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Old 11-14-2018, 09:32 AM
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Gold price at near speed of light

Hi, (theoretically or otherwise and aside from the cost to get it up to that speed) if here on earth you accelerate a quantity of gold to near light speeds, the mass increases, so the weight would increase relative to earth gravity, would you then have more weight in gold and be richer, and could you cash in?
Then if you decelerated it back to nil, would it be a crime to keep the money?
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Old 11-14-2018, 09:33 AM
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I assume that this is a whoosh and not a serious question.
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Old 11-14-2018, 09:34 AM
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If you can figure out how to accelerate to close to the speed of light cheaper than gold, than, go for it!
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Old 11-14-2018, 09:37 AM
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The mass does not increase in any sense relevant to selling and buying the gold.
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Old 11-14-2018, 09:41 AM
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I assume that this is a whoosh and not a serious question.
you can look at it how you want, but isn't the dollar is based on gold locked away in fort Knox etc, no, probably never to be used? what is the difference if you hitch a bar of gold on a space ship going very fast, or centrifugal or other accelerator built for experiment purposes?
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Old 11-14-2018, 09:45 AM
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The mass does not increase in any sense relevant to selling and buying the gold.
So the extra weight is just ignored?
On the moon the gold does not weigh much, does it still have the same value?
If gold was found on the moon, would they have to bring it back to earth gravity to weigh it to price it or base the value on the weight on the moons gravity?
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Old 11-14-2018, 09:49 AM
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1. Gold is not the basis of US currency value
2. Weight is not mass.
3. For those moving with the gold, the mass is at rest relative to them, so there is no additional "mass" to worry about.
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Old 11-14-2018, 09:54 AM
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Originally Posted by Grey View Post
1. Gold is not the basis of US currency value
2. Weight is not mass.
3. For those moving with the gold, the mass is at rest relative to them, so there is no additional "mass" to worry about.
1) ok.
2) I thought that the reason one can never reach the speed of light is because the mass increases which makes or at the same time the object becomes heavier and harder to accelerate to get to the speed of light.
3) ok
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Old 11-14-2018, 09:54 AM
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So the extra weight is just ignored?
There is no extra weight. If you put the gold on a scale it will weigh the same. Mass and weight are not the same thing. And observed mass is relative. If you and your buyer are traveling along with the gold, you will not notice any difference in mass.
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Old 11-14-2018, 10:29 AM
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Originally Posted by Grey View Post
1. Gold is not the basis of US currency value
2. Weight is not mass.
3. For those moving with the gold, the mass is at rest relative to them, so there is no additional "mass" to worry about.
Number 3 is the key.
If you are sitting there with a mass of gold, it "weighs" the same (by whatever means you choose to determine its mass) whether you are sitting on earth, the moon, or a spaceship doing 0.9c compared to the earth.

What relativity is saying is that as a mass whooshes by you at 0.9c you will see its effect on other masses (i.e. gravitational effect) as being much larger that it would be if the same mass at rest were nearby. Similarly, a person on a spaceship doing 0.9c would as they zip past the earth feel the gravitational effect of the earth (how it deflect the path) as if the earth were much more massive... which makes sense, time is slowed down from POV of , so the deflection of the ship's trajectory appears much stronger in (apparent) slo-mo than in Newtonian time. The apparent increase in mass, decrease in length, and slowdown in time are a result of altered points of view.
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Old 11-14-2018, 10:40 AM
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"Relativistic Mass" as used in the OP is an artifact of a thought experiment and not a real effect.

The gamma factor changes but the intrinsic mass does not. Under GR inertial mass and gravitational mass are equivalent and in fact the entire theory depends on it so it is easy to get stuck in the traditional mass/weight confusion and this is why the whole concept of "relativistic mass" has been dropped in the field for a very long time.
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Old 11-14-2018, 10:45 AM
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From Einstein's paper, showing it is a base assumption

Source: Relativity: The Special and General Theory © 1920

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A satisfactory interpretation can be obtained only if we recognise the following fact : The same quality of a body manifests itself according to circumstances as " inertia " or as " weight " (lit. " heaviness ').
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Old 11-14-2018, 10:47 AM
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The idea that mass increases with speed is a analogy for thinking about relativity that tries to use our intuition about mass in every day life to help gain an understanding of how the equations of relativity work. Like all analogies it is imperfect. I believe that the concept of relativistic mass is falling out of favor because people feel it creates more confusion than understanding.
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Old 11-14-2018, 10:49 AM
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On a side note about where relativity does apply to gold.

