B Layman's Question about Special Relativity

[Peter Mole]

I'm just an undergraduate with a layman's interest in Physics. With regards to special relativity, I think I grasp the concept that the laws of physics are the same for all observes in uniform motion relative to one another. So if I am standing still and a spaceship zooms past me at 80% the speed of light, then I'm within my rights to say that relatively to me, the spaceship is moving at 80% the speed of light. However, there's nothing special about my state and the spaceship can say that it is standing still and that I am moving by at 80% the speed of light and that declaration is no less valid than my own.

Likewise, if I am driving down the highway at 50 mphs and a car in the opposite lane passes me and goes 60mph in the other direction, then by my measure, the other car is moving 110mph.

So what happens if I am in Spaceship A, moving along at 80% the speed of light and I meet Spaceship B that approaches and passes me in the opposite direction, also moving at 80% the speed of light. After Spaceship B passed me, if I were to measure his speed wouldn't it be 80% the speed of light + 80% the speed of light, thus exceeding the speed of light?

 

[jbriggs444]

So what happens if I am in Spaceship A, moving along at 80% the speed of light and I meet Spaceship B that approaches and passes me in the opposite direction, also moving at 80% the speed of light. After Spaceship B passed me, if I were to measure his speed wouldn't it be 80% the speed of light + 80% the speed of light, thus exceeding the speed of light?

Velocity addition does not work that way under special relativity. You can Google "relativistic velocity addition" and see that velocities combine according to a rule of
$$v_{tot} = \frac{v_1 + v_2}{1+\frac{v_1v_2}{c^2}}$$
For automobiles going down the highway, the denominator is so close to one that it can be ignored. For spacecraft moving at significant fractions of the speed of light, it cannot be ignored.

One might wonder why velocities do not add directly. It seems blatantly against the rules of common sense that they would not. One way of addressing that concern is to note that it's like adding apples and oranges. You have $v_1$, the velocity of some hypothetical space station relative to you. You have $v_2$, the velocity of spacecraft B according to that space station. You consider adding these together directly. But they are velocities measured against different reference frames. They do not add directly. Instead, they "compose" or "boost". And for that, you need the formula above.

Edit: You can take your velocity of 0.8c and the other fellow's velocity of -0.8c and obtain a "closing velocity" of 1.6c -- the rate at which your mutual separation decreases as judged by a bystander on the space station. But that's not a relative velocity of anyone thing in the rest frame of another.

 

[jedishrfu]

No you have to use the relativistic velocity addition to figure it out.

You've also introduced a new observer one that sees both spaceship A and spaceship B moving at 80% the speed of light in opposite directions.

The relativistic velocity addition allows the spaceship observer to compute the speed of the other spaceship and it will be less than the speed of light.

https://en.wikipedia.org/wiki/Velocity-addition_formula

Here's a video that describes it:

 

[Peter Mole]

No you have to use the relativistic velocity addition to figure it out.

You've also introduced a new observer one that sees both spaceship A and spaceship B moving at 80% the speed of light in opposite directions.

The relativistic velocity addition allows the spaceship observer to compute the speed of the other spaceship and it will be less than the speed of light.

https://en.wikipedia.org/wiki/Velocity-addition_formula

Here's a video that describes it:

Thank you for your response and I did check out the video. To be clear, I accept your conclusions and I do follow the formula provided, but I still don't understand WHY it is so. Or in response to the first jbriggs444, I understand that "it doesn't work that way", but I don't understand WHY it doesn't work that way. Also, I didn't mean to introduce a new observer. I only meant to consider the viewpoint of the person in Spaceship A, trying to measure the speed of Spaceship B without any consideration for a 3rd observer. I suspect the variable that I'm not considering has something to do with space or time dilation?

Let me try to understand with a similar example. Spaceship A is traveling at .9900c towards Spaceship B which is also traveling at .9900c towards Spaceship A. While Spaceship B is still many light years away I, sitting in spaceship A, decide to determine the speed of spaceship B. What result will I get? Then, light years later, the ships nearly hit head on, but miss and keep their constant speeds. Now Spaceship A is traveling at .9900c and Spaceship B is traveling at .9900c directly away from each other. Using the formula, I understand that, measuring from Spaceship A, Spaceship B is traveling at only .9999c. That's bizarre to me, but I understand that's the correct result.

Put another way, let's pretend that instead of a massive black hole, there is a planet in the exact middle of the milky way galaxy. Drawing a line through the poles of the planet, let's say Spaceship A moves at .9900c straight "north" or "up" while Spaceship B moves at .9900c straight "south" or "down" with each ship heading towards opposite edges of the galaxy. Just after launch inside Spaceship A, I look back at the planet. By my observation, I'm standing still and the planet is moving away at .9900c, right? (Likewise, an observer on the planet would say he was standing still and I was moving away at .9900c) So far so good?

Now, looking out my rear window, I decide to also measure the speed of SpaceShip B. According to the formula, SpaceShip B is moving at .9999c instead of my erroneous calculation of .99c+.99c. Okay.

Okay so here I am in spaceship A and a year goes by. By my calculation, I should find myself .9900 light years away from the planet. Likewise, by using the formula to calculate, Spaceship B should be .9999 light years away, just .0099 light years further than the planet. How can this be? During my "year" of travel inside Spaceship A, Spaceship B has been moving at .9900c in the opposite direction from the planet (relative to the planet). Yet, during my "year" of travel in the opposite direction from Spaceship B, I'm .99 light years away from the planet, while Spaceship B is only 0.0099 light years away from the planet in the opposite direction (or in other words spaceship B has only traveled 1% of the distance I have traveled in Spaceship A).

Is this because of time dilation? How much time has passed for Spaceship B during the year I spend recording time inside Spaceship A? Is it approximately 1/100th of a year?

 

[jbriggs444]

I suspect the variable that I'm not considering has something to do with space or time dilation?

Time dilation, length contraction and relativity of simultaneity. The last is the one that most laymen miss.

You can't add a velocity from frame A to a velocity from frame B if your rulers aren't the same length, your clocks don't tick at the same rate and weren't synchronized the same way in the two frames.

 

[Dale]

I still don't understand WHY it is so.

The reason “why” for all relativistic effects is:

1) the principle of relativity
2) the invariance of c

 

[Peter Mole]

Time dilation, length contraction and relativity of simultaneity. The last is the one that most laymen miss.

