed is always the same at 300,000 km/s.

Well, the 600000 km/s velocity change might help some newbies to see how light can travel between two spaceships whose distance is increasing by nearly 600000 km/s. (according to an observer that sees both spaceships moving at near c into opposite directions)

 

[Nugatory]

Well, the 600000 km/s velocity change might help some newbies to see how light can travel between two spaceships whose distance is increasing by nearly 600000 km/s. (according to an observer that sees both spaceships moving at near c into opposite directions)

That's a good point... And now that I think about it, you don't need the reflection off of one the spaceships to make it, just consider two flashes of light moving past each other in opposite directions.

 

[ghwellsjr]

Well, the 600000 km/s velocity change might help some newbies to see how light can travel between two spaceships whose distance is increasing by nearly 600000 km/s. (according to an observer that sees both spaceships moving at near c into opposite directions)

But that would be the wrong way to explain it to a newby.

In an Inertial Reference Frame (IRF) in which two spaceships are traveling in opposite directions at nearly the speed of light and one of them sends a light signal to the other one, the light signal travels at c relative to the IRF, not relative to either spaceship. That is why it has no trouble reaching the other spaceship but it will take a very long time according to the IRF. However, since the spaceships are traveling at a very high speed in the IRF, their clocks are running very slowly compared to the coordinate time of the IRF and so it will not take as long for them for the light to traverse the distance between them.

Think of speeds relative to an IRF, not relative to observers and you'll have no problem. After you set up a scenario in a given IRF, you can then transform the coordinates of the significant events defined according to that IRF into another IRF moving with respect to the first IRF and see how light also travels at c in the new IRF and produces all the same observables and measurements for each observer as the first IRF did.

This is the correct way to explain to newbies how Special Relativity describes what is happening.

 

[ghwellsjr]

I've drawn a diagram to show what happens in an IRF with two spaceships traveling in opposite directions at 0.8c. They both leave the blue spacestation at time 0 when they all set their clocks to 0. The dots mark off one-minute intervals for each spaceship and the spacestation. At 0.8c, gamma is 1.6667 so the dots for the spaceships are farther apart by that amount compared to the coordinate time. After one minute, the red spaceship sends a signal to the black spaceship at the speed of light according to the IRF. The black spaceship receives this signal when his clock reads 9 minutes even though it took over 13 minutes according to the IRF:

 

[K^2]

It might be useful to have the same diagram in IRF of each of the ships as well.

 

[ghwellsjr]

It might be useful to have the same diagram in IRF of each of the ships as well.

Ok, here's the one for the black spaceship's IRF:

Notice that the blue spacestation is now traveling at -0.8c and the red spaceship is traveling at -0.9756c. The time dilation for the spaceship is 1.6667 and for the red spaceship is 4.5556. The light signal, emitted by the red spaceship at its one-minute mark, travels in this IRF at c to the black spaceship at its nine-minute mark, just like in the original IRF.

And here's the one for the red spaceship's IRF:

The blue spacestation is traveling at 0.8c and the black spaceship is traveling at 0.9756c. The time dilation for the spaceship is 1.6667 and for the black spaceship is 4.5556. The light signal, emitted by the red spaceship at its one-minute mark, travels in this IRF at c to the black spaceship at its nine-minute mark, just like in the other two IRF's.

We could also pick any other IRF to show all the same events and they would all be in agreement. There is nothing special about any particular IRF, even one for which any observer is at rest--what we call its own IRF. That's the whole point of Special Relativity.

 

[K^2]

We could also pick any other IRF to show all the same events and they would all be in agreement. There is nothing special about any particular IRF, even one for which any observer is at rest--what we call its own IRF. That's the whole point of Special Relativity.

Of course. This just happens to be a very nice illustration to point to. It shows, visually, how the velocities add, how the times of events are different in each coordinate system, and how despite that, the proper time for each intercept remains the same. It'll be nice to point to if anybody else asks related questions. Thanks for taking the time.