Due to the specific type of orbitals, which allow the electron clouds do be tighter than in other substances, those electrons actually travel a significantly faster speed and undergo relativistic effects which result in the color of the material itself.

Gold would be silver in color if it wasn't for the effects of relativity and it would also "weigh" less for a similar volume too.
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Old 11-14-2018, 10:50 AM
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I for one would pay money to buy a huge amount of gold moving at a speed that I cannot possibly possess it, or even perceive it. But it would not be very much money.
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Old 11-14-2018, 10:57 AM
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I think your best bet may be to weigh the gold while travelling in an elevator between the ground floor and top floor in a tall building. Do it in an Up elevator if you're selling the gold; Down elevator if you're buying. (This won't work with ordinary balance scales.)

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Originally Posted by rat avatar View Post
On a side note about where relativity does apply to gold.

Due to the specific type of orbitals, which allow the electron clouds do be tighter than in other substances, those electrons actually travel a significantly faster speed and undergo relativistic effects which result in the color of the material itself.

Gold would be silver in color if it wasn't for the effects of relativity and it would also "weigh" less for a similar volume too.
Interesting. Thanks.
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Old 11-14-2018, 10:59 AM
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Originally Posted by rat avatar View Post
"Relativistic Mass" as used in the OP is an artifact of a thought experiment and not a real effect.

The gamma factor changes but the intrinsic mass does not. Under GR inertial mass and gravitational mass are equivalent and in fact the entire theory depends on it so it is easy to get stuck in the traditional mass/weight confusion and this is why the whole concept of "relativistic mass" has been dropped in the field for a very long time.
Here is an other quote from Einstein against using "relativistic mass", from Wikipedia's bit about relativistic mass:

Quote:
Einstein never derived an equation for "relativistic mass", and in later years he expressed his dislike of the idea:

It is not good to introduce the concept of the mass [relativistic mass formula] of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the írest massí m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion.
Mass is easier to grasp for many than momentum and energy, which is why relativistic mass still makes it into high school lessons, pop-sci and badly researched thought experiments.
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Old 11-14-2018, 11:20 AM
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“Larry’s we-buy-gold, good morning”
‘Yes, hi, I got about half a kilo of gold, what’s it worth? Wanna buy it?”
“Depends. Is it coins, bar, jewellery?”
“It’s a Krugerrand!”
“yeah, they don’t come over 34 grams - not sure what you got th-“
“But mine’s on a spaceship! Going really realy quickly!”
“Well, bring it in, we’ll take a look at it”
“Zounds! Foiled again!”
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Old 11-14-2018, 11:27 AM
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With the problems of relativistic mass and not using the Lorentz factor it should also be noted that the SI system is also expressly defined now to indicate that these are only apply to local experiments.

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The definitions of the base units of the SI were adopted in a context that takes no account of relativistic effects. When such account is taken, it is clear that the definitions apply only in a small spatial domain sharing the motion of the standards that realize them. These units are known as proper units; they are realized from local experiments in which the relativistic effects that need to be taken into account are those of special relativity. The constants of physics are local quantities with their values expressed in proper units.
https://www.bipm.org/en/publications...ection1-5.html

(emphasis mine)

It is very problematic and complex to try and move these units past their useful domain.
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Old 11-14-2018, 11:39 AM
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If mass doesn't increase, what is it that prevents one from approaching the speed of light then?
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Old 11-14-2018, 11:50 AM
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If mass doesn't increase, what is it that prevents one from approaching the speed of light then?
The Lorentz term which impacts time, length, and the energy required for acceleration.

This is known as γ or gamma.

https://en.wikipedia.org/wiki/Lorentz_factor

Last edited by rat avatar; 11-14-2018 at 11:51 AM.
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Old 11-14-2018, 11:50 AM
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If mass doesn't increase, what is it that prevents one from approaching the speed of light then?
As above, it's better, equation wise, to discuss momentum and energy rather than mass.

