I How Does Special Relativity Affect Perceived Distances Between Planets?

[dwspacetime]

You don't need planets in your scenario. Planets suggest a natural frame of reference in which the planets are at rest. You don't want that.

Likewise, a spacetime diagram picks out a frame of reference - determined by the specific axes you draw.

That's why I was trying to get you towards a scenario with just A and B moving relative to each other. That scenario has two equally naturals frames of reference - the rest frames of A and B. That allows you to examine the symmetry between A and B.

i guess the reason I was puzzled is because I thought when tom at A and Mary at B the distance is between them is Absolut

That depends what you mean by "when" - there are several definitions available. Your confusion comes from the fact that Tom and Mary are using different definitions when they measure different separations "at the same time" and you are implicitly assuming they're using the same one. If they were using the same one then there would be a paradox.

Tom and Mary are going to meet at some point. Both will say that five years before that (by their own clocks) the other one was four light years away. But both will also say that, at the same time they are making this claim the other's clock would show only three years to the meeting. This is how there's no paradox - Tom knows that Mary isn't measuring the same distance at the same time.

You don't need a planet, just for them to meet twice. Pick any inertial frame and write down their velocity as a function of time. Then compute each of their ages using $\int\sqrt{1-v^2/c^2}dt$, where the limits of the integrals are the meeting times specified using your arbitrarily chosen frame. The lower value is the younger one.

I kind think it has nothing to do with "when". the distance btw A and B is 4 lys for Tom nonmatter when since they are stationary to Tom. but to Mary both A and B are moving towards her, it is always 2.4 lys btw them whenever.
According to your equation, to use either Tom or mary as reference, Tom or Mary would have a v=0, the other one is always younger.

.

 

[Ibix]

According to your equation, to use either Tom or mary as reference, Tom or Mary would have a v=0, the other one is always younger.

They don't meet twice in the scenario we are discussing, so one of the limits of the integral isn't defined. If they do meet twice, at least one of them must accelerate so at least one of them can't always have speed zero in the arbitratily chosen inertial frame.

 

[PeroK]

i guess the reason I was puzzled is because I thought when tom at A and Mary at B the distance is between them is Absolute

It's the "when" that is not absolute. That's what I was trying to emphasise.

Although I see now that you have moved on to a different question altogether.

 

[Orodruin]

TL;DR Summary: Relative distance

Quite simple question. There are two planets A and B, they are 4 light years apart measured by tom on planet A. Say both A and B remain stationary. Mary flys 0.8c to tom on planet A. When she passes planet B she should see Tom or planet A 2.4 light years away, am I correct? What about tom now? Does he see both planet B and Mary 4 light years away? Thanks

Misconceptions regarding special relativity in general and Minkowski space in particular can often be illuminated by considering the Euclidean space equivalent. What you essentially need to know are what the statements correspond to in Euclidean space. Here, in particular, the following is relevant:

The Euclidean statement corresponding to ”When A finds B to be x away” is ”for a straight line A, the line orthogonal to A crossing the line B at a distance of x”. For brevity, let’s just call x this ”the orthogonal distance from A to B”. Note that only the direction of A is important for this definition.

Let’s consider the equivalent of your scenario.

- Draw two parallel lines A and B. (These correspond to your planets)
- Draw a line T on top of A. (This corresponds to Tom)
- Draw a line M that is not parallel to A and B. (This corresonds to Mary) This line necessarily crosses both A and B.
- Draw the line orthogonal to T which crosses M at a distance of 4. Call this line C and its intersection with M you call MC.
- Determine the orthogonal distance from M to T at the point MC. (Ie, draw a line from MC that is orthogonal to M, find how long it must be to intersect T)

You should find that the result in the last step is not 4. This is completely analogous to your setup, just in a different geometry. Whether the result is smaller or larger than 4 will differ between the geometries because of a sign in the geometry definition, but the geometries are similar enough for this to be a direct analogy.

Now remove lines A and B. Does this change the result?

edit: here is a diagram

Your claim is essentially the Minkowski space equivalent of saying that C has the same length as D.

