Max/Min Time Dilation: What is the Scale?

[salvestrom]

I think you have me mixed up with someone else. What post # is this in?

In post 22 you said that einstein removed the infinities in section 4.

 

[salvestrom]

Actually, it was universally accepted from Galileo's time, except for a short, confusing period in the 1800s, before Einstein re-established Galileo's principle: you cannot distinguish a state of rest; all inertial frames are equivalent. However, this principle plus Maxwell's equations required some conceptual changes to space and time.

I was referring to the notion of two observers relative to each other both observing the other as being slower.

 

[PAllen]

I was referring to the notion of two observers relative to each other both observing the other as being slower.

Ah, but that's the only way to preserve the principle of relativity. If some inertial observer sees 'fast clocks run slow', and another inertial observer sees 'fast clocks run fast', we have different laws for different inertial observers. As soon as you admit time dilation at all, 'fast clocks slow' for both is the only way to make it work while preserving equivalence of inertial frames.

 

[salvestrom]

Traveling 22 light seconds of Anthony's distance, Cleo will experience 1 second. Traveling 22 light second of Cleo's distance, Anthony will experience 1 second.

Can you ellaborate please on "Anthoney's distance" and "Cleo's distance".

 

[PAllen]

Can you ellaborate please on "Anthoney's distance" and "Cleo's distance".

Mathematically, you define distance in SR as the invariant interval (geodesic length) between a pair of simultaneous events. In relativity, simultaneity differs between observers in relative motion. As a result, their notions of distance also differ.

More physically, you can define distance using some reasonable procedure, e.g. parallax, image size, radar ranging. However, the first two relate a nearby size or distance with a distant size or big distance. Thus they need a definition of distance to get started. You can use radar ranging (or light travel time) to get started, or as your main definition. Going with radar for simplicity (in SR it is provable that they are all the same, for inertial observers), consider what Anthony and Cleopatra do. If each measures distance to some third object (in some state of motion), the round trip light paths will be radically different because of the relative motion between Anthony and Cleopatra. Thus, they measure the universe completely differently.