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Gravity is not a force – free-fall parabolas are straight lines in spacetime

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Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#431

Post by pdonis »

rocho wrote: post #356
pdonis wrote: post #222

Earlier quoted context omitted.

> Why would acceleration not be constant? Look up the Bell Spaceship Paradox. In relativity, two spatially separated objects (or two ends of a spatially extended single object) that have the same proper acceleration in the same direction do not stay at rest relative to each other; they move apart, as seen in each of their own frames. This is different from the behavior predicted by Newtonian mechanics. In order to ha…

This is crazy, I'm finding it very hard to get an intuitive understanding of this. I guess that's why it's called "paradox".

> I'm finding it very hard to get an intuitive understanding of this.

Yes, it is certainly not intuitive. That's why Bell took the time to write a paper about it years ago.

This article might help:

https://www.physicsforums.com/insights/what-is-the-bell-spac...

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#432

Post by phizy »

CamperBob2 wrote: post #204
pdonis wrote: post #189

Earlier quoted context omitted.

> The difference is that light travels through space, but not time This is a common pop science statement, but it's not correct. A correct statement is that the concept of "speed through spacetime", which is what has to be split into "speed through space" and "speed through time" in the pop science statement, does not apply to a light ray. In more technical language, the tangent vector to the light ray's worldline is…

I wouldn't say it's incorrect at all. From the point of view of a photon, no time elapses between its the origin and destination endpoints.

There is no "point of view of a photon." Photons do not have frames of reference.

So you are completely incorrect insofar as what you are saying is physically nonsense.

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#433

Post by MockObject »

tsimionescu wrote: post #398
ben_w wrote: post #378

Earlier quoted context omitted.

Fair point — I was just rehashing a very simple thought experiment that showed why the acceleration should be the same for heavy and light objects alike, but you are totally correct, it isn’t really ok for me to count all bradyons as equivalent.

The thing is that this thought experiment is interesting, but it is wrong. It is true that it is not logically possible for a system of two objects to fall faster than both of its constituent parts, but that does not mean that it is a priori logically impossible for heavier objects to fall faster than lighter objects - the lighter object would slow down the heavier object somewhat, so the new "combined" object would…

> that does not mean that it is a priori logically impossible for heavier objects to fall faster than lighter objects

Right, but if this were the case, a dumbbell would fall about twice as fast when its axis is perpendicular to the ground, than when it's parallel to the ground. Realizing this is not true from lived experience completes the thought experiment.

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#434

Post by comboy »

Dylan16807 wrote: post #410
comboy wrote: post #366

Earlier quoted context omitted.

Relativity.

When you're asking if two objects have the same velocity, relativity does not change the answer.

I think it does if they do not occupy the exact same space. It's only objective that they have the same velocity from their point of view (but then parallel lines concept hardly makes any sense).

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#435

Post by lopmotr »

pdonis wrote: post #408
lopmotr wrote: post #296

Earlier quoted context omitted.

It still doesn't sound physically distinct any more than distinguishing any continuous quantity as being zero or nonzero. If we measure something that looks like 0, we can't be sure if it's just below the sensitivity of our instruments. For neutrinos, even if we accelerated an rocket and somehow checked if a neutrino was at rest relative to it, we might find that it's not. That means we won't know if we need more spe…

> It still doesn't sound physically distinct If you try what I described with a light ray, it will be moving away from you at c no matter how much you accelerate in its direction. If you try it with a massive object, even a neutrino with a very, very tiny invariant mass, that will not be the case; its speed relative to you will decrease as you accelerate after it, eventually to zero. There is no continuum between tho…

> Yes, you will know, because you will know if the neutrino's speed relative to you has decreased or not. If it has, it's possible to bring it to rest relative to you. If it hasn't, it's not. See above.