 

[dwspacetime]

They don't meet twice in the scenario we are discussing, so one of the limits of the integral isn't defined. If they do meet twice, at least one of them must accelerate so at least one of them can't always have speed zero in the arbitratily chosen inertial frame.

I am trying to simply it by spreading the acceleration to speed. to meet again some of the speeds have to be negative. but since is v square, so it doesnt affect the result.

my original question is still a paradox. I was assuming A and B stay stationary to Tom. in the meantime we can also assume planet C and D are stationary with Mary 4 lys apart. Then to Tom C and D are 2.4 years apart.... so "NOW" we have 4 planets.

 

[PeroK]

my original question is still a paradox.

It's not a paradox. There's only your failure to understand the basics of SR.

 

[Orodruin]

to meet again the some of the speeds have to be negative

Pet peeve: Speed is never negative. It is the absolute value of velocity (which may be negative depending on direction and chosen coordinates).

 

[dwspacetime]

Pet peeve: Speed is never negative. It is the absolute value of velocity (which may be negative depending on direction and chosen coordinates).

that is fine. I am trying to tell you they will meet after all kinds of speed. since somebody says they dont meet again assuming no one turning back. if that is true, Tom travels from A to B and wait for mary from A to B also. they do meet again without turning back. if we consider either one of them as a reference they other one will have a speed which will result a less number in time. so the other one is always younger

 

[dwspacetime]

It's not a paradox. There's only your failure to understand the basics of SR.

my failure of understanding your whatever. regardless "when", or whatever "when" you applies to Tom it shoudl applies to Mary. without a reference independent from them whatever assumption you made to one of them you can just switch btw them

 

[dwspacetime]

It's not a paradox. There's only your failure to understand the basics of SR.

at whatever "when" Mary is 4 lys away to Tom there is another "when" the totally opposite is also true

 

[Orodruin]

that is fine. I am trying to tell you they will meet after all kinds of speed. since somebody says they dont meet again assuming no one turning back. if that is true, Tom travels from A to B and wait for mary from A to B also. they do meet again without turning back. if we consider either one of them as a reference they other one will have a speed which will result a less number in time. so the other one is always younger

No, if they both travelled from A to B their frames were not always inertial and therefore could not be used* with the quoted formula.

* You can use noninertial frames as well, but it typically is more mathematically involved and gives the same result

 

[dwspacetime]

It's not a paradox. There's only your failure to understand the basics of SR.

let us put it this way. I agree the "when" of Tom is red is not the same as the "when" Mary is red. but for the same original question I asked there must be a "when" Mary is red and all the charts you drew still apply which is why it is a paradox.

 

[Orodruin]

let us put it this way. I agree the "when" of Tom is red is not the same as the "when" Mary is red. but for the same original question I asked there must be a "when" Mary is red and all the chart you drew still apply which is why it is a paradox.

It is not a paradox. It is geometry. Try the Euclidean space equivalent!

 

[dwspacetime]

let us put it this way. I agree the "when" of Tom is red is not the same as the "when" Mary is red. but for the same original question I asked there must be a "when" Mary is red and all the chart you drew still apply which is why it is a paradox.

It is not a paradox. It is geometry. Try the Euclidean space equivalent!

let's do this. just go back to your original charts. just switch Tom and Mary and forget about the planets. do those charts still apply? why not? I know when you switch them the "when" is not the same as the "when" you did them the first time.

It is not a paradox. It is geometry. Try the Euclidean space equivalent

 

[Orodruin]

You messed up your quotes, but yes, you can do exactly the same statements from Mary’s frame. It is unclear why you think this is a paradox. Again I refer you to try the same in the Euclidean case. It is just a fact of geometry. Nothing strange is going on.