Would it be possible for you or someone to help me understand this in the context of my example scenario? In my last example, after the occupant in Spaceship A has experienced a year passing, how much time has gone by on the planet and how much time has gone by for the Spaceship B which is traveling .99c in the opposite direction from the planet?

 

[Peter Mole]

The reason “why” for all relativistic effects is:

1) the principle of relativity
2) the invariance of c

Do you think that's helpful. Really?

 

[Grinkle]

@Peter Mole Post 6 is the answer. These two items are axioms from which the rest of the stuff is derived. Item 1 is intuitively appealing, and item 2 is experimentally verified. Niether 1 or 2 is, as far as I know, derived from more fundamental axioms.

I like the below thread on the twin paradox as good discussion for the question in your post 7.

https://www.physicsforums.com/threads/twin-paradox-and-the-body.940272/

 

[phinds]

Do you think that's helpful. Really?

Since it is the correct answer and ultimately explains everything in SR, I for one think it could not possibly BE more relevant. If you don't get that, don't blame Peter.

 

[Peter Mole]

Since it is the correct answer and ultimately explains everything in SR, I for one think it could not possibly BE more relevant. If you don't get that, don't blame Peter.

Dude, I get it. No one here owes me anything. I'm just someone of average intelligence who didn't go much beyond high school algebra but who is also fascinated by relativity and quantum physics and so I'm trying to understand these fascinating concepts for no other reason than intellectual curiosity and I really do appreciate being able to engage with other people who are generous enough to share their understanding and share my wonder of it all.

That said, I'm not asking philosophical questions nor am I trying to challenge anyone's answer so much as I'm humbly trying to understand them. Jbriggs44 and others understood the context of what I was asking. Dale (not Peter, as I'm Peter) was, at best being just a little be snarky, and at worst, he was being condescending. His answer might as well have been "Because of Physics". And finally, I'm not trying to blame anyone for anything and I think it's strange that you inferred as much.

 

[Dale]

Dale (not Peter, as I'm Peter) was, at best being just a little be snarky, and at worst, he was being condescending

I was being neither snarky nor condescending. I was giving you a direct answer to the question you asked in the only way that science can answer such questions. I don’t know why you chose to interpret my motives so negatively. Of course, it is notoriously easy to misinterpret motives in this medium, so I suspect it was simply one such misunderstanding.

That said, a more complete explanation would have connected the postulates with the specific relativistic effect in question. But many people understand how to go from the postulates to the relativistic effect in question once it is pointed out to them where to start with any “why” question. So (being pressed for time) I chose to provide the simple answer immediately and a more complete answer later if you requested further details.

 

[phinds]

... Dale (not Peter, as I'm Peter) was, at best being just a little be snarky, and at worst, he was being condescending.

I COMPLETELY disagree. He was giving the straightforward answer. Your reading attitude into it is your problem, not his.

EDIT: I see he beat me to it.

 

[Peter Mole]

@Peter Mole

I like the below thread on the twin paradox as good discussion for the question in your post 7.

https://www.physicsforums.com/threads/twin-paradox-and-the-body.940272/

Thanks for the reply, but that thread doesn't seem to address my confusion. The OP in that discussion seems to struggling with the idea of how time can be moving normally for the traveler, before being corrected by Phinds later on down the thread. Likewise the accelerations aspects of that discussion seem to be more liken to general relativity where my questions are more solidly in the realm of SR.

 

[jartsa]

Put another way, let's pretend that instead of a massive black hole, there is a planet in the exact middle of the milky way galaxy. Drawing a line through the poles of the planet, let's say Spaceship A moves at .9900c straight "north" or "up" while Spaceship B moves at .9900c straight "south" or "down" with each ship heading towards opposite edges of the galaxy. Just after launch inside Spaceship A, I look back at the planet. By my observation, I'm standing still and the planet is moving away at .9900c, right? (Likewise, an observer on the planet would say he was standing still and I was moving away at .9900c) So far so good?

Now, looking out my rear window, I decide to also measure the speed of SpaceShip B. According to the formula, SpaceShip B is moving at .9999c instead of my erroneous calculation of .99c+.99c. Okay.

Okay so here I am in spaceship A and a year goes by. By my calculation, I should find myself .9900 light years away from the planet. Likewise, by using the formula to calculate, Spaceship B should be .9999 light years away, just .0099 light years further than the planet. How can this be? During my "year" of travel inside Spaceship A, Spaceship B has been moving at .9900c in the opposite direction from the planet (relative to the planet). Yet, during my "year" of travel in the opposite direction from Spaceship B, I'm .99 light years away from the planet, while Spaceship B is only 0.0099 light years away from the planet in the opposite direction (or in other words spaceship B has only traveled 1% of the distance I have traveled in Spaceship A).

Is this because of time dilation? How much time has passed for Spaceship B during the year I spend recording time inside Spaceship A? Is it approximately 1/100th of a year?

Let's say mile-stones have been placed along the galaxy, one mile apart in the rest-frame of the galaxy. Let's say everything stays still in said galaxy, except for those two spaceships.

Ok, now pilots in both spaceships say: "The other pilot passes mile-stones at 1/70 of the rate that I pass mile-stones. And the mile-stones are 1/70 miles apart in this galaxy".

Time dilation factor and length contraction factor are both 1/70, when speed is 0.9999 c.Oops, the mile-stones are 1/7 miles apart according to a pilot that is traveling at 0.99 c, relative to the mile-stones.

 

[Peter Mole]

I was being neither snarky nor condescending. I was giving you a direct answer to the question you asked in the only way that science can answer such questions.

At this point, as I mentioned, it seems to me you interpreted my question as philosophical or existential in nature. It wasn't, but I can see why such questions, particularly from bible thumpers and the like, might well grow tiresome and elicit a short dismissive reply. Likewise, I'm sure a lot of people simply come here perplexed by the ramifications of relativity and so they (mostly innocently) start wading into questions of why reality is the way it is instead of trying to understand how it works. It's a like the guy who wants to know WHY you can't know both the location and velocity of the electron at a specific instant in time. Again, these aren't the "why" questions I was asking, but I can see why you might have thought so and why a short dismissive answer might have seemed appropriate, but nevertheless, from my perspective, not very helpful.

I don’t know why you chose to interpret my motives so negatively. Of course, it is notoriously easy to misinterpret motives in this medium, so I suspect it was simply one such misunderstanding.

