Are the theories of relativity real?

[Qfwfq]

Craig, tell me what brand of vodka you've been drinking and I'll make it my own!

:hihi:

I was already thinking this thread has turned definitely into philosophy of science but, instead of asking, I decided it should be moved. :evil:

 

It seems to me that the difference between "what happens in" and "how it's described according to" is directly relevant to the thread. The question was "Are the theories of relativity real"? That is a metaphysical question. So the question is whether the transformations represent real, actual, difference in the passage of time and spatial distances, or just abstract mathematical relationships?

Take a staff with one green and one red end and toss it in the middle of a room so that it lands on the floor somewhere somehow. Now, leaving it perfectly still on the floor, choose different horizontal x and y axes (perpendicularly and without reflection, for simplicity) and measure the coordinates according to each of these. Now take [imath]\Delta x=x_{\rm g}-x_{\rm r}[/imath] and[imath]\Delta y=y_{\rm g}-y_{\rm r}[/imath] for each choice of coordinates. It is well known that the relation between the [imath]\Delta[/imath]s depends on angle of rotation according to linear combinations with [imath]\sin\phi[/imath] and [imath]\cos\phi[/imath]. Do these represent "real, actual, difference in the [imath]\Delta[/imath]s", or "just abstract mathematical relationships"?

 

In the Lorentz transforms, the relation between [imath]\Delta t[/imath] and [imath]\Delta x[/imath] (or y or z...) is formally similar but, due to Minkowski's metric, has [imath]\sinh\phi[/imath] and [imath]\cosh\phi[/imath] (hyperbolic) instead of the ordinary ones.

 

These are both subgroups of the Lorentz group and epistemologically well supported; you are free to meditate upon the ontology of each, with or without the vodka. ;)

 

The high energy muon has an enormous and real kinetic energy.

Now a reference frame according to which that muon is at rest is just as good as any other, including one in which the galaxies we see have the least overall kinetic energy. Imagine the kinetic energy of even just our puny little galaxy, let alone all the observed ones, according to that muon's rest frame.

 

Coordinates are quantities which play a part in the kinematic description of things, kinetic energy is a quantity playing a crucial part in the dynamic description of things. How real is kinetic energy? I'll let you ponder it over but, Craig especially, go easy on the vodka! :D

[jedaisoul]

With respect to GR, I stated "It's a model that is built on the assumption that time travel is possible (though not necessarily feasible). It does not comply with causality." I would question the reply:

Formally, this is not true. Relativity is not derived from such an assumption. The possibility of causation violations – ie: closed timelike curves (CTCs) – is a derived consequence of the theory, not an assumption.

It is true that CTC's are a possible consequence of the theory, but I do not see that as being directly relevant. I said two things:

 

a) That GR is a model that is built on the assumption that time travel is possible.

 

I said this because in his 1916 paper, when introducing the principle of general co-variance, Einstein said "So there is nothing for it but to regard all imaginable systems of co-ordinates, on principle, as equally suitable or the desription of nature". So the principle of general co-variance inherently and unavoidably includes systems of co-ordinates that are moving in the timelike dimension of the four dimensional space-time continuum. It is explicit in the definition of it. So the assumption that time travel is possible is an axiom on which GR is based, not a consequence.

 

:hihi: That this does not comply with causality.

 

I said this because the presence of an object that is moved back in time is, itself, a violation of causality. What put it there is an event in the future!

 

I hope this clarifies my thoughts.

 

Regards, Terry.

[jedaisoul]

Take a staff with one green and one red end and toss it in the middle of a room so that it lands on the floor somewhere somehow. Now, leaving it perfectly still on the floor, choose different horizontal x and y axes (perpendicularly and without reflection, for simplicity) and measure the coordinates according to each of these. Now take [imath]Delta x=x_{rm g}-x_{rm r}[/imath] and [imath]Delta y=y_{rm g}-y_{rm r}[/imath] for each choice of coordinates. It is well known that the relation between the [imath]Delta[/imath]s depends on angle of rotation according to linear combinations with [imath]sinphi[/imath] and [imath]cosphi[/imath]. Do these represent "real, actual, difference in the [imath]Delta[/imath]s", or "just abstract mathematical relationships"?