I don't think this quite works because of relativistic addition of velocities. Naively, it seems to. For example, if the object was travelling at 0.999999c relative to you (appears to be 1.0c according to your limited instruments), then you accelerate to 0.50c in its direction, you'd see its speed reduce to 0.50c (same 2s.f. instrument), which would clearly prove it's not massless. But velocities don't add like that relativistically and I think you'd still see it as travelling at 1.0c because it only decreased a tiny amount, below what you instrument can detect. If you use a more precise instrument or a faster rocket, you might measure it as 1.00000c but then you still won't know if it's exactly c or a smidgen less.

Maybe I've got my relativistic velocity addition wrong? But it still looks like the same measurement problem as trying to prove a classical object has a speed of exactly 0, which can't be done no matter how accurate our instruments are.

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#436

Post by lopmotr »

ymolodtsov wrote: post #316
lopmotr wrote: post #296

Earlier quoted context omitted.

It still doesn't sound physically distinct any more than distinguishing any continuous quantity as being zero or nonzero. If we measure something that looks like 0, we can't be sure if it's just below the sensitivity of our instruments. For neutrinos, even if we accelerated an rocket and somehow checked if a neutrino was at rest relative to it, we might find that it's not. That means we won't know if we need more spe…

With neutrinos we might find that it's not but it'd be impossible to catch a photon as it would always have the same speed of c in our reference frame. > I'd like to add that even photons have a nonzero upper bound to their possible rest mass. At least they used to. Not sure what you're talking about, their momentum? No object with mass can reach the speed of light and we know they're travelling at that exact speed.

How do we know they're travelling at exactly c? That's my concern. Last I heard, a couple of decades ago, physicists would occasionally measure a new maximum possible rest-mass for photons. It would be very tiny, of course, but they couldn't say it's exactly zero.

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#437

Post by tsimionescu »

MockObject wrote: post #433
tsimionescu wrote: post #398

Earlier quoted context omitted.

The thing is that this thought experiment is interesting, but it is wrong. It is true that it is not logically possible for a system of two objects to fall faster than both of its constituent parts, but that does not mean that it is a priori logically impossible for heavier objects to fall faster than lighter objects - the lighter object would slow down the heavier object somewhat, so the new "combined" object would…

> that does not mean that it is a priori logically impossible for heavier objects to fall faster than lighter objects Right, but if this were the case, a dumbbell would fall about twice as fast when its axis is perpendicular to the ground, than when it's parallel to the ground. Realizing this is not true from lived experience completes the thought experiment.

The difference between the total force acting on the horizontal dumbbell and the total force acting on the vertical dumbbell is 2/(height-dumbbell_length)^2. Given that height should be measured from the center of the Earth, this is ~0 for any length of dumbbell you can conceivably imagine. So even if lighter objects fell more quickly than heavier objects, you wouldn't expect to see oriented dumbbells fall at different rates.

However, what you could expect to see is that dumbbells with different weights for the two parts would never fall horizontally, they would tend to reorient vertically, with the heavier end first. Not sure how likely it would be to have noticed that this is not the case from lived experience.

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#439

Post by [deleted] »

pdonis wrote: post #430
CamperBob2 wrote: post #414

Earlier quoted context omitted.

Dude, this is basic theory at the high school level. Here's how it works: spacetime is 4-dimensional, and a vector in spacetime is always c units long. You can restrict your travel solely to X, Y, Z, or time if you like. If you do that, the other three components are going to be zero. Photons put it all into the X, Y, and Z components, leaving nothing for the t component. They experience a change of position in space…

> Dude, this is basic theory at the high school level. No, Tyson's claim is not "basic theory at the high school level". It is a particular interpretation of a theory (Special Relativity) that does not work, for the reasons I gave. > Photons put it all into the X, Y, and Z components, leaving nothing for the t component. Wrong. The spacetime vector that describes a photon's trajectory does have a t component. > Seems…

[deleted]

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#440

Post by ithkuil »

comboy wrote: post #434
Dylan16807 wrote: post #410

Earlier quoted context omitted.

When you're asking if two objects have the same velocity, relativity does not change the answer.

I think it does if they do not occupy the exact same space. It's only objective that they have the same velocity from their point of view (but then parallel lines concept hardly makes any sense).

are you talking special relativity or general?
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