I really didn't interpret them so negatively. Perhaps I should have said "slightly glib" or "dismissive" on the one side of the scale instead of "snarky".

That said, a more complete explanation would have connected the postulates with the specific relativistic effect in question. But many people understand how to go from the postulates to the relativistic effect in question once it is pointed out to them where to start with any “why” question. So (being pressed for time) I chose to provide the simple answer immediately and a more complete answer if you requested further details.

Rather than point to mathematical theorems, I'm better off getting an understanding by dealing with concepts. So in my example where Spaceship A and Spaceship B are both approaching each other on a straight line each at .99c, what value for speed will the captain of Spaceship A calculate for Spaceship B? Thanks to jbriggs444 and jedishrfu, I have the formula for A & B moving away from each other, but it doesn't seem to work for A & B heading towards each other, although I'm certain I could be mistaken.

Beyond that I'll repeat my above question. Say observer A leaves Earth at .99c going "up" and observer B stays on the planet, and observer C leaves Earth at .99c doing "down" in the opposite direction of A. As I understand it, Observer B (on earth) can fairly state that both A and B are moving away from the Earth at .99c. Likewise, Observer A can state that Earth is moving away at .99c and Observer B can likewise state that Earth is moving away at .99c. What I get hung up on is why, according to Observer A, observer C only appears to be moving away at .9999c (only .0099c greater). It has been explained to me this is because of time and space dilation which, at least in terms of time, I think I understand. Relative to Observer B (earth), time is moving slower for A and for C. However slower, I don't have the math to calculate, but it seems to me that the degree to which time is moving more slowly for A it would be slowing to the same degree for C, at least according to Observer B (earth). So if a year passes for A, then how much time is passing for C during the same "year" that passes for A? And for good measure, how much time would have passed for B (on earth), during A's year of time passing. (I ask so I can compare it to what has passed for C).

Is this all related to time/space dilation or is there something about the fact that A & C are moving in opposite directions that has a baring? I feel like there's more than just time/space dilation that I'm not accounting for.[/QUOTE]

 

[Peter Mole]

I COMPLETELY disagree. He was giving the straightforward answer. Your reading attitude into it is your problem, not his.

EDIT: I see he beat me to it.

Good grief man, you didn't even get the posters name right so why are you looking to fight his battles? Go someplace else to look for an online fight. I'm not interested.

 

[Peter Mole]

Let's say mile-stones have been placed along the galaxy, one mile apart in the rest-frame of the galaxy. Let's say everything stays still in said galaxy, except for those two spaceships.

Ok, now pilots in both spaceships say: "The other pilot passes mile-stones at 1/70 of the rate that I pass mile-stones. And the mile-stones are 1/70 miles apart in this galaxy".

Thanks for the reply. I'm a little confused if you are continuing with my example or starting fresh. So both pilots are traveling at .9999c? Relative to what? And they are traveling on such a path that at some point they will hit the first and then the second milestone? Does it matter if they are traveling one after the other along the path or if they are coming from opposite directions? I'm not trying to be pedantic, but I'm a little confused at the details or if the details I'm asking about are even important. Can you clarify a little more?

Time dilation factor and length contraction factor are both 1/70, when speed is 0.9999 c.Oops, the mile-stones are 1/7 miles apart according to a pilot that is traveling at 0.99 c, relative to the mile-stones.

Thanks!

 

[Dale]

At this point, as I mentioned, it seems to me you interpreted my question as philosophical or existential in nature.

I assumed your question was scientific and so I answered it scientifically. My understanding from your stated background is that you have no formal training in relativity, but a curiosity. You understand what the effect is, but not why it occurs.

The scientific reason why is because of the two postulates. If you can accept those two statements as true, then all the other relativistic effects logically follow. As a student, when you get stuck in relativity, it is nice to have a firm footing that you can always go back to and proceed from. Those postulates are that firm footing, the answer to all “why” questions in relativity.

Perhaps I should have said "slightly glib" or "dismissive"

It wasn’t dismissive. You asked a question which had a direct and brief answer, which I provided. It was brief, but with 5 kids and a homestead sometimes brief is all I can do. I also prefer brief answers whenever possible as there is less room for confusion.

Rather than point to mathematical theorems, I'm better off getting an understanding by dealing with concepts.

Well, concepts and mathematical theorems are pretty close in relativity. The problem is that this is a realm of the universe where instinct and intuition are fairly useless. Our caveman ancestors did not need to factor in relativity when throwing spears at a wolly mammoth, so our brains did not evolve over millennia to instinctively understand these concepts. So instead we rely on math to guide us and then on experiments to check our math.

In a conceptual way, from the two postulates you can obtain the Lorentz transforms, and then from the Lorentz transforms you can obtain the relativistic velocity addition.

It has been explained to me this is because of time and space dilation which, at least in terms of time, I think I understand.

Well, it is because of the Lorentz transform, which includes time dilation, length contraction, and also the relativity of simultaneity. The latter effect is the one that most frequently trips new students. It is also the effect which is most difficult to grasp. This is what you are missing here.

I feel like there's more than just time/space dilation that I'm not accounting for.

Yes, the relativity of simultaneity.

It is easier to use the Lorentz transform than it is to piecemeal use length contraction, time dilation, and relativity of simultaneity. Are you familiar with the Lorentz transform?

 

[SiennaTheGr8]

Beyond that I'll repeat my above question. Say observer A leaves Earth at .99c going "up" and observer B stays on the planet, and observer C leaves Earth at .99c doing "down" in the opposite direction of A. As I understand it, Observer B (on earth) can fairly state that both A and B are moving away from the Earth at .99c. Likewise, Observer A can state that Earth is moving away at .99c and Observer B can likewise state that Earth is moving away at .99c. What I get hung up on is why, according to Observer A, observer C only appears to be moving away at .9999c (only .0099c greater).

But this is precisely why @Dale's explanation was correct in the first place: it would violate the second postulate if observers A or C could measure the other moving at or faster than c. The invariance of c makes it a universal speed limit—no matter how hard you try to "catch up" to a light wave, its speed remains the same. So even before doing the math to figure out the details, you know that A and C must measure each other moving slower than c.

