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PostPosted: Sat Jul 17, 2010 7:21 am 
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According to Hawkins: "the mass of an object traveling at 10% of the speed of light is roughly 0.5% 'more' than it is at rest, and traveling at 90% of the speed of light its mass has more than doubled"

I am having some difficulty understanding this, from a mathematical perspective (using E=mc^2):

Let m = mass of object at rest (lets say 100kg)
Let c = speed of light (lets say 300,000 km/s)

Now, mathematically, Hawkins says the following:

At 10% of c, it follows that:
m' = 1.005*m

At 90% of c we have:
m'' = 2*m

from the quantities above we have that

m' = 1.005*100kg = 100.5kg and
m'' = 2*100kg = 200kg

Does this result follow intuitively from E=mc^2 ? If not, is there any other way to understand this.

Any help on this would be appreciated.


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PostPosted: Sat Jul 17, 2010 7:38 am 
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Extracted from ???, didn't make note of the site, should have:

To get straight to the point the mass of an object will increase when traveling at relativistic speeds. The equation for calculating the mass as seen by an outside observer is as follows:

m = m0/((1 - v2/c2))1/2

where: m0 = the mass measured at rest relative to an observer traveling with the same velocity as the mass, the "rest mass".

m = the mass measured by the observers on the other reference frame.
v = the speed of the object
c = the speed of light in a vacuum


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PostPosted: Sat Jul 17, 2010 8:06 am 
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boykie wrote:
According to Hawkins:

Hawking? :wink:

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PostPosted: Sat Jul 17, 2010 10:50 am 
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Cool thanks for the input. M54, I assume you meant "sqrt((1-v2/c2))", which lead me to Lorentz' formula and the following calcs:

Mr. HawkinG was spot on it would seem :lol: , who would have thought that!
:lol:

Image

but thanks, now i can read in peace, until the next concept kills me, which shouldn't take too long :)


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PostPosted: Fri Jul 23, 2010 8:08 pm 
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boykie wrote:

According to Hawkins: "the mass of an object traveling at 10% of the speed of light is roughly 0.5% 'more' than it is at rest, and traveling at 90% of the speed of light its mass has more than doubled"



He is wrong...mass does not increase.....it just appears to as our means of measuring mass are affected by the relativistic speeds involved.


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PostPosted: Mon Aug 02, 2010 1:43 am 
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boykie wrote:
Does this result follow intuitively from E=mc^2 ? If not, is there any other way to understand this.


It doesn't follow on from E=mc^2 as that is the rest equation, there's a slightly more complicated formula for masses in relative motion, which is energy squared = (mc^2)^2 + (pc^2)^2 - and the increase in mass at relative velocities will be included in the momentum term, p.

But you'd need a bigger T-shirt to print the full thing on.


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PostPosted: Wed Sep 22, 2010 7:44 pm 
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There is a slight problem with this theory. To get to the bare roots of this argument we have to go to an extreme. Imagine that there are two spaceships sat in a vacuum one mile apart with no other nearbye witnesses. One of the spaceships decides to accelerate to 90% of C. The calculations are made and it is established that the spaceship has double its normal mass. A huge problem occurs, there are no relative viewpoints to establish which spaceship has accelerated in the first place and according to relativity they are indeed moving apart but there is absolutely no indication of suggesting which is stationary due to the lack of a third party. This means potentially they are both stood still. This unfortunately means that every mass in our Universe is potentially stood still even though it may not appear this way from our prospective. You could argue that all mass has 'this reality tunnel' and that all movement in the Universe is based on relativalistic viewpoints so Kev is indeed correct.


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PostPosted: Sat Oct 02, 2010 10:31 am 
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Dear Quasar
I may well be missing something in your argument so I hesitate to say you are wrong (?).
However, I don't think you are entirely correct.
1)First let's forget any third party for a bit. As I see it the accelerating spacecraft you mention as observable effects relative to crew in the other spacecraft. Similarly the non accelerating spacecraft has observable afects relative to the accelerating craft crew.
2) Now bring in a third party.
I won't even try to go into thinking into the detal about this because I might trip myself up. However, my initial thought is that bringing in the third party (might) make the problem quite complicated.
I am thinking (possibly wrongly !) that bringing in a third party is a bit like "the third body problem in what I'll call basic newtonian mechanics.
If you have ony two bodies to deal with doing the maths is fairly simple, bring in an extra body and the maths becomes "fun" for them who like doing that sort of thing. For me it might be a nightmare !
Best wishes from Cliff


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PostPosted: Sat Oct 02, 2010 11:55 am 
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Quasar wrote:
This means potentially they are both stood still.

Well, obviously that doesn't make sense if both of them observe the other spaceship moving away. If you say an object in space is "stood still", then we have to ask relative to what? What object(s) in the universe is stationary?

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PostPosted: Mon Oct 04, 2010 7:51 pm 
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joe wrote:
Quasar wrote:
This means potentially they are both stood still.