 

[dwspacetime]

It is not a paradox. It is geometry. Try the Euclidean space equivalent!

let's make it very simple. let me modify my original question to this. Tom and Mary in spacetime. in Tom's frame Mary is moving towards him in 0.8C and in Mary's frame Tom is moving towards her in 0.8C. when Mary is 4 lys away from Tom in Tom's frame how far is Mary from Tom? why

 

[Orodruin]

let's make it very simple. let me modify my original question to this. Tom and Mary in spacetime. in Tom's frame Mary is moving towards him in 0.8C and in Mary's frame Tom is moving towards her in 0.8C. when Mary is 4 lys away from Tom in Tom's frame how far is Mary from Tom? why

Define what you mean by ”when”. This is what seems to confuse you.

 

[dwspacetime]

let's make it very simple. let me modify my original question to this. Tom and Mary in spacetime. in Tom's frame Mary is moving towards him in 0.8C and in Mary's frame Tom is moving towards her in 0.8C. when Mary is 4 lys away from Tom in Tom's frame how far is Mary from Tom? why?

 

[Orodruin]

Also specify what distance you want to know and according to what convention.

 

[dwspacetime]

Also specify what distance you want to know and according to what convention.

use whatever convention you want to use. then ask the same question with Tom and Mary switched. you should get the same answer for the two questions by using whatever convention if you are consistent or you are wrong.

 

[dwspacetime]

Define what you mean by ”when”. This is what seems to confuse you.

I let you define the "when" whatever way you want. once you answer the question. I will ask you the second question with all the wording the same as i used in the first except switch Tom with Mary. answer the 2nd question with the same definition of "when" you use for the first question then compare the two answers.

 

[Orodruin]

use whatever convention you want to use

No I won’t because it will just lead to you misunderstanding things as this thread has shown. You need to specify what you want to know.

you should get the same answer for the two questions by using whatever convention if you are consistent or you are wrong.

No, you are wrong here. Switching Tom and Mary also switches the ”according to whom”.

Say for example:
M is 4 ly away from T in T’s rest frame, the same event for M is 2.4 ly away from T in M’s rest frame.

The switching is:
T is 4 ly away from M in M’s rest frame, the same event for T is 2.4 ly away from M in T’s rest frame.

Both are true and there is no paradox. Although the statements are the same, the events involved are not. Please refer to the Euclidean analogue (which you have completely ignored so far - that’s just bad form).

 

[dwspacetime]

No I won’t because it will just lead to you misunderstanding things as this thread has shown. You need to specify what you want to know.No, you are wrong here. Switching Tom and Mary also switches the ”according to whom”.

Say for example:
M is 4 ly away from T in T’s rest frame, the same event for M is 2.4 ly away from T in M’s rest frame.

The switching is:
T is 4 ly away from M in M’s rest frame, the same event for T is 2.4 ly away from M in T’s rest frame.

Both are true and there is no paradox. Although the statements are the same, the events involved are not. Please refer to the Euclidean analogue (which you have completely ignored so far - that’s just bad form).

 

[dwspacetime]

it is a paradox. basically my two questions are the same question even I switched them. but you get me two different answers. mary moving towards tom is the same as tom moving towards mary

 

[Orodruin]

it is a paradox. basically my two questions are the same question even I switched them. but you get me two different answers.

I gave you exactly the same answer for the switched question.

Here is the Euclidean equivalent:

Basically you are confused that I could make C and C’ the same length and still have D and D’ the same length.

There is no paradox here. Just you confusing yourself with your own misconceptions about what the answer should be.

 

[dwspacetime]

I gave you exactly the same answer for the switched question.

Here is the Euclidean equivalent:
View attachment 337740
Basically you are confused that I could make C and C’ the same length and still have D and D’ the same length.

There is no paradox here. Just you confusing yourself with your own misconceptions about what the answer should be.

sir what you did is "correct" after wrongfully made my two same statements stated in two different ways two different statements. the two statements are the exactly same although I switched two names. but for the same statements you answered in M is frame T is 4 lys in one answer but in the other T is 2.4ly.

 

[dwspacetime]

I gave you exactly the same answer for the switched question.

Here is the Euclidean equivalent:
View attachment 337740
Basically you are confused that I could make C and C’ the same length and still have D and D’ the same length.