Say that light is emitted in the "down" direction from "above" observer A. Observer A says it's moving at c, but A also knows that if he switched to C's reference frame the light would still be moving "down" at c, even though C is moving very fast in the same direction as the light from A's perspective. If switching to C's reference frame leaves the light's velocity unchanged, then C must be moving slower than the light in A's frame, and indeed in all frames.

 

[Grinkle]

that thread doesn't seem to address my confusion

Fair enough. I am not sure if you are confused about how to do a specific calculation or about something more fundamental. So acknowledging that I am not confident my further comments are helpful for you, I offer them anyway for fwiw.

It helped me a lot to take the two axioms separately. The principle of relativity leads to two consistent models of the universe - Galilean invariance and Lorentz invariance.

Edit - hit save too soon.

If you can follow the arguments that either of these systems (and only these systems) yield a universe in which the principle of relativity holds, then it is a small jump to accepting the experimental evidence that our Universe is in fact Lorentz invariant. It needn't be, for the principle of relativity alone to be true, but it is.

Then the rest of the details in the problem you are asking about are math - not really intuitive (at least not at all for me) until one has deliberately trained the intuition by working out the math on many such problems.

 

[Peter Mole]

I assumed your question was scientific and so I answered it scientifically. My understanding from your stated background is that you have no formal training in relativity, but a curiosity.

yep

You understand what the effect is, but not why it occurs.

Right, I was trying to understand if the effect was a matter of time/space dilation or if it somehow had to do with the direction or distance in space itself or by some other misunderstanding I had about how relativity worked. I'm hoping to better understand through examples that show how much time has passed for the observers inside the senarios I have asked about.

The scientific reason why is because of the two postulates. If you can accept those two statements as true, then all the other relativistic effects logically follow. As a student, when you get stuck in relativity, it is nice to have a firm footing that you can always go back to and proceed from. Those postulates are that firm footing, the answer to all “why” questions in relativity.

It wasn’t dismissive. You asked a question which had a direct and brief answer, which I provided. It was brief, but with 5 kids and a homestead sometimes brief is all I can do. I also prefer brief answers whenever possible as there is less room for confusion.

Nonsense. Scroll back up an look at my unedited OP. Flawed as my understanding may be, my question clearly demonstrated that I was familiar with the theory of relativity. In fact, I explicitly mentioned it an even alluded to the definition. Furthermore, the nature of my question clearly shows that I was aware there was a problem with going faster than the speed of light. Clearly, if I wasn't aware of the theory of relativity and the constant speed of light, I wouldn't have even been able to form the question.

Yet, when I asked "why" at one point, you decided the correct response was to point me to the theory I was already using, breaking it up into two postulates that my question demonstrated I was already aware of. You might as well have answered, "Because of Physics". Perhaps your household duties and children meant you didn't have the time to read my OP.

Well, concepts and mathematical theorems are pretty close in relativity. The problem is that this is a realm of the universe where instinct and intuition are fairly useless. Our caveman ancestors did not need to factor in relativity when throwing spears at a wolly mammoth, so our brains did not evolve over millennia to instinctively understand these concepts. So instead we rely on math to guide us and then on experiments to check our math.

Yep, I'm still aware of the concept of relativity and the fact that it doesn't follow instinct and intuition, as my OP clearly demonstrates. Also, having a layman's understanding of relativity (as my OP clearly shows), of course I'm aware that mathematics plays a crucial role, although I don't claim to have a good grasp of the math which is why I'm trying to understand it conceptually.

In a conceptual way, from the two postulates you can obtain the Lorentz transforms, and then from the Lorentz transforms you can obtain the relativistic velocity addition.

Well, it is because of the Lorentz transform, which includes time dilation, length contraction, and also the relativity of simultaneity. The latter effect is the one that most frequently trips new students. It is also the effect which is most difficult to grasp. This is what you are missing here.

Yes, the relativity of simultaneity.

It is easier to use the Lorentz transform than it is to piecemeal use length contraction, time dilation, and relativity of simultaneity. Are you familiar with the Lorentz transform?

Okay thanks. Relativistic velocity addition was already mentioned to me as was relativity of simultaneity. I'll add Lorentz transform to my list of things to research. I'm not smart enough absorb these ideas without investing a lot of time. Maybe I can utilize these theorms to answer the specific questions I've asked here in the thread which would go a long way to helping me understand what's actually happening in terms of time/space dilation, which is all I'm really interested in anyway.

 

[ZapperZ]

So, this is the reason why I tried to highlight MinutePhysics' current "project" in "teaching" SR.

https://www.physicsforums.com/threads/minutephysics-special-relativity-series.938686/

Many of the issues you brought up in your original post can be found in at least a couple of videos listed in that thread. Even Fermilab's Don Lincoln is doing his own series on SR, and his videos are also included in the thread.

Maybe you might want to start with those. And as to a direct answer to your original post, the answer is no, you can't add velocities that way. The way we commonly add velocities is called Galilean transformation. It turns out, as I've pointed out in the Insight article, this is simply an approximation that is valid for v<<c. The more GENERAL description, as you've been told, is the Lorentz transformation. If you had done a search on "relativistic velocity addition", you would have found several websites illustrating to you how this is done.

So before moving on further in the "why's", which seems to be what you are asking in your subsequent posts, can we first get THIS ONE clarified to your understanding?

Zz.

 

[SiennaTheGr8]

Nonsense. Scroll back up an look at my unedited OP. Flawed as my understanding may be, my question clearly demonstrated that I was familiar with the theory of relativity. In fact, I explicitly mentioned it an even alluded to the definition. Furthermore, the nature of my question clearly shows that I was aware there was a problem with going faster than the speed of light. Clearly, if I wasn't aware of the theory of relativity and the constant speed of light, I wouldn't have even been able to form the question.

Yet, when I asked "why" at one point, you decided the correct response was to point me to the theory I was already using, breaking it up into two postulates that my question demonstrated I was already aware of. You might as well have answered, "Because of Physics". Perhaps your household duties and children meant you didn't have the time to read my OP.

#DaleDidNothingWrong

 

[Peter Mole]

Say that light is emitted in the "down" direction from "above" observer A. Observer A says it's moving at c, but A also knows that if he switched to C's reference frame the light would still be moving "down" at c, even though C is moving very fast in the same direction as the light from A's perspective. If switching to C's reference frame leaves the light's velocity unchanged, then C must be moving slower than the light in A's frame, and indeed in all frames.