 

[bobc2]

Ok, here's the one for the black spaceship's IRF:

Notice that the blue spacestation is now traveling at -0.8c and the red spaceship is traveling at -0.9756c. The time dilation for the spaceship is 1.6667 and for the red spaceship is 4.5556. The light signal, emitted by the red spaceship at its one-minute mark, travels in this IRF at c to the black spaceship at its nine-minute mark, just like in the original IRF.

And here's the one for the red spaceship's IRF:

The blue spacestation is traveling at 0.8c and the black spaceship is traveling at 0.9756c. The time dilation for the spaceship is 1.6667 and for the black spaceship is 4.5556. The light signal, emitted by the red spaceship at its one-minute mark, travels in this IRF at c to the black spaceship at its nine-minute mark, just like in the other two IRF's.

We could also pick any other IRF to show all the same events and they would all be in agreement. There is nothing special about any particular IRF, even one for which any observer is at rest--what we call its own IRF.

Great job witht the space-time diagrams, ghwellsjr!

That's the whole point of Special Relativity.

That may be a little bit of an overstatement, but the intended spirit of it works fine, and you did make very good points.

 

[Vandam]

Gwelsjr,
I really appreciate your effort drawing diagrams. Good job.
Unfortunately I am not too happy with your text.
The way you explain it is as if the time dilation occurs due to the further dots pacing of clockticks on the clock worldline.
There is also a danger of interpreting your diagrams as if timedilation happens because of the taking into account of the lightbeams.
Let me put it this way:
You have drawn three different diagrams, but to see how timedilation works it is better to look at one diagram only with more information on it. I did it for you:
(For simplicity I omited what red says):
Blue notices black (and red) time dilation because when his blue clock ticks 15 (not 13 as you wrote;)), in his BLUE frame (=3D spaceworld) the black and red clock show 9.
So far so good.
Now what black says:
Black notices time dilation of blue time because "when his black clock ticks 9 seconds, IN HIS BLACK FRAME (=3D spaceworld) the blue clock is only at 5,399 sec. (9 / 1,6667).
And still IN HIS BLACK 3D world the blue 'time dilation' means: red clock is only at 1,975 sec (9 / 4,5556).
Here you see clearly that the 'slowing down' of the blue and red clock have NOTHING to with the further spacing of blue or red dots relative to the black dots (red dots are equally spaced as black, blue dots are less spaced relative to the black ones!).

On a Loedel diagram (I'm now too lazy too make one) you would see that the time dilation has nothing to do with the further spacing of clock ticks on the worldline of a clock. Time dilation is about relativity of simultaneity. (And that's only possible if you consider all events out there as observer independent entities time indications included (block universe).

Just in case you wonder what the reciprocal time dilation is for blue at 9 (see sketch below):
in blue 3D space black clock is at 5,389.
In blue 3D space when blue clock is at 5,399 the black clock is at 3,238 (= 5,399 : 1,667 ).
3D cuts through 4D block spacetime!

 

[Dale]

The way you explain it is as if the time dilation occurs due to the further dots pacing of clockticks on the clock worldline.

He said "compared to coordinate time", which is completely correct.

Here you see clearly that the 'slowing down' of the blue and red clock have NOTHING to with the further spacing of blue or red dots relative to the black dots (red dots are equally spaced as black, blue dots are less spaced relative to the black ones!).

No, his statement is still correct. The black dots are the most closely spaced "compared to coordinate time" for black. The blue dots are further spaced and the red dots even further. "Compared to coordinate time" measures only distance normal to the lines of simultaneity, what you have labeled "spaceworld".

On a Loedel diagram (I'm now too lazy too make one) you would see that the time dilation has nothing to do with the further spacing of clock ticks on the worldline of a clock. Time dilation is about relativity of simultaneity.

This is also true, but doesn't make ghwellsjr's statements wrong. The relativity of simultaneity is what changes the meaning of "compared to coordinate time" for the different frames.