Well, obviously that doesn't make sense if both of them observe the other spaceship moving away. If you say an object in space is "stood still", then we have to ask relative to what? What object(s) in the universe is stationary?

The two spaceships have both the potential to be stationary and to be accelerating at the same time. Until a witness appears and observes them then you have the exact scenario as in the double slit experiment.
Events at both Quantum levels and up here in the ordinary world seem to be related because of this fact and the pure fact that we witness them changes history. I've got a clouded general idea of what is happening but it doesn't fit into accepted theories. In this clouded idea all mass is stationary at all times but has several potentials according to how it is observed.


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PostPosted: Mon Oct 04, 2010 9:30 pm 
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Quasar wrote:
The two spaceships have both the potential to be stationary and to be accelerating at the same time.

How?

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PostPosted: Mon Oct 04, 2010 9:55 pm 
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joe wrote:
Quasar wrote:
The two spaceships have both the potential to be stationary and to be accelerating at the same time.

How?

Lets forget spaceships for a second and simplify it a little. I have covered this before in another thread. Imagine two particles in a vacuum that has no visible boundaries or witnesses. One particle begins to move away from the other at an undefined velocity. Which particle is stationary and which is moving? There is no answer because relativity doesn't exist for any of the particles. Each particle has the potential to be stood still or moving away from the other, indeed there is also the potential for both of them to be moving away at a different velocity in an infinite number of possibilities.
It is not until we introduce plaforms of observation and third parties that relativity can begin to take place and start to make assumptions. Now imagine if we go back to the two spaceships and place them in a environment where there are witnesses on platforms measuring what takes place and decide that it is infact spaceship 'X' is the one that is accelerating.
Unfortunately spaceship 'X' from its own relative viewpoint cannot possibly be related to any witness observing it and as far as it is concerned it is stationary just like one of the particles. Spaceships do not recognise witnesses and as far as it's concerned it is stood still and the other spaceship moved away from it. All matter has it's own reality tunnel
within this Universe and has the potential to be stood still no matter how fast someone else percieves it to be travelling. It also has the potential to be moving at the same time. Those two potentials are infinite in their nature and cannot be possibly compromised by a third party viewpoint.
When the space shuttle takes off from Earth the shuttle has as much right to claim the Earth moved away from it as the Earth has to suggest it was the shuttle that moved. Hope you understand that.


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PostPosted: Mon Oct 04, 2010 10:49 pm 
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Quasar wrote:
When the space shuttle takes off from Earth the shuttle has as much right to claim the Earth moved away from it as the Earth has to suggest it was the shuttle that moved.

I think you need to look again at the differences between inertial frames and accelerated reference frames. A body accelerating away from another body that is in constant non-accelerated motion is not experiencing the same "force". They are not equivalent.

But without moving off to look at particles, spaceships will either observe movement with reference to their position or they won't, not "potentially" both.

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PostPosted: Mon Oct 04, 2010 11:42 pm 
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joe wrote:
Quasar wrote:
When the space shuttle takes off from Earth the shuttle has as much right to claim the Earth moved away from it as the Earth has to suggest it was the shuttle that moved.

I think you need to look again at the differences between inertial frames and accelerated reference frames. A body accelerating away from another body that is in constant non-accelerated motion is not experiencing the same "force". They are not equivalent.

But without moving off to look at particles, spaceships will either observe movement with reference to their position or they won't, not "potentially" both.

Constant to what or whom? non-accelerated in comparison to what or whom?
If the 2 spaceships took the place of the two particles and there are no boundaries or witnesses then your argument falls short. You yourself have created the boundaries, force and motion from which you speak. Matter does not recognise any of those criteria and as far as it's concerned is the only thing present in the Universe. The spaceship you speak about does not recognise any other matter, it cannot see it, hear it or feel it. The only way matter can be related to any event taking place is from your own biased viewpoint of what is taking place and your own personal experience of it. All bodies of matter in this Universe have no relationship with other bodies and as far as they are concerned they are alone and their experience of where and what they are in this Universe is strictly only available to them. Even when Gravity attracts bodies toward them there is no other force acting upon that bodie and that body is still a free spirit within this Universe always having the right to suggest it is stationary at all times, doesn't matter how you percieve it Joe, you cannot possibly nail any piece of matter down and dictate to it 'how things are'.
When you are in a spaceship that accelerates, as far as the spaceship is concerned it is stationary and there are three astronauts trying to accelerate their way through the back door for some reason. It doesn't know why.


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PostPosted: Tue Oct 05, 2010 10:15 am 
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Well, ok, but it all boils down to being able to describe what is observed. If there is an alternative, more suitable way to describe matter and motion then let's use it. We had different descriptions in the past but they have been superseded and corrected. That's what science has been doing for millenia and what we have at the moment seems to be the most useful. That's about all we can do for the time being, is it not? It may not be an exact description of reality but you seem to be wanting a description of the universe without observers - which is somewhat contradictory, to say the least.

Meanwhile, anyone can speculate. If a tree falls in the woods....etc.

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