Yep, I understand that the speed of light is constant and that it cannot be exceeded.

Let me just ask the same question again and see if someone can help give me mathematically answers or point me to mathematical equations to get my own answers, although I'm not well versed in much beyond high school algebra.

Three positions. A, B, C, all starting at the same point in space. Next, by B's observation, A instantly begins to move west at .9900c. Also by B's observation, C instantly begins to move east at .9900c.

By A's observation, A is moving at .9900c relative to B. By C's observation, C is moving at .9900c relative to B.

EDIT: (thanks jbriggs444) I meant to say By A's observation, B is moving away at .9900c relative to A. Also, by C's observation, B is moving away at .9900c relative to C.

Using the relativistic velocity addition provided above, I know that by A's observation, C is moving at .9999c, and that by C's observation, A is moving at .9999c.

Now, staying with A's frame of reference, a year passes. Relative to B, A has been moving at .9900c for a year. Although I don't know how to do the calculation, I understand that much less time has passed from B's perspective during the time that a year has passed for A. My question is, how much time has passed for C, and how far away is C from A at the moment that a year has passed for A's inside A's frame of reference. If the math is too involved to give me specific answers of time and distance, just knowing approximate answers might be enough to bridge my understanding of what's going on.

 

[ZapperZ]

Yep, I understand that the speed of light is constant and that it cannot be exceeded.

Let me just ask the same question again and see if someone can help give me mathematically answers or point me to mathematical equations to get my own answers, although I'm not well versed in much beyond high school algebra.

Three positions. A, B, C, all starting at the same point in space. Next, by B's observation, A instantly begins to move west at .9900c. Also by B's observation, C instantly begins to move east at .9900c. By A's observation, A is moving at .9900c relative to B. By C's observation, C is moving at .9900c relative to B. Using the relativistic velocity addition provided above, I know that by A's observation, C is moving at .9999c, and that by C's observation, A is moving at .9999c.

Now, staying with A's frame of reference, a year passes. Relative to B, A has been moving at .9900c for a year. Although I don't know how to do the calculation, I understand that much less time has passed from B's perspective during the time that a year has passed for A. My question is, how much time has passed for C, and how far away is C from A at the moment that a year has passed for A's inside A's frame of reference. If the math is too involved to give me specific answers of time and distance, just knowing approximate answers might be enough to bridge my understanding of what's going on.

This is not an "exotic" question. In fact, it is rather common and something I ask my students in class or as part of their homework.

A similar scenario can be found here, with the appropriate mathematics:

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

Zz.

 

[jbriggs444]

By A's observation, A is moving at .9900c relative to B.

By A's observation, A is at rest.
By A's observation, B is moving at .9900c relative to A.

 

[Peter Mole]

So, this is the reason why I tried to highlight MinutePhysics' current "project" in "teaching" SR.

https://www.physicsforums.com/threads/minutephysics-special-relativity-series.938686/

Many of the issues you brought up in your original post can be found in at least a couple of videos listed in that thread. Even Fermilab's Don Lincoln is doing his own series on SR, and his videos are also included in the thread.

Thanks I appreciate that and will look into it. Besides watching every documentary/video I can find, I've read a few books by Brian Greene and Michio Kaku, and even struggled through most of Hawkin's "Brief History of time" so I'm happy watch the video you provided as well. Currently, I'm working my way through "Einstein's Relativity and the Quantum Revolution" a great courses lecture by professor Richard Wolfson (currently available on youtube). It follows the usual course of discussing classical physics, discussing Maxwell's equations, the discarded ether theory, etc, but I'm interested to see how MinutePhysics helps my understanding. I've already watched one part of his linked video above but I became confused because the scenarios expressed didn't quite match the ones I was asking about, or maybe they did, but I mistook the variations in the scenario and relevant when maybe they were arbitrary to the concept.

Maybe you might want to start with those. And as to a direct answer to your original post, the answer is no, you can't add velocities that way. The way we commonly add velocities is called Galilean transformation. It turns out, as I've pointed out in the Insight article, this is simply an approximation that is valid for v<<c. The more GENERAL description, as you've been told, is the Lorentz transformation. If you had done a search on "relativistic velocity addition", you would have found several websites illustrating to you how this is done.

So before moving on further in the "why's", which seems to be what you are asking in your subsequent posts, can we first get THIS ONE clarified to your understanding?

Zz.

Yes, I do believe it was wrong to add velocities that way. Knowing it was wrong (if for no other reason than because it exceeded light speed) is why I posted the question in the first place. The first two replies to my OP gave me information on the relativistic velocity addition, which did help me derive the right answer. Now I'm curious about what's happening to time and space to make the answer valid. I proposed a scenario involving three observers (A, B, C), and then asked questions about it. I think if I get answers as to what's actually happening to space and time for different observers then I'll get a better understanding what I'm confused about. To be clear, I've no doubt the answers are in the material you've presented and in the material I've already reviewed. I'm just not clicking on some concepts enough to put it all together.

 

[jbriggs444]

I think if I get answers as to what's actually happening to space and time for different observers

One answer is that space-time does not change for different observers. Only the coordinates used to locate an event in "space" and "time" change. The Lorentz transformations are how you take a coordinate 4-tuple used by one observer to locate an event and convert it to a coordinate 4-tuple used by a different observer to locate the same event.

 

[Peter Mole]

By A's observation, A is at rest.
By A's observation, B is moving at .9900c relative to A.

Good call. I have edited my post to reflect your correction. I actually understood this but misstated it.

 

[Peter Mole]

This is not an "exotic" question. In fact, it is rather common and something I ask my students in class or as part of their homework.

A similar scenario can be found here, with the appropriate mathematics:

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

Zz.

I'm not claiming my question is exotic. It may well be mundane. I freely acknowledge that I may be missing something that even an average student of yours grasps immediately.

I guess in the interest of not wanting to spoon feed me, you've decided it's not in my best interest to simply tell me the answers to the questions I've specifically asked? To you, just mixing the variables around may not matter but to me it's confusing. In my example, I'm establishing the velocity of A, relative to B and of C, relative to B with both A and C moving in opposite directions away from B. I can clearly see that your link is putting me where I need to be and that it gives me a way to address this scenario, but for me the concepts are not intuitive and I'm not great at math so working through those equations to get the answers I want for the scenario I posted is going to take me a long time. I will look into further when I have more time. Thank you for the link.

