Time paradox

PeterDonis

Could you elaborate? I don't understand what point you're trying to make. The only "postulate" I can think of that you could be referring to is the one that says the laws of physics must be invariant under Lorentz transformations; that means the laws have to be written in terms of invariant expressions. That would seem to support what I've been saying.

Mentz114

How would you express "The laws of physics are the same for all frames" without using frame independent concepts ? Nor do I believe "inertial hyperplanes of simultaneity are exactly those for which Einstein’s postulate holds". I think you may be confused.

PeterDonis

In other words, this observation is irrelevant to the rest of the discussion? Fair enough; then I won't bother commenting further on it.

I am familiar with Russell's writings on these concepts; the best exposition I know of is in Russell's book Our Knowledge of the External World. I have no problem with the general claims Russell makes in that book, and I would agree that the views Einstein expressed in general terms were similar. The basic idea is that, even if we start by only granting "existence" to our direct sense-impressions, we can't make sense of those sense-impressions without committing ourselves to the existence of an "external world".

However, the disagreement we're having is not about whether an external world exists; it's about *what*, specifically, we are entitled to claim "exists" based on a certain set of sense impressions--i.e., what, exactly, is the "external world" that we need to believe in in order to make sense of a given set of sense impressions. See further comments below.

Nobody here is making a "positivist denial" of external reality. But you have assumed, without proof, that the sense impressions we receive from our past light cone *force* us to believe in an "external reality" consisting of an instantaneous 3-D world. That's simply not a valid claim. To see why, contrast it with the following alternative claim:

Based on the sense impressions we receive, we can only make sense of them by believing in the existence of external objects that send us light signals containing information about them. But the information we receive this way is time-delayed; for example, the Sun that I see is the Sun as it was eight minutes ago, *not* the Sun as it is "now". So the "external world" that I am *forced* to believe in based on my sense impressions does not include the Sun "now"; it only includes the Sun up to eight minutes ago.

I can, of course, make the further claim that, since it is highly unlikely that anything significant will have happened to the Sun in the eight minutes it took for the light I am seeing now from the Sun to get to me, it is highly probable that there is in fact a Sun now--i.e., that the Sun's worldline extends beyond the portion I have direct evidence of in my past light cone. But that is a *different* kind of claim from the claim that I have to believe in an external world based on my sense impressions. The claim that the Sun exists now is an *extrapolation* from the direct data in a way that the claim that the Sun existed eight minutes ago is not.

Einstein's postulate says nothing about hyperplanes of simultaneity. Go look at the relativistic formulations of any law of physics--Maxwell's Equations, the Einstein Field Equations, quantum field theory--and tell me where in those laws the hyperplanes of simultaneity are.

DaleSpam

It isn't about connecting dots. You claimed that Einstein said something that he simply did not say. You may believe that he meant to say what you claimed, or that what you claimed is implied by things that he said, but the unavoidable FACT is that he simply didn't say what you claimed he said.

Why don't you take ownership of your own opinions rather than trying to foist them off to Einstein? Say what you think, defend your ideas on their own merits, and simply leave Einstein out of it. Even where he shares your opinion, that is just a fallacious appeal to authority.

The invariants are also the same for all frames, so I don't know what makes you think that we are ignoring the significance of the first postulate by focusing on them instead of frame-variant quantities.

bobc2

I'm really getting confused about what your fundamental objections are aside from the side bars on interpretations and philosophy.

Are you claiming that Event C is not in the travelling twin's simultaneous space at the start of his journey?

Are you claiming that Events A and B are not in the simultaneous space of the twin just after he has completed his turnaround?

Are you claiming that Events D and C are not in the simultaneous space of the twin when the twin has arrived on his worldline at Event D?

PAllen

I object to giving any physical meaning to simultaneous space. Simultaneity is a convention. For inertial observers (or in an inertial frame used to analyze some overall scenario), there is a standard convention any reasonable person would use; how far it makes sense to extend it (for an observer) depends on how long they have been inertial. For non-inertial observers there is no preferred convention except 'locally'. A non-inertial observer is analogous to the GR situation - only local frames (with standard simultaneity convention reasonably preferred sufficiently locally in time and space).

I believe this is how Einstein viewed it, but that is neither here nor there.

[There is also the sense of relatively arbitrarily chosen simultaneity surfaces used to construct coordinates useful for some problem. Obviously, I don't consider coordinates a feature of physical reality.]

PeterDonis

I'm not objecting to any of the statements you have made about what events are in which simultaneous spaces. If those statements are all you've been trying to say, they strike me as too obvious to be worth taking all this time over.

The sidebars are only there because you have made claims about the interpretation and philosophy of simultaneous spaces. If you would refrain from making such claims we wouldn't need any sidebars.

If you had said things like "I find that looking at hyperplanes of simultaneity helps me to make sense of what is going on" (which is pretty much what LastOneStanding said right before you entered the thread to support what he was saying), I doubt we would have had any sidebars. But you insist on saying things like "hyperplanes of simultaneity are fundamental to relativity", which implies (incorrectly) that they are necessary to *any* understanding of relativity, and then claiming that Einstein said so too, which is a strained (at best) interpretation of what he said.

bobc2

ghwellsjr, I have searched through most of my Einstein writings and must concede that I'm not able to find the reference that I am recalling. Of course there is the possibility that I am mistaken in my recollection, so I'll just have to retract my reference to Einstein discretizing the turnaround into incremental boosts (incremental inertial frames) as I've been describing. Of course the concept is not original with me. You were right to have challenged that. If I ever do come up with it I'll let you know.

