Your speculative financial gain cannot be infinite, because as you offer more gold on the market, the price would decrease to nothing. Meanwhile, the cost of accelerating the gold to light speed approaches infinity. Therefore this venture can be dismissed purely on its expected return on investment.
There are probably physics reasons too.
sorry to disappoint you but if you are referring to me I am not.
Maybe you had this conversation as a teenager but I did not.
It came across my mind and I wanted to see what other opinions are out there.
vy VY
Back then, I bet that most popular science explanations of relatively used the increasing mass of an object as their basis. It’s an easy way to forcing people to think about what would otherwise be counterintuitive. It’s not the best way of really understanding what’s going on, though, and the posters above are giving the more modern view. That seems to be less graspable. It’s a problem of balancing rigor with general understanding, and both ways of putting it fail to land on the sweet spot.
But I thought any clocks that I had on board would still look to me like they are moving at the same rate?
I can calculate my velocity with the formula V = at correct? I know the acceleration and I know the time. I don’t need another reference point.
I admit I might be wrong, but I don’t see how, in the reference frame of the accelerating spaceship, you could need more energy to achieve the same absolute acceleration. By absolute acceleration I mean that which can be measured inside the space ship.
Say I have a technomagical space ship that can do 1g from 0 to .5 of light speed. Fast enough to relativistic effects, but not so fast we’re really messing up our view of the universe. Now to my mind, whether at 0 or .5 of c, we measure 1g acceleration inside the ship.
But if you try to calculate your acceleration relative to the universe outside, you find that that acceleration is lower than 1g.
I don’t even want to try doing the math involved. Length contraction and relative speeds are bad enough to deal with in special relativity. But I’d love to see the numbers, whether they support my view or not.
ETA: I think this is the same as what rat avatar wrote above starting “You can apply the same force, which will locally appear like you are accelerating …”
The V that comes out still has to be relative to something.
They will, but remember time dilation is a difference in the elapsed time measured by two observers and each of the observers will perceive the other’s clock as ticking at a slower the local clock. With acceleration time dilation is not symmetric and due to the speeds one has to consider the hyperbolic effects.
Really one has to resort to math to explain this but consider that in 4D spacetime diagrams the hyperbole is the “invariant” shape in rotation similar to how a circle is in 2D and a sphere is in 3D.
It is very very hard to describe the implications here without math and your intuitions will fail you here.
Nope, that formula only works at slow speeds and in local contexts with inertial frames. That formula is really from Galilean relativity.
To add parallel velocities in the same direction SR requires the following which is one of the simplest cases:
u + v
w = ---------
1 + uv/c^2
I can’t get the preview to work well enough on here to even try to describe the implications of rapidity as a measure for relativistic velocity or the implications of boosts.
But in general your assumption only holds if one has a problem that simplifies to the Newtonian model which is not typical once your speed becomes a significant percentage of the speed of light. Fortunately they do often reduce to the SR case for many thought experiments which does help.
Why would that violate anything? The beautiful symmetry of special relativity is that classical Newtonian physics holds completely within the reference frame of the spaceship. You continue accelerating as long as you want, and appear to reach and exceed the speed of light with no special difficulty. It’s only from an external frame of reference that the speed of light is seen to be approached asymptotically, matched exactly by a corresponding observation of time dilation, so that the spaceship passengers are unaware of any of it and simply observe themselves traveling faster than light. What are you trying to say that I’m missing?
If the question is what it would look like to you, inside your magic spaceship as you accelerate at 1g, it would look like you accelerate at 1g. You turn on the drive, head for Tau Ceti, and according to your shop clock it would take exactly as much time to get to Tau Ceti as if relativity didnt exist.
You’d see some strange things happen to the stuff outside your ship. Light from stars ahead of you would measure as moving at exactly c as per usual. Except that light would be blue shifted and have higher energy than the light you measured back on Earth. Same thing but in reverse for.stars behind you. Light fro. Them would travel at exactly c, but the light would have lower energy and be red shifted.
Also, when you get to Tau Ceti you find that everyone else’s clocks have mysteriously slowed down as you made your trip.
If you had a magic box that could accelerate you to .999999999999 c without crushing you, you could travel to Tau Ceti in just a few minutes or seconds. According to your clock that is. To everyone else it would take you 11 years. But to you it could take an arbitrarily short time, depending on how many nines your magic box can produce.
Here is a paper that does a good job of describing the one-dimensional equations which may help understand the changes compared to classical mechanics.
Even if you only look at the graphs at the end the hyperbolic relationship with the future horizon will be somewhat intuitive.
That said I have to do the math here, so hopefully others may have more cognitive success in directly visualizing the effects but it is probably beyond me unless I do the math with more than even one spacial dimension let alone 3 + time.