There is no paradox here. Just you confusing yourself with your own misconceptions about what the answer should be.

let me make it simple. basically I stated T and M are moving towards each other which is all i tell you. and you tell me T is 4 lys in M's frame and is also 2.4 lys in M's frame

 

[Histspec]

let's make it very simple. let me modify my original question to this. Tom and Mary in spacetime. in Tom's frame Mary is moving towards him in 0.8C and in Mary's frame Tom is moving towards her in 0.8C. when Mary is 4 lys away from Tom in Tom's frame how far is Mary from Tom? why?

Note that your statement "when Mary is 4 lys away" from Tom has to be the result of a measurement along a distance separated by two endpoints that are constantly at rest, otherwise there is no "distance" onto which we can apply the length contraction formula, and there would be nothing to discuss about.... So there is always something equivalent to your planets, if you want it or not.

It's like the relativity of motion: If a ball is at rest in Tom's frame, it is obviously in motion in Mary's frame. Do you think this "asymmetry" violates the relativity principle?

Now let's discuss your length contraction experiment along the same lines:
a) An experimentalist defines a distance of 4 lightyears in Tom's frame S, consisting of endpoints that are both constantly at rest with respect to Tom.
b) So in all other inertial frames those endpoints have a constant speed different from zero and the distance in between them is length contracted. So Tom measures a (proper) length of 4 lightyears, while Mary measures a (contracted) length of 2.4 lightyears.
c) What is the cause of this asymmetry? Well, simply YOUR (being an experimentalist) decision to measure endpoints that are at rest in S.
d) Of course, the experimentalist can decide to choose ''another set of endpoints'' constantly at rest in Mary's frame S' that are separated by 4 lightyears. In this case everything is reversed: The S' observer measures the length of 4 lightyears, while the S observer measures 2.4 lightyears. However, since this distance is defined by a new set of endpoints, it has nothing to do with the distance measured by Tom...

 

[Orodruin]

sir what you did is "correct" after wrongfully made my two same statements stated in two different ways two different statements. the two statements are the exactly same although I switched two names. but for the same statements you answered in M is frame T is 4 lys in one answer but in the other T is 2.4ly.

I did nothing of the sort. I switched M and T everywhere in the original statement, which is the only way you can claim symmetry. Please stop being disingenuous.

Here is the case of your actual setup in Minkowski space. Based on the inertial frame where both T and M have the same speed so you do not misconstrue either of them being assumed to be stationary.

C and C’ are both 4 ly and D and D’ are both 2.4 ly. Everything is symmetric. The ”weird” orthogonality is just how orthogonality works in Minkowski space.

 

[dwspacetime]

Note that your statement "when Mary is 4 lys away" from Tom has to be the result of a measurement along a distance separated by two endpoints that are constantly at rest, otherwise there is no "distance" onto which we can apply the length contraction formula, and there would be nothing to discuss about.... So there is always something equivalent to your planets, if you want it or not.

It's like the relativity of motion: If a ball is at rest in Tom's frame, it is obviously in motion in Mary's frame. Do you think this "asymmetry" violates the relativity principle?

Now let's discuss your length contraction experiment along the same lines:
a) An experimentalist defines a distance of 4 lightyears in Tom's frame S, consisting of endpoints that are both ''constantly at rest'' with respect to Tom.
b) So in all other inertial frames those endpoints have a constant speed different from zero and the distance in between them is length contracted. So Tom measures a (proper) length of 4 lightyears, while Mary measures a (contracted) length of 2.4 lightyears.
c) What is the cause of this asymmetry? Well, simply YOUR (being an experimentalist) decision to measure endpoints that are at rest in S.
d) Of course, the experimentalist can decide to choose ''another set of endpoints'' constantly at rest in Mary's frame S' that are separated by 4 lightyears. In this case everything is reversed: The S' observer measures the length of 4 lightyears, while the S observer measures 2.4 lightyears. However, since this distance is defined by a new set of endpoints, it has nothing to do with the distance measured by Tom...

dont confuse yourself too much. again T and M are moving towards each other in whatever speed if numbers confuse you. in M's frame there should be one distance from T or two different distances? why dd you tell me in M's frame T is both 4 lys and 2.4 lys.