 

[Peter Mole]

#DaleDidNothingWrong

Yep, I agree that he didn't do anything wrong.

 

[jbriggs444]

Now, staying with A's frame of reference, a year passes. Relative to B, A has been moving at .9900c for a year. Although I don't know how to do the calculation, I understand that much less time has passed from B's perspective during the time that a year has passed for A. My question is, how much time has passed for C, and how far away is C from A at the moment that a year has passed for A's inside A's frame of reference. If the math is too involved to give me specific answers of time and distance, just knowing approximate answers might be enough to bridge my understanding of what's going on.

Let's actually stay with A's frame of reference instead of jumping to B and C.

How far away is C from A at the moment that a year has passed according to A's rest frame? Multiply velocity according to A by time according to A. .9999c times one year is 0.9999 light years.

How much time has passed for C by this point? There are a couple of ways to calculate the answer. One way is to use time dilation. The gamma factor $\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$ for 0.9999c is roughly 71 to 1. So 1/71 of a year.

The other way to calculate time elapsed would be to compute the invariant interval between t=0, x=0 and t=1, x=0.9999. That's $\sqrt{1^2-0.9999^2}$ which is approximately 1/71.

 

[ZapperZ]

I'm not claiming my question is exotic. It may well be mundane. I freely acknowledge that I may be missing something that even an average student of yours grasps immediately.

I guess in the interest of not wanting to spoon feed me, you've decided it's not in my best interest to simply tell me the answers to the questions I've specifically asked? To you, just mixing the variables around may not matter but to me it's confusing. In my example, I'm establishing the velocity of A, relative to B and of C, relative to B with both A and C moving in opposite directions away from B. I can clearly see that your link is putting me where I need to be and that it gives me a way to address this scenario, but for me the concepts are not intuitive and I'm not great at math so working through those equations to get the answers I want for the scenario I posted is going to take me a long time. I will look into further when I have more time. Thank you for the link.

This is why you need to draw a sketch (a requirement that all of my students realizes very quickly). In your example, in Reference frame A, both B and C are moving in the SAME direction. The velocity of C is defined in reference to B.

In the example in the link I gave you, this is what "C" sees, and the velocity of A is defined in reference to B. It is the SAME situation!

Zz.

 

[SiennaTheGr8]

Yes, I do believe it was wrong to add velocities that way. Knowing it was wrong (if for no other reason than because it exceeded light speed) is why I posted the question in the first place. The first two replies to my OP gave me information on the relativistic velocity addition, which did help me derive the right answer. Now I'm curious about what's happening to time and space to make the answer valid.

Lorentz transformation: follow that link and simply divide $x^\prime$ by $t^\prime$ (or divide $x$ by $t$ for the "inverse" transformation given a few paragraphs later). Really, you want to divide change in $x^\prime$ by change in $t^\prime$, but the transformation is linear so you can throw some $\Delta$'s in there and you're good.

What's happening is that when you switch frames (accelerate), your coordinate system changes to ensure that you always measure the speed of light as $\Delta x / \Delta t = c$. The Lorentz transformation gives the details.

 

[Peter Mole]

Let's actually stay with A's frame of reference instead of jumping to B and C.

How far away is C from A at the moment that a year has passed according to A's rest frame? Multiply velocity according to A by time according to A. .9999c times one year is 0.9999 light years.

So far so good.

How much time has passed for C by this point? There are a couple of ways to calculate the answer. One way is to use time dilation. The gamma factor $\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$ for 0.9999c is roughly 71 to 1. So 1/71 of a year.

The other way to calculate time elapsed would be to compute the invariant interval between t=0, x=0 and t=1, x=0.9999. That's $\sqrt{1^2-0.9999^2}$ which is approximately 1/71.

Okay, so this is what jartsa was starting to explain to me. So from A's frame of reference, 1 year has gone by. Meanwhile, over at C's frame of reference, 1/71th of one year has gone by, or, to put it in plainer terms, only 5.14 days have gone by for C in C's frame of reference.

Now, from A's frame of reference, A knows that C is moving away from A at .9999c and that B is moving away from A at .9900c. Without referring back to your dilation formula, I at least already know that... During the year that passed by for A, the amount of time that passed by for B must be more than 5.14 days simply because B wasn't moving as fast and the faster the clock, the slower in runs as observed from A's perspective.

Moving on, using your time dilation formula... I multiply the time that's passed for A (1 year) by the velocity of B, according to A's reference point, which is .9900 giving me a result of .9900 which is now the value for "v" in your time dilation equation. Compute and I come up with 1/7.09 or 1/7th. So take one seventh of a year and you get about 52 days. So... during the time a year has passed by A's frame of reference, 5 days have passed for C, and 52 days have passed for B. Right?

Now here's what I'm having trouble with it conceptually.

Same scenario. A,B,C all start together. Let's stick with B's frame of reference. According to B's frame of reference A is moving away at .9900c and C is moving away at .9900c (in the opposite direction from A). Still staying within B's frame of reference, 52 days go by.

My intuitive non-relativistic thinking tells me that if I know that if 1 year passing on A is the same as 52 days passing on B, then it must be true that 52 days passing on B is the same as 1 year passing on A.

Therefore, when 52 days passes on B, 365 days have passed for A. What I don't understand is why only 5 days have passed for C during the 52 days that passed on B given that both A & C left B at the same time at the same velocity going opposite directions. My non-relativistic thinking tells me that whatever time dilation occurs for A & C, that is should be the same, according to B's frame of reference. But that doesn't appear to be true. Or, in terms of relativity, if by B's frame of reference, A is moving away at .9900c, then time should be moving more slowly for A, but instead it's going faster and a whole year is passing by while only 52 days have gone by for B.

This is a conceptual problem for me. It seems the above assumption I made in bold is, bizarrely, not correct.

I can use your same dilation equation from B's frame of reference. Same setup as before, but for easy math, I'll say a year has gone for B according to B's frame of reference. According to B, A is moving away at .9900c. Multiply again by 1 year. This time I get 1/7.09 for the time that's passed for A, or 52 days. Because C is also moving away at .9900c, I get the same answer for C. In other words, by B's frame of reference, when 1 year goes by, only 52 days have gone by for A and 52 days have gone by for C.

Am I doing this right?

