Q: "Time Dilation: Faster = Longer Wait?

[PeterDonis]

Do you believe in a 3D world made of observer independent events?

I find it interesting that you keep insisting that the "block universe" does *not* involve a 3-D space evolving in time, and yet you also keep insisting on a "3D world" as a fundamental concept.

To me, the whole point of relativity of simultaneity is that a "3D world" is *not* a fundamental concept, because it's not frame-invariant. The key lesson of relativity is that all the physics in a theory is contained in the invariants: the things that *don't* change when you change reference frames. Light cones are invariant, so they are part of the physics of the theory. "3D worlds" are *not* invariant, so they are *not* part of the physics of the theory; they're just convenient abstractions to make calculations easier.

 

[bobc2]

..."3D worlds" are *not* invariant, so they are *not* part of the physics of the theory...

It's the observed continuous sequence of 3-D cross-sections of the 4-D universe that present reality to us. It's the objects we observer. It's processes involving objects that we observe--tracks in elementary particle experiments, rays of light, etc. That's not part of the physics?

These continuous sequence of 3-D worlds are not just any sequence--they are very special--the laws of physics are the same for any of the 3-D worlds identified through the use of some member of the group of Lorentz transformations. And these worlds are so special that a measurement of the speed of light is the same for each of them.

I guess your view would be that physics is not concerned with an external reality--perhaps just the rules of engagement for the objects.

 

[Dale]

Of course. You call everything that does not apprear on your calculator a philosophical consideration.

No, I call everything that cannot be tested experimentally philosophy. Experimental evidence is the key difference between philosophy and science. There is no experiment which can distinguish between the LT in a 3D universe evolving in time and the LT in a 4D universe.

I am not prepared to discuss physics on that bases.

That much is certainly clear. When you have prepared yourself sufficiently, then please return and we can carry on the discussion.

 

[PeterDonis]

It's the observed continuous sequence of 3-D cross-sections of the 4-D universe that present reality to us.

No, it isn't. It's the succession of past light cones along our worldline that presents reality to us. The 3-D cross sections are logical constructions from the data we get from our past light cones; we don't perceive them directly. Perceiving them directly would require signals to travel faster than light.

It's the objects we observer. It's processes involving objects that we observe--tracks in elementary particle experiments, rays of light, etc. That's not part of the physics?

The worldlines of objects are invariants, so yes, they are part of the physics. But 3-D cross-sections are not made up of worldlines of objects.

These continuous sequence of 3-D worlds are not just any sequence--they are very special--the laws of physics are the same for any of the 3-D worlds identified through the use of some member of the group of Lorentz transformations.

I have two answers to this. The first is, supposing I agree with this as you state it, so what? There are an infinite number of such sequences of 3-D worlds that all are "special" in this sense. There's nothing that picks out any particular sequence of 3-D worlds as special compared to any other such sequence.

The second answer is that you've stated it wrong. The laws of physics are not written in terms of 3-D worlds. They are written in terms of local invariants at each spacetime point. You can express all of the physics and all of the laws without ever mentioning 3-D worlds at all. So everything you say about sequences of 3-D worlds, even if it's correct mathematically, is not necessary for the actual physics; it's just a convenience for calculation.

I guess your view would be that physics is not concerned with an external reality--perhaps just the rules of engagement for the objects.

My view is that our physics does not tell us everything about external reality, so taking any particular theory of physics and trying to parlay it into a blanket statement about external reality is going way beyond what's justified by our knowledge of the physics.

 

[PeterDonis]

It's the observed continuous sequence of 3-D cross-sections of the 4-D universe that present reality to us.

In addition to what I said in my previous post, I also have the same comment here as I had for Vandam: I find it interesting that you, who are defending the "block universe" viewpoint, insist on talking about 3-D worlds and 3-D cross sections, instead of 4-D spacetime and invariant objects within it, like worldlines; while I, who am saying the "block universe" is not the only possible viewpoint, am talking in terms of invariants in 4-D spacetime.

 

[bobc2]

In addition to what I said in my previous post, I also have the same comment here as I had for Vandam: I find it interesting that you, who are defending the "block universe" viewpoint, insist on talking about 3-D worlds and 3-D cross sections, instead of 4-D spacetime and invariant objects within it, like worldlines; while I, who am saying the "block universe" is not the only possible viewpoint, am talking in terms of invariants in 4-D spacetime.

I figured that I had already beat the 4-D objects to death. Of course you are probably willing to acknowledge the mathematical worldlines without the physical 4-D objects that they represent.

It's probably a good time for ZapperZ to shut this one down.

 

[Vandam]

It's probably a good time for ZapperZ to shut this one down.

I agree.

 

[Dale]

bobc2 and Vandam,

If you have a line y=mx+b you can write it as y(x)=mx+b and interpret it as a 0D point in a 1D space, y, which evolves as a function of x. Alternatively, you can write it as (x,mx+b) and interpret it as a parameterized 1D line in a non-evolving 2D space. But no matter how many points on the line you collect they will never identify which is the "right" expression or interpretation.

You both have every right to prefer the block universe interpretation, for any reason or no reason at all.

You are both wrong to assert that there is any empirical evidence favoring that interpretation over any mathematically equivalent interpretation. If you would stop pretending that your position is based on evidence rather than personal preference then you would find much more support for it.