 

[Orodruin]

and you tell me T is 4 lys in M's frame and is also 2.4 lys in M's frame

No. As you can see from the diagram - and as I also told you previously - you change the relevant events when you change the statement. You should not be surprised that T is 4 ly away at some time and 2.4 ly away at a different time.

 

[dwspacetime]

No. As you can see from the diagram - and as I also told you previously - you change the relevant events when you change the statement. You should not be surprised that T is 4 ly away at some time and 2.4 ly away at a different time.

this is interesting. but the sequence of events doesn't seem correct. that is weird

 

[Histspec]

dont confuse yourself too much. again T and M are moving towards each other in whatever speed if numbers confuse you. in M's frame there should be one distance from T or two different distances? why dd you tell me in M's frame T is both 4 lys and 2.4 lys.

a) If the experimentalist (=you) measures two endpoints at rest in Tom's frame separated by 4 light years, the only length measured by Mary is 2.4 lightyears.
b) If the experimentalist (=you) measures two endpoints at rest in Mary's frame separated by 4 light years, the only length measured by Tom is 2.4 lightyears.

You made your decision by choosing a). Is it really that hard to understand?

 

[dwspacetime]

a) If the experimentalist (=you) measures two endpoints at rest in Tom's frame separated by 4 light years, the only length measured by Mary is 2.4 lightyears.
b) If the experimentalist (=you) measures two endpoints at rest in Mary's frame separated by 4 light years, the only length measured by Tom is 2.4 lightyears.

You made your decision by choosing a). Is it really that hard to understand?

4 lys away should happen before 2.4 lys away but they seem switched somehow. if it is true the universe is wrong. sorry

 

[Orodruin]

this is interesting. but the sequence of events doesn't seem correct. that is weird

This is completely unhelpful. You cannot just state that something seems ”weird” without specifying what it is. If you do that there is no way to correct you.

(Spoiler alert: Everything in that diagram is in accordamce with what has been specified. If something seems ”weird” to you, then that is where your understanding of special relativity is lacking.)

 

[Orodruin]

4 lys away should happen before 2.4 lys away but they seem switched somehow. if it is true the universe is wrong. sorry

Look at the diagram. In both cases the 4 ly distances occur before the 2.4 ly distances. There is nothing weird going on here.

 

[dwspacetime]

This is completely unhelpful. You cannot just state that something seems ”weird” without specifying what it is. If you do that there is no way to correct you.

(Spoiler alert: Everything in that diagram is in accordamce with what has been specified. If something seems ”weird” to you, then that is where your understanding of special relativity is lacking.)

Sorry I was just talking with myself. the event M is 4 lys away in T's frame should happen before the event M is 2.4 lys away. if that is the case then the event T 2.4 lys away happens before T is 4 lys away in M' frame. is that not weird. this must be one of the weird reality of spacetime

 

[Orodruin]

if that is the case then the event T 2.4 lys away happens before T is 4 lys away in M' frame.

No, this is wrong and a misrepresentation of what the diagram shows.

T 2.4 ly away in M’s frame is the simultaneity D in the diagram. T 4 ly away in M’s frame is the simultaneity C’ in the diagram. C’ clearly lies below D.

 

[dwspacetime]

No, this is wrong and a misrepresentation of what the diagram shows.

T 2.4 ly away in M’s frame is the simultaneity D in the diagram. T 4 ly away in M’s frame is the simultaneity C’ in the diagram. C’ clearly lies below D.

no matter which event happens first one of them is going to have 2.4 lys before 4 years why

 

[dwspacetime]

No, this is wrong and a misrepresentation of what the diagram shows.