The energy requirement increases without bound the closer you want to get to c.

That's one of the things about 'tachyons' that's kind of interesting. If a faster than light particle exists, it could never slow down to light speed, either, for the same reason of an infinite energy requirement.

ETA: In 'conventional' Newtonian physics, momentum can be written as m*v and kinetic energy is 0.5*m*v*v. But those go out the window at relativistic speeds unless you let 'm' increase to some sort of 'relativistic mass'. So the idea of a relativistic mass is a not-good way to reconcile how we have taught ourselves things work in a Newtonian world with what we know at relativistic scales.

Last edited by Great Antibob; 11-14-2018 at 11:53 AM.
  #23  
Old 11-14-2018, 11:53 AM
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The Lorentz term which impacts time, length, and the energy required for acceleration.

This is known as γ or gamma.
But that's just a number in an equation. What are the real-world effects that would hinder a ship approaching the speed of light? "Mass increases" seemed pretty understandable.

If I am in a ship, who's engine is capable of accelerating it 1 m per s per s, as I notice my speed increasing, what happens?
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Old 11-14-2018, 11:55 AM
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I should add that E= mc^2 is a special case. If you consider that Einstein was talking about rest mass and consider the longer form of:

E^2 = (mc^2)^2 + (pc)^2

You will see the momentum component in p

As momentum increases the E or energy increases. It is the "(pc)^2" portion that causes you problems.

Last edited by rat avatar; 11-14-2018 at 11:57 AM.
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Old 11-14-2018, 11:56 AM
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If I am in a ship, who's engine is capable of accelerating it 1 m per s per s, as I notice my speed increasing, what happens?
You notice that maintaining that 1m per s per s requires more and more thrust from your engine as you go faster. And that eventually, it becomes impossible to maintain, even with infinite energy and that acceleration gradually gets lower and lower and you need more and more thrust just to eke out an infinitesimally small bit of additional speed.
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Old 11-14-2018, 11:59 AM
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Here is a minutephysics video which will probably help out with this intuition using simple math.

https://youtu.be/NnMIhxWRGNw

Last edited by rat avatar; 11-14-2018 at 11:59 AM.
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Old 11-14-2018, 12:13 PM
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But that's just a number in an equation. What are the real-world effects that would hinder a ship approaching the speed of light? "Mass increases" seemed pretty understandable.

If I am in a ship, who's engine is capable of accelerating it 1 m per s per s, as I notice my speed increasing, what happens?
The universe around you changes. Remember everything is relative. It's in the name of the theory.

As as your speed increases, the universe around you slows down. If you've somehow managed to invent an engine that will just keep accelerating you forever, as your speed increases the universe around you slows down sufficiently to make it take forever to reach light speed.


The best argument against relativistic mass at a more intuitive level, at least to me, is that it only works nicely for energy and momentum. If you try to apply it to F = ma you will have to divide it into transverse and longitudinal mass. Only forces working perpendicular to the direction of motion give behavior according to the same relativistic mass concept as energy and momentum. In the direction parallel to travel you need to multiply by the cube of gamma to get the longitudinal mass instead.
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Old 11-14-2018, 12:15 PM
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You notice that maintaining that 1m per s per s requires more and more thrust from your engine as you go faster. And that eventually, it becomes impossible to maintain, even with infinite energy and that acceleration gradually gets lower and lower and you need more and more thrust just to eke out an infinitesimally small bit of additional speed.
Only if you make the calculations for an external reference frame. In your own reference frame the energy requirements are the same.
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Old 11-14-2018, 12:15 PM
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You notice that maintaining that 1m per s per s requires more and more thrust from your engine as you go faster. And that eventually, it becomes impossible to maintain, even with infinite energy and that acceleration gradually gets lower and lower and you need more and more thrust just to eke out an infinitesimally small bit of additional speed.
Ok. But what has happened to you and your ship that causes the same amount of force to no longer provide the same amount of acceleration?
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Old 11-14-2018, 12:17 PM
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Only if you make the calculations for an external reference frame. In your own reference frame the energy requirements are the same.
This seems like you are saying that it doesn't take more energy to keep accelerating at 1 m per s per s.

