Relativistic Physics (& possibly its relevance to VS)

[Shissui]

This thread continues from thread 4904, as the discussion appears no longer to even contemplate the usefulness of the physics involved to any real implementation in VS.
[It would be nice if a moderator added the connecting link(s) actually.]

You, the observing rider, are not massless. Thus, you are always at rest relative to yourself. It takes the *photon* zero time, but it takes the rider proper time.

I don't see how you can think that the photon experiences no time, but an observer at rest wrt. to it does experience time.

This goes back to your observation that photons cannot exist. With that insight, I thought you actually HAD this point.

Allow me to backtrack a bit for the non-physicists. In Special Relativity, you describe most objects with 4-vectors. This changes to a rank2 (4x4) tensor when you switch to General Relativity. But, sticking with the limited case (SR) for the moment, we can describe a vector of motion as V=(x,y,z,t). In Special Relativity, we always need to know the time because observers at different speeds will (appear to) see the same object in a different absolute location. However, this discrepancy can be reconciled if we know the time; & thus the adjustment to apply to position when we change to another observer's viewpoint.

But, the math gets annoying as we get close to 'c' because of all the square roots and such. So it is actually more useful to change our coordinate system to something that is easier to work with. Assuming that we know the mass of this object, we can make an equivalent description of our object's motion by describing its momentum instead of velocity P=(px,py,pz,e{nergy}). It is a bit less intuitive, as we now have additional calculations to determine our position, however it is now a great deal easier to calculate changes in motion for two reasons.
1) If we add or subtract to momentum, then it is straight addition & subtraction -- none of these annoying square roots.
2) P is conserved! As long as we stick to SR, there is no acceleration. In this world, sqrt(Px*Px + Py*Py + Pz*Pz - E*E) = CONSTANT.

SO, back to the photon.
The photon has zero mass. It has momentum and energy (both measurable), but if we run it through our conservation equation, we will get the square root of a negative number because of the zero mass. If we returned to the velocity equations, we get the same contradiction when we try to divide by (c**2 - photon speed**2). When we calculate time dilation, it also requires us to divide by zero. But, it is commonly accepted as infinite because the limit as we approach 'c' also approaches infinity. So, if we accept this result, then we get the logical conclusion that no time passes during travel in the photon's frame of reference.

You, on the other had, *do* have mass. The velocity equations will still fail, as we will be dividing by zero again. However, the momentum equations are more interesting. You have infinite momentum AND infinite energy. We have another singularity. However, this time if we take the limit as we approach infinity, we will get whatever momentum you had in your rest frame because momentum is conserved (by definition, this is zero, as you are always at rest with yourself). SO, with a zero momentum, we can now determine that you will travel on the photon in proper time.

Is that counter-intuitive enough for you ??

[Edit: the apparent contradiction occurs because you just appeared on the photon. Had you *accelerated* to match the photon's speed (General Relativity), you would have acquired infinite momentum too. This is part of the problem with a thought experiment like this one.]

[peter]

Is that counter-intuitive enough for you ??

Yes, plenty. :/

[Edit: the apparent contradiction occurs because you just appeared on the photon. Had you *accelerated* to match the photon's speed (General Relativity), you would have acquired infinite momentum too. This is part of the problem with a thought experiment like this one.]

Ok, that helps.

Are you talking about distorting space (with a warp/Alcubierre drive) to keep up with the photon? If so, sorry; it all makes sense. I thought we had changed to talking about _just_ special relativity.

Otherwise, either you or the destination has to experience time dilation and lorenz distance contractions (right?). In whatever reference frame you choose, at least one of the traveller and the destination have to have non-zero momentum unless space is warping.) If the destination (or the whole universe) is moving relative to you, you could experience it taking proper time, but the destination would experience zero travel time.

Sorry if I'm missing your point again, here. I think I follow your momentum coordinates argument, but it seems like your dodging around the fact(?) that something has to have momentum if there's relative motion. (in flat space?)

[Shissui]

Are you talking about distorting space (with a warp/Alcubierre drive) to keep up with the photon? If so, sorry; it all makes sense. I thought we had changed to talking about _just_ special relativity.

No. I have tried my best to restrict the explanation to Special Relativity. Relativity is hard enough to make clear in its simplest form.

Otherwise, either you or the destination has to experience time dilation and lorenz distance contractions (right?).

No. You do not need to calculate dilation or contraction when you only have one frame of reference (you & the photon have the same reference frame -- that frame in which the photon is stationary). Any one frame of reference is ALWAYS at rest with itself.

You only need to calculate dilation & contraction when you want to translate the view from one reference frame into what is (or could be) observed in another.

SO, let us look at the destination frame for a moment. In this reference frame the destination is stationary & all actions occur in proper time. Through some violation of physics, the local astronomers become aware of your incoming photon but there is nothing they can do about it until it arrives as there is no possible (physics compliant) signal fast enough to convey information from your photon to the astronomers any faster than the photon itself. SO, dilation and contraction are somewhat moot.

In whatever reference frame you choose, at least one of the traveller and the destination have to have non-zero momentum unless space is warping.) If the destination (or the whole universe) is moving relative to you, you could experience it taking proper time, but the destination would experience zero travel time.

In the destination frame, you approach traveling at 'c'. You need to slow down before they can bounce a photon off of you to check if there is any dilation. (If we ran it through the equations anyway, we would just get more singularities.)

Sorry if I'm missing your point again, here. I think I follow your momentum coordinates argument, but it seems like your dodging around the fact(?) that something has to have momentum if there's relative motion. (in flat space?)

No, you are doing just fine with the implications. The conserved quantity is (P*P -E*E). In your rest frame (on the photon), P=0 & E=0, so this is zero (you are not moving relative to yourself).

In the rest frame of the destination, your vector is 'c' (toward them). Your momentum, after lorentz transform, is another singularity when we divide by sqrt(c**2-speed**2). The limit as speed approaches 'c' --> P approaches infinity. Similarly, the energy that would have been required to accelerate you to that speed, had we actually done that, would have been infinite. (P*P -E*E) = 0 (still), but both P & E are now unimaginably large.

This may be my opportunity to point out that when you arrive with infinite momentum, you will completely obliterate the destination and all evidence of civilisation. There will be nobody left to charge you with negligent genocide. Unfortunately, that includes you. From YOUR viewpoint, the destination is approaching you with infinite momentum and will completely obliterate you. Nothing will be left to be charged. All you have really accomplished is a very messy darwin award.