 

[Vandam]

He said "compared to coordinate time", which is completely correct.

No, his statement is still correct. The black dots are the most closely spaced "compared to coordinate time" for black. The blue dots are further spaced and the red dots even further. "Compared to coordinate time" measures only distance normal to the lines of simultaneity, what you have labeled "spaceworld".

This is also true, but doesn't make ghwellsjr's statements wrong. The relativity of simultaneity is what changes the meaning of "compared to coordinate time" for the different frames.

I only wanted to point out there was a danger of misinterpreting his diagrams and/or text because of the further spacing of the dots on the worldline, a feature of Minkowski diagrams. I never said his statements were 'wrong'. The 'further spacing of the dots relative to coordinate time' would still be valid if the spacing of the dots on the worldline would be equal. That's my point. (And that's why I prefer Loedell diagrams where possible).

 

[bobc2]

Gwelsjr,
I really appreciate your effort drawing diagrams. Good job.
Unfortunately I am not too happy with your text.
The way you explain it is as if the time dilation occurs due to the further dots pacing of clockticks on the clock worldline.
There is also a danger of interpreting your diagrams as if timedilation happens because of the taking into account of the lightbeams.
Let me put it this way:
You have drawn three different diagrams, but to see how timedilation works it is better to look at one diagram only with more information on it. I did it for you:
(For simplicity I omited what red says):
Blue notices black (and red) time dilation because when his blue clock ticks 15 (not 13 as you wrote;)), in his BLUE frame (=3D spaceworld) the black and red clock show 9.
So far so good.
Now what black says:
Black notices time dilation of blue time because "when his black clock ticks 9 seconds, IN HIS BLACK FRAME (=3D spaceworld) the blue clock is only at 5,399 sec. (9 / 1,6667).
And still IN HIS BLACK 3D world the blue 'time dilation' means: red clock is only at 1,975 sec (9 / 4,5556).
Here you see clearly that the 'slowing down' of the blue and red clock have NOTHING to with the further spacing of blue or red dots relative to the black dots (red dots are equally spaced as black, blue dots are less spaced relative to the black ones!).

On a Loedel diagram (I'm now too lazy too make one) you would see that the time dilation has nothing to do with the further spacing of clock ticks on the worldline of a clock. Time dilation is about relativity of simultaneity. (And that's only possible if you consider all events out there as observer independent entities time indications included (block universe).

Just in case you wonder what the reciprocal time dilation is for blue at 9 (see sketch below):
in blue 3D space black clock is at 5,389.
In blue 3D space when blue clock is at 5,399 the black clock is at 3,238 (= 5,399 : 1,667 ).
3D cuts through 4D block spacetime!

Very impressive insight, Vandam. I hadn't noticed that. Thanks for that observation. I think it is very good to point this out. You do a very good job of keeping the focus on the fundamental concept. Too often we get involved with the numbers and miss the underlying concept.

 

[Vandam]

That may be a little bit of an overstatement, but the intended spirit of it works fine, and you did make very good points.

Bob, I was wondering about ghwellsjr statement too...
I think we might have the same thoughts about this, but to me the whole point about the coordinate systems is that whatever coordinate system you use (apply to the outside observer independent events) then SR's 'relativity of simultaneity' shows you that reality out there is a 4D block spacetime/universe. But this is not allowed to be discussed here.

 

[ghwellsjr]

...
Gwelsjr,
I really appreciate your effort drawing diagrams. Good job.

Thanks.

Unfortunately I am not too happy with your text.

The feeling is mutual.

The way you explain it is as if the time dilation occurs due to the further dots pacing of clockticks on the clock worldline.

Time dilation occurs due to the speed of a clock in a given Inertial Reference Frame (IRF). Just as speeds of objects are different in different IRF's, so are time dilations. The time dilations for each of the space ships/stations in the three IRF's I drew are different. I illustrate the time dilation by marking off equal ticks of each observer's clock with dots along the path of each observer. I think it's a great way to explain it and I think it's very easy to see and comprehend for a newby which is what I was trying to do. Until some newbies comment about this, we'll never know if I'm right or wrong.