 

[Peter Mole]

This is why you need to draw a sketch (a requirement that all of my students realizes very quickly). In your example, in Reference frame A, both B and C are moving in the SAME direction. The velocity of C is defined in reference to B.

In the example in the link I gave you, this is what "C" sees, and the velocity of A is defined in reference to B. It is the SAME situation!

Zz.

Yes, I have a good feel for what you're saying. I actually have had pencil and paper in front of me this whole time, but I feel confident if I walk through step by step on your link I'll get it. I just haven't taken the time yet. Thank you for this resource.

 

[Dale]

Yet, when I asked "why" at one point, you decided the correct response was to point me to the theory I was already using, breaking it up into two postulates that my question demonstrated I was already aware of.

But you were clearly not aware that those two postulates are the answer to your "why" question. So the response was informative and should have caused some introspection rather than irritation. You already knew the answer to the question, but did not know that it was the answer. Pointing that out is not dismissive.

I'll add Lorentz transform to my list of things to research. I'm not smart enough absorb these ideas without investing a lot of time.

If you need to prioritize, then I would start with the Lorentz transform and spacetime diagrams. Those will have a larger impact than separately studying time dilation, length contraction, the relativity of simultaneity, and the velocity addition formula. If you have previous experience with vectors then spacetime diagrams and the Lorentz transform will actually be fairly simple.

 

[jbriggs444]

My intuitive non-relativistic thinking tells me that if I know that if 1 year passing on A is the same as 52 days passing on B, then it must be true that 52 days passing on B is the same as 1 year passing on A.

Time dilation is indeed symmetric. A sees B aging more slowly. B sees A aging more slowly. At first glance our intuitions, trained to assume that synchronization is absolute, reject this result as nonsensical. Instead, we tend to think "if you are slower than me, I have to be faster than you".

But that is where the relativity of simultaneity kicks in. By A's point of view, A's one-year mark corresponds to B's 52 day mark. By B's point of view, B's one year mark corresponds to A's 52 day mark. It's the failure to agree on what events are simultaneous that allows both A and B to consider the other fellow to be aging more slowly.

Edit: You could look at https://www.physicsforums.com/threads/mutual-time-dilation-seems-to-be-self-contradictory.888116/ where this exact failure of intuition is addressed.

 

[Nugatory]

My intuitive non-relativistic thinking tells me that if I know that if 1 year passing on A is the same as 52 days passing on B, then it must be true that 52 days passing on B is the same as 1 year passing on A.

That intuition is wrong, but it is hard to understand why until we phrase things more precisely.

You say "1 year passing on A is the same as 52 days passing on B". What's actually going on: At the same time that A's clock reads $T_{A0}$ B's clock reads $T_{B0}$. At the same time that A's clock reads $T_{A0}+1 year$ B's clock reads $T_{B0}+52 days$. We therefore conclude that B's clock is running slow, in a ratio of 52 days to one year.

But note that we are using A's definition of "at the same time" in this analysis. Because of the relativity of simultaneity, B does not find that that A's clock reads $T_{A0}+1 year$ at the same time that B's clock reads $T_{B0}+52 days$, so the same analysis doesn't work the other way. If we use B's definition of "at the same time" we will conclude that A's clock is running slow, by the same ratio.

 

[Peter Mole]

But you were clearly not aware that those two postulates are the answer to your "why" question.

And I'm still not aware. I'm not sure my "why" question meant what you think it did and that's not your fault, it's mine. I perceived you to have made a flippant comment and so I made a flippant comment in return. It was wrong of me to make that assumption and so I apologize. Clearly you and many others are taking time out of your day to help me understand these concepts and to further question your motivations is utter rudeness on my part.

If you need to prioritize, then I would start with the Lorentz transform and spacetime diagrams. Those will have a larger impact than separately studying time dilation, length contraction, the relativity of simultaneity, and the velocity addition formula. If you have previous experience with vectors then spacetime diagrams and the Lorentz transform will actually be fairly simple.

I'm not a math guy. I don't really know what a vector is and anything on this thread typed in subscript throws me for a loop. What I should do at this point is stop and try to explore some of the good resources I've been given. Checking out ZapperZ's link for MinutePhysics might be more my speed as well as checking out his "homework" page on calculating relativistic velocity addition.

However, I find the way these threads work is you need to stick with them "while their hot" so I'm going to try to follow out the trains of thought before going back to do my own homework.

 

[Peter Mole]

Time dilation is indeed symmetric. A sees B aging more slowly. B sees A aging more slowly. At first glance our intuitions, trained to assume that synchronization is absolute, reject this result as nonsensical. Instead, we tend to think "if you are slower than me, I have to be faster than you".

But that is where the relativity of simultaneity kicks in. By A's point of view, A's one-year mark corresponds to B's 52 day mark. By B's point of view, B's one year mark corresponds to A's 52 day mark. It's the failure to agree on what events are simultaneous that allows both A and B to consider the other fellow to be aging more slowly.

Edit: You could look at https://www.physicsforums.com/threads/mutual-time-dilation-seems-to-be-self-contradictory.888116/ where this exact failure of intuition is addressed.

This is blowing my mind. I shallowly understand the relativity of simultaneity. That link (and the references it footnotes) is pretty heady for me and my weak math background, but I will put it on my list of things to follow up on. In fact, I think it's about time I depart from this thread and explore some of these resources before continuing to waste everyone's time.

Ug, I'm just sitting here typing and backspacing over and typing again trying to form my question. I just can't understand how different frames of reference can disagree on how much time has passed. I know you and others are pointing me to a mathematical explanation, but even if I got to a point where I understood the math, that doesn't necessarily move me any further along to wrapping my mind around the concept and understanding relativity conceptually is all I've ever been interested in.

Before I wander off this thread and go do my own homework, let me expand on my A B C Scenario one more time. Same setup. A B C all start at same frame of reference. Suddenly, by B's perspective, A instantly moves one direction at .9900c while C also moves off at .9900c in the opposite direction. By B's perspective, 1 year passes. From previous calculation, we know that by B's perspective of 1 year passing, that 52 days have gone by for A and 52 days have gone by for C.

To repeat the mind blowing part... At this moment, according to A's reference point, I'm not exactly sure how much time has passed, but I know it's not 52 days. Same for C. Also, A and C both have a different perception of how much time has passed back at B's reference frame.

