The Relativity of Motion: Is it Relative to the Object or the Rest Frame?

[analyst5]

@DaleSpam

This is the first question that's on my mind:

And btw, it can be concluded that distance plays a big role in the judgement of simultaneity. For moving observers, the greater distance in space is from an event, the distant the event is in time, right?

And the second would be a combination of length contraction and composition of different temporal segments of the object. Let me explain.
What if the worldtube (the object) undergoes acceleration, would the observer still intersect it and have the object that is composed of different temporal segments in its present frame? Would he 'perceive' the object in a state which some of its parts undergo change of speed before others?

 

[Dale]

For moving observers, the greater distance in space is from an event, the distant the event is in time, right?

Yes, that follows from the Lorentz transform.

What if the worldtube (the object) undergoes acceleration, would the observer still intersect it and have the object that is composed of different temporal segments in its present frame? Would he 'perceive' the object in a state which some of its parts undergo change of speed before others?

If an object undergoes acceleration in which every part accelerates at the same time in one frame then in other frames the acceleration will be such that different parts accelerate at different times.

 

[Nugatory]

And btw, it can be concluded that distance plays a big role in the judgement of simultaneity. For moving observers, the greater distance in space is from an event, the distant the event is in time, right?

Right, or at least as close to right as a non-precise English language statement will be.

If you want to be precise, you need to work some with the math. Let's start with a frame in which you are at rest at the origin at time zero. You become aware of two events, one of them at time t=5, x=5 and the other at time t=5, x=10 (units in seconds and light seconds, for the sake of argument). Of course you won't become aware of the first event until time 10 and the second until time 15 because of the light travel time, but eventually you'll be able to say "Hmmm... Light from first event got to me at t=10, started 5 light-seconds away, seems it happened at t=5; light from second event got to me at t=15 after spending 10 seconds in flight, seems it also happened at t=5". You'll say the two events were simultaneous because they both happened at the same time, both had the same t coordinate.

Now let's consider the same two events, but working with a frame in which you are moving in the negative x direction at speed v. (This is, of course, also a frame in which someone moving in the positive x direction at speed v would be at rest). Any event that occurs at position x and time t using the first frame will occur at x' and t' in the second frame, and x, t, x', and t' will be related by the Lorentz transformations:
$$x' = \gamma(x-vt)$$
$$t' = \gamma(t-vx)$$
where the speed is measured in light-seconds per second (that way, c is equal to one) and $\gamma$ is $\frac{1}{\sqrt{1-v^2}}$

In general, two events that are simultaneous (same t value) but in different places (x values) in the first frame will not be simultaneous (different t' values) in the second frame. Larger x values make the discrepancy greater because of the $vx$ term in the equation for t'.

 

[ghwellsjr]

I'm wondering about the motivation of your question. Here is a spacetime diagram of an object (like a desk) that is 10 feet long and stationary in an Inertial Reference Frame. One end is represented in blue and the other end in red:

Now we will transform to an IRF moving at -0.6c with respect to the original IRF:

I'm wondering if you are seeing events that used to be simultaneous in the first IRF are now at different times in the second IRF and giving you the impression that they are a combination of past and future events?

That's what I was going for, thanks. So when moving in our plane of simultaneity we have an object composed of past and future particles relative to the 'descripiton' of the object in its rest frame, that also gets length contracted?

But what if we synchronized the Proper Times for the dots in the second diagram? In other words, if we set the Proper Times for the two dots at the Coordinate Time of 10 to read zero and all the other ones to correspond then in the first diagram would you say that if you're stationary with respect to the object, you "will have the cross-sectional desk, which is composed of past and future small parts of the desk in its [moving] frame"?

And btw, it can be concluded that distance plays a big role in the judgement of simultaneity. For moving observers, the greater distance in space is from an event, the distant the event is in time, right?

You seem to enjoy torture. If you would just learn to use the Lorentz Transformation, then you wouldn't have to ask questions like this, you could figure them out on your own. This is like asking questions about multiplication such as if you multiply two even numbers, do you get an even number or if you multiply two odd numbers, do you get an odd number, or what do you get if you multiply an odd number by and even number? How would you handle a child who persists in asking such basic questions but refuses to learn how to multiply?