There is also a danger of interpreting your diagrams as if timedilation happens because of the taking into account of the lightbeams.

Are you talking about Relativistic Doppler?

Let me put it this way:
You have drawn three different diagrams, but to see how timedilation works it is better to look at one diagram only with more information on it.

I started out drawing just one diagram, not to show anything about time dilation but rather to show how light travels at c, not 2c like jartsa was promoting in post #27 as a way to explain SR to newbies. You need to read my first response to him in post #29 to understand the context of my first diagram in post #30.

I later drew two more diagrams in response to K^2's request in post #31. In each of these, the signal going from the red spaceship at his 1-minute mark is received by the black spaceship at his 9-minute mark, even though the light signal takes a varying amount of time in each IRF but still travels at c in each of them and not with respect to the speeds of the spaceships. This was the whole point of these diagrams in support of my comment to jartsa in post #29:

In an Inertial Reference Frame (IRF) in which two spaceships are traveling in opposite directions at nearly the speed of light and one of them sends a light signal to the other one, the light signal travels at c relative to the IRF, not relative to either spaceship.

(For simplicity I omited what red says):
Blue notices black (and red) time dilation because when his blue clock ticks 15 (not 13 as you wrote;)), in his BLUE frame (=3D spaceworld) the black and red clock show 9.
So far so good.

First off, I did not make a mistake with regard to 13 versus 15. I was not talking about time dilation. I was talking about how long it took for the signal to get from the red spaceship to the black spaceship at the speed of light and I said "it took over 13 minutes according to the IRF". In the other two IRF's it took 4.5 minutes and 40 minutes. Light is not time dilated. I was not talking about time dilation. Please read my comments carefully before responding to them.

And now to my main point: The blue spacestation cannot notice the black (or red) spaceship's time dilation. Time dilation is not observable by anyone anywhere anytime. It is a calculation related to the speed of an object in a given IRF. If it were ever observable, then the observer would know which arbitrary IRF we were using. Or, more significantly, if it were observable, then we could identify the an absolute ether rest state and all of Special Relativity would be out the window.

Now what black says:
Black notices time dilation of blue time because "when his black clock ticks 9 seconds, IN HIS BLACK FRAME (=3D spaceworld) the blue clock is only at 5,399 sec. (9 / 1,6667).
And still IN HIS BLACK 3D world the blue 'time dilation' means: red clock is only at 1,975 sec (9 / 4,5556).
Here you see clearly that the 'slowing down' of the blue and red clock have NOTHING to with the further spacing of blue or red dots relative to the black dots (red dots are equally spaced as black, blue dots are less spaced relative to the black ones!).

Again, the black spaceship cannot notice the time dilation of the blue spacestation for the reasons I stated before.

Just because I drew three IRF's in which one of the observer's was a rest, you should not extapolate that observer's observations to what is assigned by the IRF, such as the time dilation related to the speed of the other objects. I could just as easily have drawn another diagram in which none of the observers was a rest, for example one in which the black spaceship and the blue spacestation are traveling at the same speed in opposite directions. Then how would you explain time dilation?

On a Loedel diagram (I'm now too lazy too make one) you would see that the time dilation has nothing to do with the further spacing of clock ticks on the worldline of a clock. Time dilation is about relativity of simultaneity. (And that's only possible if you consider all events out there as observer independent entities time indications included (block universe).

Just in case you wonder what the reciprocal time dilation is for blue at 9 (see sketch below):
in blue 3D space black clock is at 5,389.
In blue 3D space when blue clock is at 5,399 the black clock is at 3,238 (= 5,399 : 1,667 ).
3D cuts through 4D block spacetime!

I wasn't wondering and I have no idea what your diagram is attempting to convey. Maybe a newby can explain it to me.

