# 2 approaching objects at velocity

I have heard that in space, there is no absolute reference frame.
However, lets take everything away except for two objects.

One object is going in one direction at some considerable amount of C, say 0.9 C, and the other object is coming in the opposite direction at 0.9 C.

I know that if they are going in the same direction, then their time dilation effects on each other would be 0, since they would be both travelling at a relative speed of 0 with respect to the other object.

Now, if they are travelling in opposite directions, how do we know which one to measure relativity on? There are no absolute reference frames, so you would have no idea whether you were both travelling at 0.9 C, or one guy was at .99 C and the other guy was at .81 C. This would be strange because I would think that if an observer from Earth observed these two objects as they passed each other, the one going faster relative to Earth would be seen as having more time dilation, and the one going slower relative to Earth would be seen as having less of an effect of Time Dilation on it. When you take away the Earth and everything else except for those 2 objects, Would only one object experience time dilation, would both of them experience it, or would it be the same for both of them, equaling a 0 relative time dilation?

Also, I kind of want to learn the equation for time dilation, but wherever I go on the internet, some equation is different from the other. I know the equation for Length Dilation (√ 1-V^2/C^2, I think), but the other would would help me out as well :)

## Answers and Replies

And, sort of related to this topic, do you guys have a place where I can find the most reliable sources of equations for stuff on Black Holes, SPecial and General Relativity, and all other important Physics equations (I know the Classical Mechanics Motion equations) that is other than this forum, since I have to dig around and search through threads to find that kind of stuff?

russ_watters
Mentor
If there are only two objects, then it is implied that there are only two reference frames. So you can say nothing more than that they are moving at .9C relative to each other, which also means you can say one is stationary and the other is "the one moving".

In order to give them different speeds than that, you have to introduce a third reference frame (the Earth reappears?!) from which to measure their velocities. The point of Relativity is that all of these choices are arbitrary until/unless some action is taken which brings the two objects together at rest wrt each other. So when they meet, which one slows down?

Well, I'll answer your second question first: wikipedia. Wikipedia will (in my experience) be the best place to get familiar with equations. If you actually want to learn the equations and be able to use them, I'd get a textbook.

As for your first question, remember that no one ever thinks that they are being time dilated, they only see the effect on others. So because every reference frame is valid you can get situations where it seems like you'd have paradoxes (like in the two spaceship example, each thinks the other's time is moving slower), however it turns out that in order to actually compare the time dilations (like by meeting the two ships together) you always have to impose some acceleration so that the timelines of all the things meeting line up and there are no paradoxes.

ghwellsjr
Gold Member
I have heard that in space, there is no absolute reference frame.
However, lets take everything away except for two objects.

One object is going in one direction at some considerable amount of C, say 0.9 C, and the other object is coming in the opposite direction at 0.9 C.

I know that if they are going in the same direction, then their time dilation effects on each other would be 0, since they would be both travelling at a relative speed of 0 with respect to the other object.

Now, if they are travelling in opposite directions, how do we know which one to measure relativity on?
You can't measure time dilation. Neither is it an effect of one object on another object or between objects. Rather, it is a calculation that you make separately based on the speed of each object as defined according to an arbitrary inertial reference frame. Direction doesn't matter. So in both your examples, since both objects are traveling at the same speed, they both experience the same time dilation. The purpose of doing this calculation is to determine how much Proper Time transpires on a clock traveling with the object.
There are no absolute reference frames, so you would have no idea whether you were both travelling at 0.9 C, or one guy was at .99 C and the other guy was at .81 C.
Yes we do know how fast the two objects are traveling--you said their speeds were 0.9c. Now you can transform your scenario into another frame such that one of the objects is traveling at 0.99c but the other one will probably not being traveling at 0.81c, although it could be traveling at less than 0.9c. This means that they will be experiencing different time dilations.
This would be strange because I would think that if an observer from Earth observed these two objects as they passed each other, the one going faster relative to Earth would be seen as having more time dilation, and the one going slower relative to Earth would be seen as having less of an effect of Time Dilation on it. When you take away the Earth and everything else except for those 2 objects, Would only one object experience time dilation, would both of them experience it, or would it be the same for both of them, equaling a 0 relative time dilation?
As I have already said, Earth cannot see the time dilation of the two objects, it's a calculation that can be different for every frame.
Also, I kind of want to learn the equation for time dilation, but wherever I go on the internet, some equation is different from the other. I know the equation for Length Dilation (v 1-V^2/C^2, I think), but the other would would help me out as well :)
That should be Length Contraction which is always a factor less than one. The reciprocal is the Time Dilation factor which is always greater than one and indicates how time takes longer. However, we usually like to talk about the rate that a moving clock ticks at and so we use the same formula as for Length Contraction.