Is that what you are saying?
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Old 11-14-2018, 12:17 PM
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That is a good point, remember that a photon simply does not experience time at all. For a photon being emitted and absorbed is a single event.

As a photon doesn't even experience time how would you even calculate velocity as no time passes?

Time as a dimension is something that is experienced by us massive, slower than light objects.
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Old 11-14-2018, 12:46 PM
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you can look at it how you want, but isn't the dollar is based on gold locked away in fort Knox etc ... ?
You're thinking of the Gold Standard. The USA abandoned it in 1933.
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Old 11-14-2018, 01:06 PM
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Keep in mind the increasing amount of energy you'll need as your payload approaches light speed. The increased value of your gold holdings will be cancelled out by your higher utilities bill.
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Old 11-14-2018, 01:22 PM
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Ok. But what has happened to you and your ship that causes the same amount of force to no longer provide the same amount of acceleration?
If you are in a rocket and accelerating constantly, nothing causes the same amount of force to no longer provide the same amount of acceleration. Until you run out of fuel, which is why there are not yet five-day cruises to Saturn on offer. But, assuming you have enough magic antimatter or whatever to keep it up, you will soon enough find yourself in the Andromeda Galaxy and beyond; at the same time, an observer where you started out never sees you exceed the speed of light. In short, nothing is preventing you, it is all a matter of changing coordinates.

Your cargo of gold does not increase in mass either, as has been explained.
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Old 11-14-2018, 01:28 PM
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This seems like you are saying that it doesn't take more energy to keep accelerating at 1 m per s per s.

Is that what you are saying?
From the reference frame of the space ship doing the acceleration, yes, I believe that is the case. Otherwise speed is no longer relative.
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Old 11-14-2018, 01:31 PM
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If you are in a rocket and accelerating constantly, nothing causes the same amount of force to no longer provide the same amount of acceleration. Until you run out of fuel, which is why there are not yet five-day cruises to Saturn on offer. But, assuming you have enough magic antimatter or whatever to keep it up, you will soon enough find yourself in the Andromeda Galaxy and beyond; at the same time, an observer where you started out never sees you exceed the speed of light. In short, nothing is preventing you, it is all a matter of changing coordinates.
But I wasn't asking about an observer. I was asking about what happens in my ship as I am measuring my speed. As the speed I calculate gets closer to light speed, what happens? When the speed clicks over the SOL, and I say "Hey, we are going faster than light", does someone say "No we are not, because the math on this paper says we can't?"
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Old 11-14-2018, 01:32 PM
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Consider this - a spaceship approaches earth at 0.9c - as it gets near, its path is deflected due to the gravitational effect of the earth. However, the person on the spaceship sees it differently - to them, time is slower and the distance they are travelling toward earth appears shorter - as a result, the deflection due to earth's gravity appears to be a greater angle. The only explanation for them is that the effect of the earth deflecting their path is due to a much higher mass - i.e. the earth appears on the spaceship to have the effect of a much higher mass.
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Old 11-14-2018, 01:36 PM
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Only if you make the calculations for an external reference frame. In your own reference frame the energy requirements are the same.
Only for inertial frames of reference, for which there is no favored frame.

During acceleration, the ship is in a non-inertial frame of reference, and some frames are better than others.

The alternative is you see the earth (or whatever you are leaving behind) accelerating to beyond light speed behind you, which is not possible. There has to come a point when you see that the exertions of your engines no longer produce the same additional velocity for the same energy expenditure.

It is simply impossible to continuously accelerate at 1 m/s/s ad infinitum (assuming the energy was available, anyway). Otherwise, after 300 million seconds, you would observe the earth falling behind faster than the speed of light, which violates our known understanding of the universe.

Last edited by Great Antibob; 11-14-2018 at 01:37 PM.
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Old 11-14-2018, 01:40 PM
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Am I the only one who thinks that this guy is a wind-up merchant? This is the kind of discussion we used to have when I was a teenager.

Last edited by bob++; 11-14-2018 at 01:41 PM.
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Old 11-14-2018, 02:03 PM
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But I wasn't asking about an observer. I was asking about what happens in my ship as I am measuring my speed. As the speed I calculate gets closer to light speed, what happens? When the speed clicks over the SOL, and I say "Hey, we are going faster than light", does someone say "No we are not, because the math on this paper says we can't?"
Faster compared to what?