 

[analyst5]

But what if we synchronized the Proper Times for the dots in the second diagram? In other words, if we set the Proper Times for the two dots at the Coordinate Time of 10 to read zero and all the other ones to correspond then in the first diagram would you say that if you're stationary with respect to the object, you "will have the cross-sectional desk, which is composed of past and future small parts of the desk in its [moving] frame"?



You seem to enjoy torture. If you would just learn to use the Lorentz Transformation, then you wouldn't have to ask questions like this, you could figure them out on your own. This is like asking questions about multiplication such as if you multiply two even numbers, do you get an even number or if you multiply two odd numbers, do you get an odd number, or what do you get if you multiply an odd number by and even number? How would you handle a child who persists in asking such basic questions but refuses to learn how to multiply?

You seem to lack patience, I already explained how this knowledge would best fit me. Through some concrete examples and then through numbers. Some members here indeed provided me good, detailed answers, while your answers are solely based on maths, you behave like SR doesn't have a practical and concrete meaning. I have a feeling that if I asked you 'Is it raining outside' you would draw me a diagram instead of answering straight-forward. It's hard to understand that kind of stuff... Please stop criticizing me because I believe I'm not doing any harm to anybody by asking questions like this in a field that really interests me, and seeking an appropriate examples of it.

 

[analyst5]

Yes, that follows from the Lorentz transform.

If an object undergoes acceleration in which every part accelerates at the same time in one frame then in other frames the acceleration will be such that different parts accelerate at different times.

Here, for instance, is a perfectly understandable answer that can easily be conceptualized and connected to previous thing I've learned. I believed in something like this while waiting for your answer, glad to see it's like that.

 

[Dale]

I am glad that you have found it helpful, but in general I do agree with ghwellsjr and Nugatory. A deeper understanding will, at some point, require the math and spacetime diagrams. All of the English descriptions are, at best, imperfect representations of the math.

As long as you are making progress, I am glad to try to answer at the level you want, but eventually you will ask a question that I cannot answer without the math or I will say something that is confusing and will have to use math to clarify. The math isn't too bad, so don't wait too long before trying it out.

 

[Bill_K]

And besides, if Einstein had not expressed his theory in mathematical terms, he'd still be a patent clerk today!

 

[TheBC]

Yes, yes, I understand the second sentence, I wrote the stuff I didn't mean.

So when we have a physical object that is moving in our plane of simultaneity, is it true that this object is always composed of past and future parts of the object viewed from its rest frame?
That's what I mean by the previous question ghwellsjr. For instance, when I'm at rest with respect to my desk I will have all of its points simultaneously in my plane of simultaneity. But if I'm moving with respect to it, I will have the cross-sectional desk, which is composed of past and future small parts of the desk in its rest frame. Is this true, or at least close to being true?

Spacetime is a 4 dimensional entity (all the worldtubes...) in which the different 3D spaceworlds of the relative moving observers are different 'cuts' though 4D spacetime.

And besides, if Einstein had not expressed his theory in mathematical terms, he'd still be a patent clerk today!

I'm not sure about that. His train thought experiment does not use math but expresses exactly what relativity of simultaneity is about: different cuts through the worldtubes ...

 

[WannabeNewton]

I'm not sure about that. His train thought experiment does not use math but expresses exactly what relativity of simultaneity is about: different cuts through the worldtubes ...

Whimsical thought experiments alone wouldn't have gotten his beautiful papers published in the annals.

 

[ghwellsjr]

Yes, that follows from the Lorentz transform.

If an object undergoes acceleration in which every part accelerates at the same time in one frame then in other frames the acceleration will be such that different parts accelerate at different times.

Here, for instance, is a perfectly understandable answer that can easily be conceptualized and connected to previous thing I've learned. I believed in something like this while waiting for your answer, glad to see it's like that.

But did you understand that accelerating an object in this manner can result in it being stretched to a new length?

Here is a diagram for a ten-foot long object (like your table) having every part accelerated simultaneously in its own initial rest frame:

Now if we use the Lorentz transform to see what it looks like in its final rest frame, we get:

Note that the table is now 12.5 feet long.

 

[TheBC]

Whimsical thought experiments alone wouldn't have gotten his beautiful papers published in the annals.

What's whimsical about the train thought experiment?

The experiment shows very clearly that constant speed of light implies relativity of simultaneity. You don't need math for that.

 

[nitsuj]

The point is c, and "shows" & proves are different.

Invariance of a speed says enough imo.