Look, the reciprocal time dilation is very easily illustrated by looking at each of the IRF's for each observer and my text succinctly states what it is. For example, in the first IRF, blue's rest frame (post #30), I state that gamma for red and black is 1.6667 and I show their dots spaced by that amount with respect to the coordinates which also happens to be with respect to blue since blue is stationary in this IRF. Then if you go to the next IRF, black's rest frame (the first small IRF in post #32), I state in the text that the time dilation for the spacestation (incorrectly identified as the spaceship) is 1.6667 and you can see the exact same spacing of the blue dots in this IRF as you do for the black dots in the first IRF. You can do the same thing for each of the other pairs of space ships/station.

 

[ghwellsjr]

Bob, I was wondering about ghwellsjr statement too...
I think we might have the same thoughts about this, but to me the whole point about the coordinate systems is that whatever coordinate system you use (apply to the outside observer independent events) then SR's 'relativity of simultaneity' shows you that reality out there is a 4D block spacetime/universe. But this is not allowed to be discussed here.

Each IRF presents a different set of coordinates for each event. The time coordinate defines simultaneity.

For example, in the first IRF (post #30), minute five for the blue spacestation is simultaneous with minute three for the black and red spaceships. However in the other two IRF's (post #32) these three events occur at different coordinate times and so are not simultaneous. But minute three for the blue spacestation is simultaneous with minute five for one or the other of the two spaceships in these other two IRF's.

What are you guys concerned with?

 

[Vandam]

Thanks.

The feeling is mutual.

Time dilation occurs due to the speed of a clock in a given Inertial Reference Frame (IRF). Just as speeds of objects are different in different IRF's, so are time dilations. The time dilations for each of the space ships/stations in the three IRF's I drew are different. I illustrate the time dilation by marking off equal ticks of each observer's clock with dots along the path of each observer. I think it's a great way to explain it

My point was: I think it is not a great way to show time dilation by stressing the fact that the dots are further spaced on the worldline (unfortunately that's a minkoski fiagram feature)
It's far more correct to explain time dilation by means which clock indication (event) pops up in a selected frame (3D space), whether the dots are spaced or not is besides the point. (That's why a loedel diagram is beter to show time dilation.)
The time dilation occurs because the worldlines take a different direction in 4D spacetime, and hence the lines of simultaneity take other directions...

and I think it's very easy to see and comprehend for a newby which is what I was trying to do. Until some newbies comment about this, we'll never know if I'm right or wrong.

Are you talking about Relativistic Doppler?

I started out drawing just one diagram, not to show anything about time dilation but rather to show how light travels at c, not 2c like jartsa was promoting in post #27 as a way to explain SR to newbies. You need to read my first response to him in post #29 to understand the context of my first diagram in post #30.

I later drew two more diagrams in response to K^2's request in post #31. In each of these, the signal going from the red spaceship at his 1-minute mark is received by the black spaceship at his 9-minute mark, even though the light signal takes a varying amount of time in each IRF but still travels at c in each of them and not with respect to the speeds of the spaceships. This was the whole point of these diagrams in support of my comment to jartsa in post #29:First off, I did not make a mistake with regard to 13 versus 15. I was not talking about time dilation.

I was talking about how long it took for the signal to get from the red spaceship to the black spaceship at the speed of light and I said "it took over 13 minutes according to the IRF". In the other two IRF's it took 4.5 minutes and 40 minutes. Light is not time dilated. I was not talking about time dilation. Please read my comments carefully before responding to them.

If you talk about gamma and showing time diltation by means of further spacing of dots on a worldline, I do not see why I may not adress the issue of time dilation.

And now to my main point: The blue spacestation cannot notice the black (or red) spaceship's time dilation. Time dilation is not observable by anyone anywhere anytime. It is a calculation related to the speed of an object in a given IRF. If it were ever observable, then the observer would know which arbitrary IRF we were using. Or, more significantly, if it were observable, then we could identify the an absolute ether rest state and all of Special Relativity would be out the window.