By the way, you did a very excellent job of explaining the doppler approach. I've read a number of accounts of this, most recently Paul Davies's discussion, and yours is as good as any and better than most--particularly with your use of the diagrams.

bobc2

I guess I just don't catch on to your thinking about how to describe external objective reality with objects moving about in space and time without the use of coordinates. And particularly when we need to select the particular coordinate transformations of the Lorentz group if we are to be assured of physical processes unfolding in the various observer spaces in a manner consistent with the laws of physics.

bobc2

That's all I'm trying to say. Forum members can muse over any possible implications about the simultaneous spaces with regard to physical reality if they are so inclined. In any case I thought the way the order of the brown clock readings, as they are presented in the travelling twins's frames, was kind of interesting after Vandam had pointed it out in another thread (where is Vandam--he was so pasionate about this stuff?). Others may find nothing of interest there. I never intended to get side tracked into the philosophy of solipsism when I first posted--I tried to keep up with responses to new comments and questions but was inexorably drawn into the sid bars.

Nugatory

It can be done. Any physical situation can be described in terms of proper time along timelike worldlines and the points at which these worldlines intersect lightlike null worldlines.

However, coordinates are a really really convenient calculating tool in many problems... So we use them a lot.

DaleSpam

Think about different ways you can describe the location of your house. You can give its latitude and longitude. Alternatively you could give some landmarks e.g. 2.3 miles past the post office on Balderdash Rd.

The thing is that we already know experimentally that physical processes don't in fact transform according to the Poincare group globally, only locally. So we need to write the laws of physics in a manner that is consistent with completely arbitrary coordinate transforms because we know that the Lorentz transforms don't work globally.

Since we need to do that globally anyway, we can also do it locally. We then clearly see that the laws of physics don't care one bit what coordinate systems we use, and the actual laws of physics are expressed entirely in terms of invariant quantities.

PeterDonis

I agree that your first post in this thread (#32, unless I missed something) didn't do anything more than draw the simultaneity planes in different frames and comment on them. But your next post (#34) used the word "fundamental":

If you had qualified this with "for me", or "in at least one common method of teaching SR", it would have been different. But you made a blanket statement about what's "fundamental", which comes across as being about something more than just what works best when teaching or explaining.

Then, in post #38, you made the statement that I first responded to:

Again, if you had said "I find it much easier to understand and explain SR using relativity of simultaneity, etc., vs. doppler" that would have been different. But you brought in the "philosophical ideas" (that word had only been used once in this thread before your post, and nobody picked up on that one, by LastOneStanding).

zonde

Discussions about scientific method are philosophy. Improvements in scientific method like falsifiability are philosophy.

Yes

Can you elaborate on this? First, is invariant defined or is it undefined basic concept?
Because the way it is usually defined i.e. some quantity that does not change under coordinate transformation, is confusing as it is defining invariants using concept of coordinates and consequently coordinate dependant quantities that we are using to construct coordinates. So coordinate dependant quantities are more basic than invariants.

Invariants are not the same as physical laws. They are certainly two different things.

PAllen

I don't say you don't use coordinates. But they are analogous to the lines you draw on a globe to label positions. The globe and relief features on it exist independently of what lines I draw. Coordinates are not an aspect of reality. The Lorentz group is simply the group of transforms that preserve the flat space metric in simplest form. The physical principle of relativity is that absolute (inertial) motion cannot be detected. The difference from Galilean relativity is that light speed is included in what is the same for every inertial observer. There is nothing more special about Minkowski coordinates than there is about Cartesian coordinates on a plane (metric is in simplest form). Its geometry is there with no coordinate labels; if I draw polar coordinates, the geometry hasn't changed, only the process of computing things.

Your claim about some preferred meaning to your chosen 'simultaneity space' is equivalent to insisting that only cartesian coordinates are valid on a plane. Even more, that if we draw some arbitrary curve on a plane, and then want treat it as a coordinate axis, we must use lines perpendicular to its tangent at each point.

DaleSpam

I already covered this back in post 83 with my statement: "I cannot think of any philosophical proposition that has any scientific value except for those which are essentially restatements of Bayesian inference."

I was specifically thinking of falsifiability and Occham's razor, both of which can be derived from Bayesian inference, which is the mathematical framework for inductive reasoning. So falsifiability is not a counter-example and I stand by my previous assertion.

The term "invariant" itself is indeed defined as a quantity that does not change under coordinate transformations, so that term does presuppose the definition of coordinates etc. However, each invariant physical quantity can be defined without reference to coordinates.

For example, proper time can be defined physically as the time measured by a clock. It can also be defined geometrically as the integral of the spacetime interval along a timelike path. Neither of these definitions require coordinates. Similarly with the other invariant quantities used in physics.

You can define all of your physical theories in terms of these invariant quantities without reference to coordinates. Then, once you add coordinates, you can note that all of the quantities that show up in your physical theories are invariants, and you can refer to them collectively as "invariants" without at all implying that they are less basic than coordinates and coordinate-dependent quantities.

zonde

So how do I tell apart invariants from everything else?