T 2.4 ly away in M’s frame is the simultaneity D in the diagram. T 4 ly away in M’s frame is the simultaneity C’ in the diagram. C’ clearly lies below D.

that tells me that depending on which inertia frame you are in the sequence of events could be reversed. the reason for something to happen could be the result.

 

[Orodruin]

View attachment 337748
no matter which event happens first one of them is going to have 2.4 lys before 4 years why

This is simply wrong. This is not a proper spacetime diagram. The proper spacetime diagram was posted by me above. Please refer to that instead of making up your own faulty notions. Your diagram completely fails to account for the relativity of simultaneity. You will simply never understand relativity without a proper understanding of the relativity of simultaneity. Instead you will get lost in a quagmire of imagined paradoxes.

Note in the actual diagram how the blue and red lines do not coincide! They have different slopes. This is the relativity of simultaneity.

It is true that the event where C and D meet on M and the event where C’ and D’ meet on T have spacelike separation. This means that the order in which they will happen is going to depend on the reference frame - again relativity of simultaneity! In the frame I based the diagram on they both occur at the same time due to symmetry.

However, in T’s frame CD occurs before C’D’ but in M’s frame C’D’ occurs before CD. This must also be the case due to symmetry.

 

[dwspacetime]

This is simply wrong. This is not a proper spacetime diagram. The proper spacetime diagram was posted by me above. Please refer to that instead of making up your own faulty notions. Your diagram completely fails to account for the relativity of simultaneity. You will simply never understand relativity without a proper understanding of the relativity of simultaneity. Instead you will get lost in a quagmire of imagined paradoxes.

Note in the actual diagram how the blue and red lines do not coincide! They have different slopes. This is the relativity of simultaneity.

It is true that the event where C and D meet on M and the event where C’ and D’ meet on T have spacelike separation. This means that the order in which they will happen is going to depend on the reference frame - again relativity of simultaneity! In the frame I based the diagram on they both occur at the same time due to symmetry.

However, in T’s frame CD occurs before C’D’ but in M’s frame C’D’ occurs before CD. This must also be the case due to symmetry.

thanks for introducing all that to me.

 

[PeterDonis]

that tells me that depending on which inertia frame you are in the sequence of events could be reversed.

That is correct; the time ordering of spacelike separated events is frame dependent.

the reason for something to happen could be the result.

No, it can't, because spacelike separated events in relativity can't be causally connected. Neither can cause the other or be an effect of the other.

 

[PeroK]

the universe is wrong. sorry

That would make a great title for a book:

Sorry, The Universe is Wrong (the thoughts of a science skeptic)

 

[Orodruin]

By definition the Universe is right. Whether that conforms to one’s own prejudice or not is a different matter. The Universe is in no way obliged to make itself easy to understand.

 

[weirdoguy]

Ok, but what is the point of this thread @dwspacetime ? You want to learn something, or just simply argue with everyone knowledgeable?

 

[dwspacetime]

Ok, but what is the point of this thread @dwspacetime ? You want to learn something, or just simply argue with everyone knowledgeable?

I just watched something on YouTube about twin paradox which made me think. I was always curious about relativity but never had a chance to study it.. about a week ago i digged out the book I downloaded years ago "relativity for the questioning minds" but never had a chance to finish it. I'm reading the last chaptor and everything makes sense now. I might quit my job and go to school again for this as my retirement. Thank you guys.

 

[robphy]

"relativity for the questioning minds"

Dan Styer's book?
https://www2.oberlin.edu/physics/dstyer/

 

[dwspacetime]

Dan Styer's book?
https://www2.oberlin.edu/physics/dstyer/

Yes. It is pretty thorough which answered almost all my questions for now. It seems everything is moving in a speed of light..... The faster you move in space the slower in time...

 

[PeterDonis]

It is pretty thorough which answered almost all my questions for now.

Unfortunately, the answers it gave you do not appear to be good ones.

It seems everything is moving in a speed of light..... The faster you move in space the slower in time...

This is unfortunately a fairly common pop science viewpoint, but it doens't work. You will not find it in any actual textbooks or peer-reviewed papers, and you should not be using it.