 

[analyst5]

But did you understand that accelerating an object in this manner can result in it being stretched to a new length?

Here is a diagram for a ten-foot long object (like your table) having every part accelerated simultaneously in its own initial rest frame:

Now if we use the Lorentz transform to see what it looks like in its final rest frame, we get:

Note that the table is now 12.5 feet long.

So acceleration always results in an increase in proper length? Interesting, I didn't know about this.
Why those changes aren't noticeable on our scale?And what about decceleration?

Thanks for the example ghwellsjr, to me this gets more and more interesting.

 

[analyst5]

I am glad that you have found it helpful, but in general I do agree with ghwellsjr and Nugatory. A deeper understanding will, at some point, require the math and spacetime diagrams. All of the English descriptions are, at best, imperfect representations of the math.

As long as you are making progress, I am glad to try to answer at the level you want, but eventually you will ask a question that I cannot answer without the math or I will say something that is confusing and will have to use math to clarify. The math isn't too bad, so don't wait too long before trying it out.

Dale, I completely agree with you. I believe that maths is fundamental to understand this but I'm glad you and other members gave me some examples so at least I have the basic vision of how stuff works in SR.

 

[ghwellsjr]

So acceleration always results in an increase in proper length? Interesting, I didn't know about this.

No, it doesn't necessarily result in an increase in proper length. That happened because we accelerated all the parts of the table simultaneously in its initial rest frame. If we accelerate all the parts of the table simultaneously in its final rest frame we go from this:

https://www.physicsforums.com/attachment.php?attachmentid=60179&stc=1&d=1373472364​

where the proper length is 10 feet to this:

https://www.physicsforums.com/attachment.php?attachmentid=60180&stc=1&d=1373472364
​

where the proper length has been compressed to 8 feet.

Why those changes aren't noticeable on our scale?

Because no one has enough resources to perform these experiments. You need lots of space, lots of materials, lots of energy, lots of money, lots of instrumentation and lots of government approval.

Also, keep in mind that if you actually accelerated all parts of an object simultaneously in any frame, you would probably destroy the object. It would be similar to if you took a table and tried to stretch its length to 12.5 feet or compress it to 8 feet.

And what about decceleration?

There really is no difference between acceleration and deceleration, just what you are calling the start and ending velocity and the direction of the change in velocity.

Thanks for the example ghwellsjr, to me this gets more and more interesting.

You're welcome.

 

[ghwellsjr]

Just for fun, I decided to try some more frames with simultaneous accelerations. The next one I tried was a frame moving at -0.6 relative to the initial rest frame of the 10-foot long table. Here's the spacetime diagram for that IRF:

And here is the diagram for the initial rest frame of the 10-foot long table:

And finally for the final rest frame of the table:

Now we see that the table has been stretched to 17 feet.

I did some additional experimenting and discovered that the maximum stretching is double the initial length of the object and the maximum compression is one-half the initial length of the object. The maximum stretching occurs with simultaneous acceleration in a frame approaching -c with respect to the initial rest frame and the maximum compression occurs with simultaneous acceleration in a frame approaching c with respect to the initial rest frame.

Keep in mind that this stretching and compression has nothing to do with Length Contraction which is a frame dependent effect and not measurable. This stretching and compression is not frame dependent and is measurable (if we could actually perform the exercise).

 

[ghwellsjr]

I'm reposting post #51 because the diagrams got dropped in that post. There is no other change:

So acceleration always results in an increase in proper length? Interesting, I didn't know about this.

No, it doesn't necessarily result in an increase in proper length. That happened because we accelerated all the parts of the table simultaneously in its initial rest frame. If we accelerate all the parts of the table simultaneously in its final rest frame we go from this:

where the proper length is 10 feet to this:

​

where the proper length has been compressed to 8 feet.

Why those changes aren't noticeable on our scale?

Because no one has enough resources to perform these experiments. You need lots of space, lots of materials, lots of energy, lots of money, lots of instrumentation and lots of government approval.

Also, keep in mind that if you actually accelerated all parts of an object simultaneously in any frame, you would probably destroy the object. It would be similar to if you took a table and tried to stretch its length to 12.5 feet or compress it to 8 feet.

And what about decceleration?

There really is no difference between acceleration and deceleration, just what you are calling the start and ending velocity and the direction of the change in velocity.

Thanks for the example ghwellsjr, to me this gets more and more interesting.

You're welcome.