You can apply the same force, which will locally appear like you are accelerating but as you do your clock ticks slower and slower and slower compared to an initially co-moving observer.

To an initially co-moving frame, and compared to from your accelerating viewpoint to that same initially co-moving frame you will never reach the speed of light.

Speed is meaningless without another reference point and it will be very challenging to try and convey these effects with our intuitive assumptions.

Ignoring other matter it will still feel like you are being "accelerated" but at some point what still seems like an arbitrary segment of popper time or your local time will be so long in the initial co-moving frames time that you will exceed the heat death of the universe.

This proper acceleration is a measurable acceleration with an accelerometer, but the assumptions our minds try and make is to translate a four-dimensional motion into a three-dimensional motion that we have an intuitive understanding of.

When you get away from our slow speeds where our intuitions work our assumptions start to break down.

We simply want to use coordinate acceleration in our minds and that breaks down under GR as the universal internal frame assumption that is used in SR does not exist.

You can only use proper time, or the local clock time as coordinate time (inertial frame) simply does not hold.

Using Four-acceleration, as the proper time follows the world line there is no paradox here. The problem arises from our human mind's belief that there is some universal clock but remember that the spacetime interval is the only invariant property in GR once you move past very local and slow interactions. The spacing between events and even the ordering of events is not invariant across observers. The sequence of events, timing of events and order of events is not universal and only causality is preserved.

Note this is an oversimplification and built with bad analogies.

Last edited by rat avatar; 11-14-2018 at 02:05 PM.
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Old 11-14-2018, 02:09 PM
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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.
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Old 11-14-2018, 02:38 PM
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Am I the only one who thinks that this guy is a wind-up merchant? This is the kind of discussion we used to have when I was a teenager.
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
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Old 11-14-2018, 02:40 PM
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Am I the only one who thinks that this guy is a wind-up merchant? This is the kind of discussion we used to have when I was a teenager.
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.
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Old 11-14-2018, 03:18 PM
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Faster compared to what?

You can apply the same force, which will locally appear like you are accelerating but as you do your clock ticks slower and slower and slower compared to an initially co-moving observer
But I thought any clocks that I had on board would still look to me like they are moving at the same rate?

Quote:
Speed is meaningless without another reference point and it will be very challenging to try and convey these effects with our intuitive assumptions
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.
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Old 11-14-2018, 04:41 PM
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It is simply impossible to continuously accelerate at 1 m/s/s ad infinitum (assuming the energy was available, anyway). Otherwise, after 300 million seconds, you would observe the earth falling behind faster than the speed of light, which violates our known understanding of the universe.
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 ..."

Last edited by naita; 11-14-2018 at 04:45 PM.
  #46  
Old 11-14-2018, 04:42 PM
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Originally Posted by manson1972 View Post
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.
The V that comes out still has to be relative to something.
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Old 11-14-2018, 04:52 PM
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Quote:
Originally Posted by manson1972 View Post
But I thought any clocks that I had on board would still look to me like they are moving at the same rate?
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.

https://en.wikipedia.org/wiki/Hyperb...on_(relativity)

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.

Quote:
Originally Posted by manson1972 View Post
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.
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:

Code:
               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.

Last edited by rat avatar; 11-14-2018 at 04:54 PM.
  #48  
Old 11-14-2018, 04:54 PM
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Originally Posted by Great Antibob View Post
The alternative is you see the earth (or whatever you are leaving behind) accelerating to beyond light speed behind you, which is not possible. There has to come a point when you see that the exertions of your engines no longer produce the same additional velocity for the same energy expenditure.

It is simply impossible to continuously accelerate at 1 m/s/s ad infinitum (assuming the energy was available, anyway). Otherwise, after 300 million seconds, you would observe the earth falling behind faster than the speed of light, which violates our known understanding of the universe.
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?
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Old 11-14-2018, 04:54 PM
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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.

Last edited by Lemur866; 11-14-2018 at 04:56 PM.
  #50  
Old 11-14-2018, 05:00 PM
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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.

https://arxiv.org/pdf/physics/0601179.pdf

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.

Last edited by rat avatar; 11-14-2018 at 05:02 PM.
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