As for using a chunk of gold on a spaceship as a form of money, consider this. What if there was a solid gold asteroid near Jupiter? A million tons of gold! Worth billions or trillions of dollars! All you have to do is assert ownership of this asteroid and you are instantly the richest person on Earth.
Except that gold that you can’t touch or use is exactly toy as valuable as no gold. Gold in your hands on Earth is valuable because other people will give you goods and services in exchange for that gold. But they want the actual gold. Gold on another planet doesn’t do any good
And of course, our current fiat money is based on absolutely nothing except the US government’s assertion that it is worth something. How is that different than an imaginary mountain of gold on another planet? The difference is that the US government has cops and soldiers and judges and prison guards who will make you accept that imaginary money backed by nothing.
If the cops and the soldiers stopped enforcing the decrees of the US government, then all that fiat money would evaporate back into the nothingness from which it came. Try spending Confederate money at the local corner store and see what happens.
This is a bit overstated. There have been countries with cops and soldiers that couldn’t stop fiat money evaporating into nothing.
The collective goodwill and faith of the citizenry (and people of other countries) does actually count for something when establishing value. Always has.
Likewise, a huge chunk of gold orbiting Jupiter is worth as much as we collectively decide it is. Case in point, the stone money of the island of Yap. They used huge limestone discs as a form of currency. There is a likely apocryphal story that one such disc ended up at the bottom of the ocean but was still accepted as currency - ownership of the disc swapped, despite the fact nobody could actually retrieve it or even verify its existence.
That said, if you could accelerate (relative to Earth) a chunk of gold to nearly light speed and bring it back, it would be worth more to many collectors than its purely material value at least as an item of curiosity. But I think we’ve pretty well debunked the idea that ‘relativistic’ mass would have any bearing on an assay.
A kilo of gold is worth about $38,700. At a price of $0.05/kWh, that’s 774,000 kWh of energy, or 2.79e12 J. But that’s only equivalent to the kinetic energy of that gold at 2.36e6 m/s, or 0.79% of c. And that’s still sub-relativistic, so anything faster is going to be totally hopeless.
Of course, if you have a chunk of relativistic gold and a means of converting the KE to electricity, you could make a killing with cheap energy.
And inflationary-era Zimbabwe’s currency was based on the same thing, then? So why did it hyperinflate into nothingness? Did Zimbabwe’s government not shout loudly enough or something?
Money is as valuable as any commodity. Moreover, it’s valued the same way as any commodity: On an open market, by people who buy it or sell it based on their predictions of how its value is going to move in the future relative to other commodities. The fact some other commodities physically exist and can be used for something is secondary; to prove this, consider the diamonds-water paradox. Diamonds are, to a first approximation, completely useless. Water is essential for all life on Earth. Which is worth more on the open market? Well, money is just diamonds without that incidental industrial cutting application.
Value is psychological. It always has been. The only difference between now and the goldbug era is that now, we don’t pretend it’s based on anything but psychology.
Yes but with my limited knowledge to an observer on earth if they could see your clock it would be going slower to them I think. If I understand it correctly this is how Einstein said to himself that something had to give if he was moving faster and faster away from a clock the light from the clock would take longer to reach so the clock would be appearing to slow down, so time to you would slow down as earth time continued at same speed or something like that if I remember correctly, maybe someone can clarify better than this layman can. vy VY
Yes, this is called relativistic time dilation. Just to be clear, in a symmetric situation both you and the observer on Earth observe each other’s clock “slowed down” or red-shifted; cf. all the threads concerning the so-called Twin Paradox.
The weight/mass of the gold would be measured using a physical device. Obviously, this device would need to be traveling along with the gold, at the same rate. To your observer, the gold will not have gained any mass, because it is not moving at all.
As for your question about gold prices on the moon.
Silly boy, gold price is per Mass, not per Weight. Mass on the moon, or even in orbit, is still the same as on earth.
Yup silly me, and here I was thinking they took out the old weight and balance scale and weighed the thing. vy VY
If the gold balances a certain weight on Earth, it will balance the same weight on the Moon, Jupiter, Mars, the underworld, or anywhere else. Except for a weightless environment where traditional scales may not work too well.
There’s kind of a point there, in that in most practical circumstances – which in most cases means on the surface of the earth – weight is a perfectly acceptable proxy for mass. With a balance scale, since it measures relative to a set of fixed weights, the reported weight would be the same on the moon, too, or on the surface of any other astronomical body. A spring balance would have to be adjusted for local gravity. In weightlessness you’d have to ascertain mass some other way, like some sort of centrifuge.
ETA: That was a response to #58. Sorry to essentially repeat what DPRK just said – I didn’t see it before I posted! 