Imprecision and Special Relativity

[hoponpop]

Einstein's "On the Electrodynamics of Moving Bodies" (https://www.fourmilab.ch/etexts/einstein/specrel/www/) draws its conclusion based, at least in part, on Einstein's interpretation of simultaneity (generally, the point from which seemingly simultaneous events are observed dictates their perception, e.g., as simultaneous or "not simultaneous").

Einstein never explicitly defined simultaneity in this paper, but rather merely analogized to the arrival of a train when the hands of a clock were at a certain point.

The problem that I see with this is the degree of imprecision implicit in this definition (e.g., when does "arrival" occur, how is the position of hands on a clock measured/does a smaller gear tooth size effect simultaneity, etc.).

Applying these theories at much higher speeds than observed in daily life would greatly amplify the effect of aforementioned imprecision on any calculation involving the same.

The only impact that I can see this having is on significant digits. However, I am hopeful that someone much smarter than me can tell me why I'm wrong about all of this.

Edited October 14, 2015 by hoponpop

[swansont]

You're describing issues of measurement, not problems with the theory.

 

We don't use clocks with gears and teeth, for example, because no mechanical clock has the precision to measure relativistic effects that we are able to observe. We can do all of this electronically and at a sufficient precision to measure even small effects (better than a picosecond, for example)

[studiot]

 

The only impact that I can see this having is on significant digits. However, I am hopeful that someone much smarter than me can tell me why I'm wrong about all of this.

 

Don't forget in the realm of thought experiments we are able to escape the chains of an imperfect universe.

So all our equipment can be perfect.

Further we do not need to specify how a given state could have been arrived at, so long as it satisfies the physical laws invoked.

[Strange]

Einstein's "On the Electrodynamics of Moving Bodies" (https://www.fourmilab.ch/etexts/einstein/specrel/www/) draws its conclusion based, at least in part, on Einstein's interpretation of simultaneity

 

The conclusion is not based on relativity of simultaneity, rather relativity of simultaneity is a result of the theory.

 

 

generally, the point from which seemingly simultaneous events are observed dictates their perception, e.g., as simultaneous or "not simultaneous"

 

That is not how simultaneity is defined. It does not depend on relative position but relative velocity.

 

Einstein never explicitly defined simultaneity in this paper, but rather merely analogized to the arrival of a train when the hands of a clock were at a certain point.

 

I thought he defined it rather clearly.

 

The only impact that I can see this having is on significant digits.

 

Because it is a mathematical theory, you can calculate to as many significant digits as you wish.

[hoponpop]

I like this.

 

I agree that there is no problem with the theory (at least not that I've pointed out).

 

I am also not arguing that the theory of special relativity doesn't work in practice.

 

I agree that my very general description of the definition is simultaneity is inaccurate; you are correct that relative velocity is as generally as it can be stated.

 

swansont got me thinking though:

 

The issue of measurement and the theory of relativity are integrally tied. §2 of "The Electrodynamics of Moving Bodies" is actually titled "On Relativity of Length and Time." However, the fact that length and time are relative is not applied (or, seemingly, considered) in defining arrival or position of the hands on the clock.

 

Each of these definitions is important.

 

If arrival is defined as the point at which the train ceases motion, then we need to introduce another reference point.

 

Time, even if defined to the picosecond, is not 100% accurate. However, no matter how precisely time is defined, it is still relative, an we need yet another reference point.

 

Add another reference point and we've related three otherwise (potentially) independent events.

 

This can go on forever.

 

In my mind, any complete theory can and will be criticized as a tautology (see, e.g., Haig-Simon Equation), so I like where this is headed.

 

Maybe set up a bunch of matrices A, B, C, ... and relate them to each other, and look at the elements of the matrices for patterns....

 

More to come.

 

Please blow up anything you can find that I'm wrong about. That's how we refine.

Edited October 14, 2015 by hoponpop

[swansont]

 

Time, even if defined to the picosecond, is not 100% accurate. However, no matter how precisely time is defined, it is still relative, an we need yet another reference point.

 

In practice, yes, but as has been pointed out, in theory you can assume a perfect clock. Still a measurement issue and not a theory issue.

[hoponpop]

 

In practice, yes, but as has been pointed out, in theory you can assume a perfect clock. Still a measurement issue and not a theory issue.

Even if you assume a perfect clock, Einstein extends relativity to time. He doesn't go as far as to classify time as a unit of measure, but he acknowledges that time is relative.

 

Take that a step further: even if something is absolute, any description of it is relative. Now we're getting into philosophy, but language is essentially an abstract representation of systems of matter. Numbers are a subset of language. The only thing special about numbers is that they represent a "universally" understood system of relationships. A measurement is just a description that makes use of that relationship, and is thus understood as "definite," or "absolute." However, you still have to define what that measurement is relative to. "8 inches tall" imparts a very definitive structure to an object. The more narrowly you want to describe something, the more you compare it to other things. That is the nature of language.

 

Time is different. There is no implied "starting point" (e.g., ground for "8 inches tall"). So, while you can very well ignore that and have a legitimate theory, the theory is much broader if it encompasses the relativity of time.

[swansont]

Even if you assume a perfect clock, Einstein extends relativity to time. He doesn't go as far as to classify time as a unit of measure, but he acknowledges that time is relative.

Yes, he does. Has anyone here suggested otherwise?

 

Take that a step further: even if something is absolute, any description of it is relative. Now we're getting into philosophy, but language is essentially an abstract representation of systems of matter. Numbers are a subset of language. The only thing special about numbers is that they represent a "universally" understood system of relationships. A measurement is just a description that makes use of that relationship, and is thus understood as "definite," or "absolute." However, you still have to define what that measurement is relative to. "8 inches tall" imparts a very definitive structure to an object. The more narrowly you want to describe something, the more you compare it to other things. That is the nature of language.

 

Time is different. There is no implied "starting point" (e.g., ground for "8 inches tall"). So, while you can very well ignore that and have a legitimate theory, the theory is much broader if it encompasses the relativity of time.

The choice of starting point is arbitrary. But that doesn't matter, since we define both length and time in terms of intervals (1 meter, 1 second)and its the intervals we're comparing. The choice of starting point doesn't appear in that result. e.g. something 8 inches tall would be that height even if placed on a table. The result does not indicate if it was on the floor or table.

[hoponpop]

Not saying anyone has suggested otherwise (re. time being relative), just laying out how I got where I did.

 

I guess I'm making a big deal about nothing here.

 

I still have a problem with (at least my understanding of) Einstein's conception of time, though, so I will continue to think about that.

 

Good debating with you, swanston. You certainly know your shit. Lol

Edited October 15, 2015 by hoponpop

[Phi for All]

Good debating with you, swanston. You certainly know your shit. Lol

 

Pretty handy to have a physicist working with atomic clocks for the US Naval Observatory when it comes to questions about time, isn't it?

[hoponpop]

Lol awesome. Where else can you get that?

 

My background is in biomedical engineering, but I'm currently in law school with no one to talk to about fun things like this.

[swansont]

Lol awesome. Where else can you get that?

A lot of people know about relativity, but there's only a few places where you get to play with clocks and/or frequency standards. Basically your national standards lab for countries that have a big enough budget; in the US that's NIST, and the USNO does time because of its tie with navigation. Penn State (Gibble) has some related research, too, and Harvard-Smithsonian Center for Astrophysics has done some related work, but otherwise timing isn't really something you learn in a university setting.

 

Some people take similar devices and measure things other than time, e.g. gravity measurements at Stanford (Kasevich), among others.