Hi Qfwfq, I'm afraid I fail to follow your meaning. I would have though that the differences in the Deltas were abstract mathematical relationships, but I'm not sure whether you would agree with that or not?

 

In the Lorentz transforms, the relation between [imath]Delta t[/imath] and [imath]Delta x[/imath] (or y or z...) is formally similar but, due to Minkowski's metric, has [imath]sinhphi[/imath] and [imath]coshphi[/imath] (hyperbolic) instead of the ordinary ones.

 

These are both subgroups of the Lorentz group and epistemologically well supported.

I'm guessing, but the juxtaposition of these statements suggests that the Lorentz transforms are also abstract mathematical relationships? If so, how do they give rise to actual time dilations and distance contractions?

 

Or are you suggesting that the Lorentz transforms do not give rise to actual time dilation and distance contraction? I'm confused!!!

 

Regards, Terry.

[Qfwfq]

Einstein said "So there is nothing for it but to regard all imaginable systems of co-ordinates, on principle, as equally suitable or the desription of nature". So the principle of general co-variance inherently and unavoidably includes systems of co-ordinates that are moving in the timelike dimension of the four dimensional space-time continuum.

:hihi: This is a non sequitur, actually it's really not well defined because in relativity time is itself a coordinate, but in any case general covariance doesn't imply that a particle may have a spacelike world line. If it is massless its worldline is null, otherwise it's timelike at each point. This is of course an assumption based on how we observe causality, not something that relativity demonstrates. As for weird topologies, I already said I'm doubtful of real space-time having any of them.

 

I said this because the presence of an object that is moved back in time is, itself, a violation of causality. What put it there is an event in the future!

Obviously.

[Qfwfq]

I'm guessing, but the juxtaposition of these statements suggests that the Lorentz transforms are also abstract mathematical relationships? If so, how do they give rise to actual time dilations and distance contractions?

 

Or are you suggesting that the Lorentz transforms do not give rise to actual time dilation and distance contraction?

I'm saying that time and the three spatial coordinates are "almost as much" one of a kind as the three spatial ones are, amongst each other.

[jedaisoul]

I'm saying that time and the three spatial coordinates are "almost as much" one of a kind as the three spatial ones are, amongst each other.

 

I understand what you have said, but I cannot tell whether you interpret all four as being real, or abstractions?

 

Ho hum, I think the message for Inter is that the question "Are the theories of relativity real?" has opened a can of worms. There are some people, like me, who would say a very firm "no". Its a mathematical tool, nothing more. There are others equally convinced that the answer is "yes", it tells us what is real. And, I suspect, there are many people who aren't that bothered with the metaphysics.

 

All I can say is, I've spent thirty years trying to answer that question. Some of the conclusions I've come to I've expressed here, others would really be more appropriate in a separate thread. Perhaps.

 

Regards, Terry.

[Qfwfq]

I cannot tell whether you interpret all four as being real, or abstractions?

First of all, semantic issues, is there an aut-aut between "real" and "abstraction"? I could say in some sense that they are real and in some sens that the are abstractions. They are an excellent description of reality (whatever the hack that is) at scales we have so far observed. Reaching the so-called Planck scale of length (including time) the description is not expected to be the same because gravitation is expected to exhibit quantum nature.

 

If you read about string and membrane theories, there is a whole zoology of them: distinct theories that all give predictions compatible with what we are currently able to observe. These are constructed in terms of manifolds having more dimensions than the known ones of space-time and typically they conjecture some fundamental things such as causality being different at such small scales but becoming statistically as we know them on the large scale. So far, these theories are not distinguishable from each other by currently observable predictions.

 

Relativistic quantum field theory is the best description we have at the smallest scales currently observable; it is stark raving zany, worse than the more well known quantum mechanics, it's absolutely crazy but it works. The famous Standard Model (of particle physics) is built in terms of it and, to boot, on a wacky notion called spontaneous symmetry breaking. This matches with all that's known about the whole zoo of subatomic particles, including the quark flavours observed after prediction, and the only beast remaining to be seen is the Higgs boson.

 

Considering the way quantum field theory works, I wouldn't be surprised if, one day, we found some proof that in principle all these possible sub-Planck descriptions are equally valid, with none more nor less true than the other.