Now, instantly A and C both turn and begin their journey back the way they came. Putting the equations aside... Can you help me understand what happens when A & C rejoin B's frame of reference? I assume the math must work out such that the contradiction of perception of how much time has passed is somehow rectified or reversed.

 

[ZapperZ]

Turning around and coming back makes this problem complicated, because you are now adding acceleration to the issue. Furthermore, if you had looked at one of Don Lincoln's video in the link I gave earlier, you would have seen this VERY exact issue being addressed, i.e. the issue of a person changing reference frame even if there is no acceleration/deceleration.

The problem here is that you are jumping into multiple reference frame scenario without understanding yet something simpler. Rather than having THREE reference frame, go back to the simpler example of two reference frame, A and B, where one is moving with respect to the other. This is because it appears that you still do not understand the "time dilation" issues seen in each frame of the other, i.e. A seeing B, and B seeing A. Straighten that out FIRST before jumping to 3 frames, because I don't see the point of doing that when you don't understand the former.

Zz.

 

[jbriggs444]

To repeat the mind blowing part... At this moment, according to A's reference point, I'm not exactly sure how much time has passed, but I know it's not 52 days. Same for C. Also, A and C both have a different perception of how much time has passed back at B's reference frame.

One note: A reference frame is not a place. It is not a thing you can be in. It is a coordinate system that you lay down to assign coordinate values to events.

A "moment in time according to A" would be set of all events that have the same time coordinate according to clocks synchronized according to A's rest frame.

Now, instantly A and C both turn and begin their journey back the way they came. Putting the equations aside... Can you help me understand what happens when A & C rejoin B's frame of reference? I assume the math must work out such that the contradiction of perception of how much time has passed is somehow rectified or reversed.

If you change your state of motion, the frame of reference in which you are at rest changes. It is a new frame. If you want to use that frame, you need to assign new coordinates to all the events whose places and times you thought you knew. The Lorentz transform is the set of equations that tell you how to calculate the new coordinates based on the old.

 

[Grinkle]

@Peter Mole I know I said this already and you looked already, but I really suggest you look at

https://www.physicsforums.com/threads/twin-paradox-and-the-body.940272/

Post #10.

Unless I am very much missing where you are, this post explains things without needing a lot of math.

 

[Peter Mole]

That intuition is wrong, but it is hard to understand why until we phrase things more precisely.

You say "1 year passing on A is the same as 52 days passing on B". What's actually going on: At the same time that A's clock reads $T_{A0}$ B's clock reads $T_{B0}$. At the same time that A's clock reads $T_{A0}+1 year$ B's clock reads $T_{B0}+52 days$. We therefore conclude that B's clock is running slow, in a ratio of 52 days to one year.

But note that we are using A's definition of "at the same time" in this analysis. Because of the relativity of simultaneity, B does not find that that A's clock reads $T_{A0}+1 year$ at the same time that B's clock reads $T_{B0}+52 days$, so the same analysis doesn't work the other way. If we use B's definition of "at the same time" we will conclude that A's clock is running slow, by the same ratio.

At this time I'm not really understanding the math notations, let alone the math equations. I might be able to follow Einstein's train and lightning bolts example enough to accept both frame's of reference are just as valid, but how can two different frame's of references disagree on how much time has passed for the other and both be just as valid? I know, it's in the math, but even if I could do the math myself, I'm not sure that would make it any clearer.

I'm going to need some time with this...

 

[Peter Mole]

@Peter Mole I know I said this already and you looked already, but I really suggest you look at

https://www.physicsforums.com/threads/twin-paradox-and-the-body.940272/

Post #10.

Unless I am very much missing where you are, this post explains things without needing a lot of math.

Okay, thank you. I'll revisit it maybe with a newer understanding. I'm so far down the rabbit hole now...

 

[Peter Mole]

One note: A reference frame is not a place. It is not a thing you can be in. It is a coordinate system that you lay down to assign coordinate values to events.

A "moment in time according to A" would be set of all events that have the same time coordinate according to clocks synchronized according to A's rest frame.

I meant to say frame of reference rather than reference point. I'm not sure if I've waded into some misuse of terms or if there's a greater truth you're trying to convey, but I think I need to take a break as my head is already spinning.

If you change your state of motion, the frame of reference in which you are at rest changes. It is a new frame. If you want to use that frame, you need to assign new coordinates to all the events whose places and times you thought you knew. The Lorentz transform is the set of equations that tell you how to calculate the new coordinates based on the old.

I'm mentally tapped out. It seems that I've turned my scenario into a version of the twin paradox and now we've moved into general relativity. Mostly I was just curious about the conflicting perceptions of how much time had passed would work themselves out by the time A & C returned to B's frame of reference. You and everyone else have been extremely patient with me in trying to convey these concepts but I think my brain is full and I need to digest a bit.

 

[Peter Mole]

Turning around and coming back makes this problem complicated, because you are now adding acceleration to the issue. Furthermore, if you had looked at one of Don Lincoln's video in the link I gave earlier, you would have seen this VERY exact issue being addressed, i.e. the issue of a person changing reference frame even if there is no acceleration/deceleration.

The problem here is that you are jumping into multiple reference frame scenario without understanding yet something simpler. Rather than having THREE reference frame, go back to the simpler example of two reference frame, A and B, where one is moving with respect to the other. This is because it appears that you still do not understand the "time dilation" issues seen in each frame of the other, i.e. A seeing B, and B seeing A. Straighten that out FIRST before jumping to 3 frames, because I don't see the point of doing that when you don't understand the former.

Zz.

Yes, I understand your point. I really will be looking into the Lincoln's MinutePhysics' as well as the homework sheet as these are both good resources. I realize I have homework to do but I just wanted to follow the train of thought I was having while the topic was "hot" so to speak. Thank your for your patience and the links.

 

[Dale]

And I'm still not aware. I'm not sure my "why" question meant what you think it did and that's not your fault, it's mine. I perceived you to have made a flippant comment and so I made a flippant comment in return. It was wrong of me to make that assumption and so I apologize. Clearly you and many others are taking time out of your day to help me understand these concepts and to further question your motivations is utter rudeness on my part.

Wow! That is one of the most classy responses I have ever seen after a misunderstanding like this. I am sincerely glad you are here!

Checking out ZapperZ's link for MinutePhysics might be more my speed

They are very good videos, and I will try to post a graphical explanation when I have time.