I recently made a lot of posts on another thread regarding Time Dilation which you might find interesting:

one-way tests of special relativity

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Ferraridude,

Try this fact for size in your thought process - an observer at rest, watching two particles traveling at nearly 'c' w.r.t. the observer in opposite directions and approaching each other, will in fact see them approaching each other with a relative velocity of nearly 2c!

This is something the observer can measure and verify, since he can determine the distance between the particles at a point in time and again when the particles reach each other, as well as the elapsed time in between the two measurements!

This is in fact the case in high-energy particle collisions in accelerators. It is called 'closing velocity', is nearly 2c, and doesn't contradict SR!

This is one of the strange outcomes of SR, which allows each of the particles to travel at c or less in any direction w.r.t. the observer at rest, but not w.r.t. each other (length contraction is used to deal with this issue).

Application of SR in isolation gives rise to many such contradictions, explained away with weird mathematics and logic, while actually all of it should really be seen in the context of GR for a more logical understanding (just my opinion).

Thanks, guys! I enjoy thinking about Physics, and it has become one of my hobbies. I hope to study Physics in college, and then go on to work in Astrophysics and other forms of Theoretical Physics, since it is the big questions that amaze me.

I have only recently gotten interested in Physics on the mathematical side (Only about 8 months), but I hope to get a head start so I have a good chance at getting the best Physics education. So, thanks for all the help, guys!

ghwellsjr
Gold Member
Try this fact for size in your thought process - an observer at rest, watching two particles traveling at nearly 'c' w.r.t. the observer in opposite directions and approaching each other, will in fact see them approaching each other with a relative velocity of nearly 2c!
No, there is never any relative velocity in Special Relativity with inertial frames that are equal to or greater than c, let alone approaching 2c.
This is something the observer can measure and verify, since he can determine the distance between the particles at a point in time and again when the particles reach each other, as well as the elapsed time in between the two measurements!
There is no measurement that will yield a speed of colliding particles at c or greater than c.
This is in fact the case in high-energy particle collisions in accelerators. It is called 'closing velocity', is nearly 2c, and doesn't contradict SR!
The numeric addition of the speeds of two colliding particles is called the 'closing velocity' but it's just a calculation and doesn't represent the speed of anything with respect to anything else or with respect to any inertial frame.
This is one of the strange outcomes of SR, which allows each of the particles to travel at c or less in any direction w.r.t. the observer at rest, but not w.r.t. each other (length contraction is used to deal with this issue).
No particle can travel at c and you have to use the Velocity Addition formula (see the wikipedia article) to correctly calculate the relative speed between the two particles--it's not a simple addition.
Application of SR in isolation gives rise to many such contradictions, explained away with weird mathematics and logic, while actually all of it should really be seen in the context of GR for a more logical understanding (just my opinion).
There are no contradictions in SR. There's no weird mathematics or logic and you don't need GR for a more logical understanding. What you need is a correct understanding of SR.

Ferraridude,

Great to know you are so interested in learning and hopefully improving upon existing theory. Best wishes on that.

I hope you will keep your mind open in you future education, and not accept everything that 'appears to be well-verified truth'.

This is what Einstein himself said about SR once he had formulated GR - 'There could be no fairer destiny for any physical theory than that it should point the way to a more comprehensive theory in which it lives on as a limiting case.'

What he meant was that SR has a strict domain of applicability (of absense of gravity, or 'flat spacetime' so to say), and was superceded by GR as a more generalized theory of relativity. Likewise, there could be even more general theories of relativity, and you may find it as long as you don't accept the notion that GR is "God's truth and 100% correct" and cannot be improved upon.

And yet, even today, SR is often applied far beyond its domain of applicability. You will find respectable texts using 'acceleration' to explain apparent paradoxes in SR!

ghwellsjr
Gold Member
And yet, even today, SR is often applied far beyond its domain of applicability. You will find respectable texts using 'acceleration' to explain apparent paradoxes in SR!
There's nothing wrong with using acceleration in SR. The only thing SR can't deal with is gravity, as you correctly pointed out earlier.

Thanks George for looking up the article I mentioned. You were right of course, and you will see that what I said was also correct. Perhaps different ways of looking at the same thing...?

On the note of acceleration vs. gravity, the equivalence principle seems to state they are essentially indistinguishable. Why then do you feel that acceleration can be used in SR but not gravity? (I am no relativity expert, so this may be a stupid question)

And, sort of related to this topic, do you guys have a place where I can find the most reliable sources of equations for stuff on Black Holes, SPecial and General Relativity, and all other important Physics equations (I know the Classical Mechanics Motion equations) that is other than this forum, since I have to dig around and search through threads to find that kind of stuff?
Wikipedia was mentioned.
- Great for a first introduction: the articles are of ever varying reliability but usually not too bad (good point: you can quickly check their variability and the number of editors - and on the Talk page you can even trace disagreements! ).
- Great for reliable references: good references are provided at the bottom of the articles, often just a mouse click away! Wikipedia leans heavily on secondary sources which are not always reliable. However, primary sources are now also increasingly provided. For example, you can (and should!) judge for yourself the intro in http://en.wikipedia.org/wiki/General_relativity by directly reading the explanations in the primary reference which is not linked from the intro but you can find it at the bottom: http://web.archive.org/web/20060829045130/http://www.alberteinstein.info/gallery/gtext3.html
(note the use of Internet Archive to recover lost documents!)

