Layman's Question about Special Relativity

[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.

 

[phinds]

I just can't understand how different frames of reference can disagree on how much time has passed.

Although it will likely NOT be clear on first reading it, it will be very easily clear once you get into this stuff, that this is EXACTLY analogous to having one driver go from DC straight to NY and register one distance and another go by way of Chicago and the have a different odometer reading and they disagree on how many miles it takes to drive from DC to NY. It's an ANALOGY, so you have to ignore the fact that they can look at a map and see that the straight-line distance is not what either of them got but is something they can agree on. The analogy is just about their odometer readings, which are analogous to the clock readings on two different travelers at relativistic velocities. Different paths through space-time, from one event to another, can take different amounts of time.

 

[jbriggs444]

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.

This is still pure special relativity.

 

[Grinkle]

This is still pure special relativity.

The post I referred him to may not be pure SR or it may be.

IMO, understanding the demarcation line between SR and GR is not required to understand the resolution to the twin paradox. Also IMO, understanding that demarcation is harder than understanding the resolution to the twin paradox.

 

[Nugatory]

IMO, understanding the demarcation line between SR and GR is not required to understand the resolution to the twin paradox. Also IMO, understanding that demarcation is harder than understanding the resolution to the twin paradox.

The easiest way of saying it: if there's a gravitating mass involved you need GR. Otherwise SR works just fine.

As a historical note, the twin paradox is introduced and explained as part of Einstein's first paper on SR, the 1905 "On the electrodynamics of moving bodies"

 

[Herman Trivilino]

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.

This is true, but be aware that if all you do is 50 plus 60 you're using an approximation. An extremely good approximation but nevertheless an approximation. The higher the speeds the poorer the approximation.

So your question is about why a low speed approximation won't work at high speeds.

 

[Aufbauwerk 2045]

I think it's excellent that you are interested, in spite of being a "layman" as you put it. Einstein wrote a famous book just for people like you. (Actually he was co-author. The book is the result of a collaboration with Leopold Infeld.)

https://www.amazon.com/dp/0671201565/?tag=pfamazon01-20

 

[Aufbauwerk 2045]

The two big theories to come out of 20th century physics are relativity and quantum theory. In addition to The Evolution of Physics by Einstein and Infeld, I strongly recommend this book by Gamow, since it is a great introduction to the development of quantum theory. Between these two books, you get a very good introduction to the physics breakthroughs of the early 20th century.

https://www.amazon.com/dp/048624895X/?tag=pfamazon01-20

 

[Peter Mole]

I think it's excellent that you are interested, in spite of being a "layman" as you put it. Einstein wrote a famous book just for people like you. (Actually he was co-author. The book is the result of a collaboration with Leopold Infeld.)

https://www.amazon.com/dp/0671201565/?tag=pfamazon01-20

Thanks, I've read a few and I'll check this one out when I get a chance. I don't know that I'm as interested in the other one you mentioned but I'll keep it in mind.

I've read all the comments here and I may check back from time to time, but I think I'm going back to my documentaries/lectures for a while.

Thanks to everyone not only for the information but for your patience in explaining (and re-explaining). :)

 

[PeroK]

I am in the same position as you. I am an engineer with training but I have NEVER seen an understandable explanation of special relativity. I think that most people (and perhaps all who attend this site) know the actual physics but have no real understanding of it and hence cannot give a layman's explanation.

Try, for example:

https://www.goodreads.com/book/show/6453378-special-relativity

 

[PeterDonis]

Moderator's note: Off topic posts deleted. The thread has run its course and is now closed.