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**Physics, Astronomy & Cosmology / What limits does relativity put on acceleration of long objects?**

« **on:**19/10/2018 12:54:07 »

This thread is meant to investigate relativistic limits on the acceleration of large objects. To drive the points home, my objects will be large and fast, but never with impossible properties like being massless, infinite rigidity, or with instantaneous acceleration, all of which can be shown to violate fixed speed of light.

Consider a long object, say a light year in length, which is fairly fragile in that it will allow only negligible physical compression or stretching before it breaks. Hence the force of propulsion is spread as needed over the entire length of the object. Our engines/rail-guns are as powerful as they need to be.

For slow accelerations, the clock at the front of the object will get ahead of the ones further back, so the acceleration further forward run is lower, but for a longer time. If the rear acceleration takes 10 years (measured in local accelerating frame) to get up to say .866c, the front acceleration will take place for 10.866 years to get to that speed iff it ignites and ceases at the same time (object frame) as the rear acceleration. The points in between can accelerate proportionally. In this way, the entire object might be under acceleration at once, but only in the object's own frame.

That seems viable for only slow accelerations, and even then, in any other frame, part of the object is accelerating and the part of it not, so right there it seems on first glance to be putting strain on our object, but I cannot prove that since the two parts are always separated in a space-like manner, and so cannot directly effect each other.

Scaling up the acceleration demonstrates the limits if not the deficiencies of my proposed methods. Clearly at some point there is strain the way I am doing it. Is there a strain-free way of accelerating a long object? More exactly, is there a way to do it that never changes the object's proper length?

There is proof of sorts that there is a correct solution, since if there is compression or tension somewhere in the object, we could compensate for that with a thrust function that applies more or less force at points further forward. There must be a solution that involves zero strain, but even then the length of the object puts an absolute limit on the magnitude of the acceleration.

Edit: There seems to be nothing impossible about near instantaneous acceleration. Many of my examples assume as a limit an acceleration to a desired speed in negligible time. If this is found to violate finite light speed or some other law, kindly post details since it will effect my answers for minimum time to get a big thing somewhere.

Update, Feb 2019: I think I found that very violation. See post 97. Infinite acceleration makes the speed undefined, and without a defined speed, the proper length is undefined. Acceleration can be arbitrarily high, but not infinite.

Consider a long object, say a light year in length, which is fairly fragile in that it will allow only negligible physical compression or stretching before it breaks. Hence the force of propulsion is spread as needed over the entire length of the object. Our engines/rail-guns are as powerful as they need to be.

For slow accelerations, the clock at the front of the object will get ahead of the ones further back, so the acceleration further forward run is lower, but for a longer time. If the rear acceleration takes 10 years (measured in local accelerating frame) to get up to say .866c, the front acceleration will take place for 10.866 years to get to that speed iff it ignites and ceases at the same time (object frame) as the rear acceleration. The points in between can accelerate proportionally. In this way, the entire object might be under acceleration at once, but only in the object's own frame.

That seems viable for only slow accelerations, and even then, in any other frame, part of the object is accelerating and the part of it not, so right there it seems on first glance to be putting strain on our object, but I cannot prove that since the two parts are always separated in a space-like manner, and so cannot directly effect each other.

Scaling up the acceleration demonstrates the limits if not the deficiencies of my proposed methods. Clearly at some point there is strain the way I am doing it. Is there a strain-free way of accelerating a long object? More exactly, is there a way to do it that never changes the object's proper length?

There is proof of sorts that there is a correct solution, since if there is compression or tension somewhere in the object, we could compensate for that with a thrust function that applies more or less force at points further forward. There must be a solution that involves zero strain, but even then the length of the object puts an absolute limit on the magnitude of the acceleration.

Edit: There seems to be nothing impossible about near instantaneous acceleration. Many of my examples assume as a limit an acceleration to a desired speed in negligible time. If this is found to violate finite light speed or some other law, kindly post details since it will effect my answers for minimum time to get a big thing somewhere.

Update, Feb 2019: I think I found that very violation. See post 97. Infinite acceleration makes the speed undefined, and without a defined speed, the proper length is undefined. Acceleration can be arbitrarily high, but not infinite.