Time dilation is not observable?

Again, the black spaceship cannot notice the time dilation of the blue spacestation for the reasons I stated before.

Just because I drew three IRF's in which one of the observer's was a rest, you should not extapolate that observer's observations to what is assigned by the IRF, such as the time dilation related to the speed of the other objects. I could just as easily have drawn another diagram in which none of the observers was a rest, for example one in which the black spaceship and the blue spacestation are traveling at the same speed in opposite directions. Then how would you explain time dilation?

I do not get your point at all.

I wasn't wondering and I have no idea what your diagram is attempting to convey. Maybe a newby can explain it to me.

Look, the reciprocal time dilation is very easily illustrated by looking at each of the IRF's for each observer and my text succinctly states what it is. For example, in the first IRF, blue's rest frame (post #30), I state that gamma for red and black is 1.6667 and I show their dots spaced by that amount with respect to the coordinates which also happens to be with respect to blue since blue is stationary in this IRF. Then if you go to the next IRF, black's rest frame (the first small IRF in post #32), I state in the text that the time dilation for the spacestation (incorrectly identified as the spaceship) is 1.6667 and you can see the exact same spacing of the blue dots in this IRF as you do for the black dots in the first IRF. You can do the same thing for each of the other pairs of space ships/station.

Maybe it does make sense mathematically. I was thinking physics, what's out there to be measured by any coordinate systems. Maybe your diagrams are only mathematical models, mine a representation of what's out there. But I know that defending an observer independent reality is not appreciated here...

 

[bobc2]

Vandam, I feel like your point was very well placed and fully appropriate to the discussion. Not to take away from the basic point ghwells was making--that was a good response to the original post. But, you certainly brought additional valuable insight to the discussion. Your emphasis on relativity of simultaineity really needed to be presented. It's always good to put the discussion in the context of the foundational physical concepts available to us with special relativity theory.

 

[ghwellsjr]

Vandam, ... Your emphasis on relativity of simultaineity really needed to be presented. It's always good to put the discussion in the context of the foundational physical concepts available to us with special relativity theory.

Bob, why did you think there needed to be an additional emphasis on relativity of simultaneity after I explained this fully in post #41 (as if it needed any further explanation):

Each IRF presents a different set of coordinates for each event. The time coordinate defines simultaneity.

For example, in the first IRF (post #30), minute five for the blue spacestation is simultaneous with minute three for the black and red spaceships. However in the other two IRF's (post #32) these three events occur at different coordinate times and so are not simultaneous. But minute three for the blue spacestation is simultaneous with minute five for one or the other of the two spaceships in these other two IRF's.

What are you guys concerned with?

 

[bobc2]

Bob, why did you think there needed to be an additional emphasis on relativity of simultaneity after I explained this fully in post #41 (as if it needed any further explanation):

You did a good job, ghwellsjr. Your comparative time increments in the three inertial reference frames was a good direct reponse to the confusion with the 2c expressed in the earlier posts. I hope my original post reinforced the correctness of your analysis, particularly with your illustrations using the space-time diagrams. There didn't really need to be any further explanation on that point. I simply acknowledged that Vandam's additional presentation that included the hyperplanes of simultaneity was helpful as well. I think the supplemental sketches provided by Vandam, showing graphically the hyperplanes of simultaneity--with the actual time dilation values shown on the sketches, provided additional helpful information. But, again, I have no quarrel with your response to the prior posts.

Beyond that I thought perhaps you may have over emphasized the significance of the derived basis of the "measurement" of time dilation:

"And now to my main point: The blue spacestation cannot notice the black (or red) spaceship's time dilation. Time dilation is not observable by anyone anywhere anytime. It is a calculation related to the speed of an object in a given IRF. If it were ever observable, then the observer would know which arbitrary IRF we were using. Or, more significantly, if it were observable, then we could identify the an absolute ether rest state and all of Special Relativity would be out the window."

