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

[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.