And if you click at the right spot in the references in
http://en.wikipedia.org/wiki/Special_relativity
then you will find an English translation of a milestone paper on special relativity:
http://www.fourmilab.ch/etexts/einstein/specrel/www/

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Thanks George for looking up the article I mentioned. You were right of course, and you will see that what I said was also correct. Perhaps different ways of looking at the same thing...?

On the note of acceleration vs. gravity, the equivalence principle seems to state they are essentially indistinguishable. Why then do you feel that acceleration can be used in SR but not gravity? (I am no relativity expert, so this may be a stupid question)

Acceleration can be easily used in SR. Remember: the equivalence principle hadn't been thought up yet. SR applies in every non-gravitational situation.

ghwellsjr
Gold Member
Thanks George for looking up the article I mentioned. You were right of course, and you will see that what I said was also correct. Perhaps different ways of looking at the same thing...?
The article says that calculating the speed between the two particles using Galilean relativity is wrong, which is what you were doing when you said an observer "will in fact see them approaching each other with a relative velocity of nearly 2c". It then goes on to say you must use Special Relativity to get the correct answer which will never be greater than c.

In order to avoid confusion, especially when trying to help others learn about relativity, it is important to use proper terminology. Relative velocity refers to the velocity that each object determines another object is traveling at relative to itself and is never greater than c. Closing speed refers to a simple algebraic addition (or subtraction) of the speeds of two objects relative to a third object or reference frame and doesn't correspond to the relative speed of anything relative to anything else.
On the note of acceleration vs. gravity, the equivalence principle seems to state they are essentially indistinguishable. Why then do you feel that acceleration can be used in SR but not gravity? (I am no relativity expert, so this may be a stupid question)
I think the best way to answer your question is to say that the equivalence principle applies to a single object experiencing the effect of gravity but when extended over larger ranges to multiple objects, Special Relativity cannot handle that because, for example, one object on one side of the earth will be accelerated in one direction but another object on the other side of the earth will be accelerated in the opposite direction. Gravity is explained in GR as a curvature of spacetime. There is no curvature in spacetime in inertial frames in SR. SR can handle multiple objects accelerating in arbitrary ways over any distances but it ignores the effect of these objects influencing each other due to their masses.

[..] it is important to use proper terminology. Relative velocity refers to the velocity that each object determines another object is traveling at relative to itself and is never greater than c. Closing speed refers to a simple algebraic addition (or subtraction) of the speeds of two objects relative to a third object or reference frame and doesn't correspond to the relative speed of anything relative to anything else. [..]
For me that is improper terminology; just as with such words as "mass", "inertial" etc. the unnecessary modification of perfectly functional definitions causes an ever increasing stream of confusions. Regretfully we can't change this situation, and the reasonable solution is to make clear what we mean when we use such words that have different meanings in different schools.

Note: Most of the time I think to give the good example in this. Please don't hesitate to tick me on my fingers when I forget!

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ghwellsjr
Gold Member
Exactly what is improper terminology?

Exactly what is improper terminology?
I slightly exaggerated, but what one may find proper, someone else may find not so proper.
http://dictionary.reference.com/browse/proper?s=t
Do you find Orwell's Newspeak proper? For example, the introduction of a new term could be based on misunderstanding. Promoting it would then sustain misconception. Probably this forum is not the place to discuss such philosophical issues (and certainly not this thread!), but I think that we should have a place to discuss that kind of things on PF. Regretfully even the "PF lounge" doesn't have place for that anymore (the rules were changed) while it does have place for science fiction and relationships. :uhh:
If you agree with my wish, I'll bring it up in the Forum Feedback.

I do consider to make a blog on that topic, some time in the future.

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ghwellsjr
Gold Member
When I asked "Exactly what is improper terminology?", I wasn't asking for a definition of "improper terminology". I was asking which of the several terminologies in your quote of mine in post #18 you considered "improper".

When I asked "Exactly what is improper terminology?", I wasn't asking for a definition of "improper terminology". I was asking which of the several terminologies in your quote of mine in post #18 you considered "improper".
OK, I already elaborated on that in post #15 - and I further replied:
[..] Probably this forum [Special and General Relativity] is not the place to discuss such philosophical issues (and certainly not this thread!), but I think that we should have a place to discuss that kind of things on PF. [..] If you agree with my wish, I'll bring it up in the Forum Feedback. [..]
Well?

ghwellsjr