 

[bobc2]

p.s. Vandam also made the very significant observation that for the red and black guys going in opposite directions with the same relativistic speed, the spacing of the minute marks on the two time axes are the same. So, you could not use the spacings to tell you anything at all about time dilation. His emphasis of the use of the hyperplanes of simultaneity was quite appropriate. The hyperplanes of simultaneity are always different in the 4-dimensional universe for any two observers moving with respect to each other. And their space-time diagram minute mark spacings may or may not be the same, depending on the choice of charts used in the diagram. Penrose highlights this even for two observers just walking past each other (his Andromeda Paradox).

 

[ghwellsjr]

p.s. Vandam also made the very significant observation that for the red and black guys going in opposite directions with the same relativistic speed, the spacing of the minute marks on the two time axes are the same. So, you could not use the spacings to tell you anything at all about time dilation. His emphasis of the use of the hyperplanes of simultaneity was quite appropriate.

When I first read this, I was amazed that you could make such a statement. I explained how time dilation works in post #29:

...However, since the spaceships are traveling at a very high speed in the IRF, their clocks are running very slowly compared to the coordinate time of the IRF...
Think of speeds relative to an IRF, not relative to observers and you'll have no problem. ...

And I illustrated it in post #30 with further explanation:

I've drawn a diagram to show what happens in an IRF with two spaceships traveling in opposite directions at 0.8c. They both leave the blue spacestation at time 0 when they all set their clocks to 0. The dots mark off one-minute intervals for each spaceship and the spacestation. At 0.8c, gamma is 1.6667 so the dots for the spaceships are farther apart by that amount compared to the coordinate time...

So how could you say my diagram does not show anything at all about time dilation? Of course the spacing of the dots for the red and black spaceships is the same. That's because, as you said, they are traveling at the same speed and the time dilation is based on the speed.

But then it finally dawned on me. Apparently you and Vandam take the viewpoint that time dilation is calculated based on the relative speed between the clock and the observer, not between the clock and the coordinate time of the IRF.

When I said in another thread:

For example, let's say you are moving in an IRF at some high speed.

Vandam responded by saying:

You never move in your IRF. Never.

So apparently he and maybe you, believe that time dilation cannot be calculated based on the speed of an observer/clock in an IRF, correct? Is this why you said that my first graph did not show anything at all about time dilation?

 

[Vandam]

Ghwellsjr,
You show us 3 sketches but apparently have big problems of reading my sketch of post #35.
No offence, but do you know how to read a 4D Minkowski spacetime diagram?
I never said your IRF charts are wrong. But if you would be able to read your 3 charts all in one spacetime diagram only, then you would immediately see what's really going on, in 4D.

 

[ghwellsjr]

Ghwellsjr,
You show us 3 sketches but apparently have big problems of reading my sketch of post #35.
No offence, but do you know how to read a 4D Minkowski spacetime diagram?

If you are asking about diagrams promoting the block universe concept like the ones on the first page of this thread, I already gave you a thorough answer here. But if you are asking about legitimately drawn Minkowski diagrams with correct labeling (not your sketches on my graphs in post #35) which are nothing more than combining two or three IRF's like the ones I drew on this thread, then, yes, I can read those but I think they are much more difficult for a newby to understand because of the multiple axes that are combined on one chart.

I never said your IRF charts are wrong.

Then why did you feel the need to mark one of them up along with complaints about my text? If you had it to do all over again, would you have not made post #35? Will you promise to not make negative comments about my charts or explanations again, unless I make a legitimate mistake?

But if you would be able to read your 3 charts all in one spacetime diagram only, then you would immediately see what's really going on, in 4D.

This is where the problem lies. You believe that combining the information from three separate charts on to one diagram creates or reveals additional meaning about reality.

 

[K^2]

Vandam, this is a 2D problem. There is no 4D. There is one time dimension and one spatial dimension. A single diagram shows everything that's going on.