Moving at light speed

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#1 tom

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Posted 23 April 2005 - 12:39 PM

Is the following statement true. If no why?

When a body with mass m0 moves at light speed his energy is infinity.

E = mc^2 = m0 * c^2 / sqrt ( 1 - c^2 / c^2) = m0 *c^2 / 0 = infinity

I know it's impossible for a body with mass to reach that speed, this is a theoretical question.

#2 Buffy

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Posted 23 April 2005 - 12:51 PM

Is the following statement true. If no why?

When a body with mass m0 moves at light speed his energy is infinity.

E = mc^2 = m0 * c^2 / sqrt ( 1 - c^2 / c^2) = m0 *c^2 / 0 = infinity

I know it's impossible for a body with mass to reach that speed, this is a theoretical question.

That's why its impossible to push a mass to the speed of light because it takes "infiinte energy" which obviously isn't available...

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#3 tom

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Posted 23 April 2005 - 12:56 PM

#4 Damo2600

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Posted 24 April 2005 - 12:59 PM

The Hubble limit is where galaxies are receding at c. The light is no longer travelling fast enough to ever reach us. This limit is an event horizon. Relatively these galaxies are travelling at the speed of light.

We have no reference frame to suggest otherwise.

#5 Buffy

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Posted 24 April 2005 - 01:04 PM

This limit is an event horizon. Relatively these galaxies are travelling at the speed of light.

Slight correction: they are "traveling relatively" slower than light, but the expansion of the universe creates the perception of faster than light "speeds". In their local frame of reference of course, they may not be perceived to be moving at all (depeding on what the defined reference frame is...)..

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#6 Tormod

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Posted 24 April 2005 - 01:05 PM

Do we know any galaxies even appearing to recede close to the speed of light?

#7 Tormod

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Posted 24 April 2005 - 01:06 PM

In their local frame of reference of course, they may not be perceived to be moving at all (depeding on what the defined reference frame is...)..

In fact, wouldn't they see all other galaxies as receding away from themselves?

#8 Buffy

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Posted 24 April 2005 - 01:14 PM

Do we know any galaxies even appearing to recede close to the speed of light?

There was a great discussion of the above in the March 2005 Scientific American article "Misconceptions About the Big Bang." The basic idea here is that objects that are furthest away from us in the universe are "receding" at the greatest "relative speeds" and the Hubble limit is defined as the point at which they appear to be moving at the speed of light. If they're further away, they're "receding" at more than the speed of light and the light will never reach us. The article points out that most of this "speed" is simply the expansion of the universe and in local frames of reference, they're not moving at anywhere near the speed of light....

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#9 Damo2600

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Posted 24 April 2005 - 01:16 PM

The reference frame is right underneath forehead. All other reference frames are null and void due to the theory of relativity. A galaxy, receding at c, would not appear to be travelling at c, however, because *you* would no longer see it.

#10 Tormod

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Posted 24 April 2005 - 01:17 PM

Thanks - I actually have that issue in my bag for reading on the local train in the mornings so I'll check it out tomorrow.

#11 Damo2600

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Posted 24 April 2005 - 01:18 PM

Do we know any galaxies even appearing to recede close to the speed of light?

Just before the hubble limit, Yes.

#12 Tormod

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Posted 24 April 2005 - 01:18 PM

The reference frame is right underneath forehead. All other reference frames are null and void due to the theory of relativity. A galaxy, receding at c, would not appear to be travelling at c, however, because *you* would no longer see it.

I understand that. My question was whether we actually have any observations of galaxies receding even close to c.

Edit: Thanks, you replied while I typed this.

#13 Buffy

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Posted 24 April 2005 - 01:18 PM

In fact, wouldn't they see all other galaxies as receding away from themselves?

Oh of course! Because as we all know from the Cosmological Principle, the Universe is isotropic....

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#14 Damo2600

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Posted 24 April 2005 - 01:21 PM

The reference frame is right underneath forehead. All other reference frames are null and void due to the theory of relativity. A galaxy, receding at c, would not appear to be travelling at c, however, because *you* would no longer see it.

#15 Damo2600

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Posted 24 April 2005 - 02:23 PM

"The article points out that most of this "speed" is simply the expansion of the universe and in local frames of reference, they're not moving at anywhere near the speed of light...."

Time is slower for an observer, on a train, moving away from a static observer. But it is not really slower because an observer driving in a car beside the train does not experience a time difference.

So you are saying that relativity is only relative when the observer chooses. Nice way to get around the absurdities. Time is not relative if you don't want it to be either?

If only einstein had thought of that.

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#16 Buffy

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Posted 24 April 2005 - 02:31 PM

So you are saying that relativity is only relative when the observer chooses. Nice way to get around the absurdities. Time is not relative if you don't want it to be either?

Nah, you're reading too much into this. The only point here is that people make the argument that the observations you've cited are proof that things can move faster than the speed of light, which of course they can't, and the article points out that the expansion of the universe becomes the dominant factor in observed speed at these distances, but that expansion is not valid for defining speed--which is based on distance-because the distance is actually changing!

Everything is always relative, and local frames of reference are implicit in relativity ("where ever you are, that's what you see!")...

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#17 Damo2600

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Posted 24 April 2005 - 02:56 PM

Ah, but you see, that's not how relativity works. If that were true I could just minus the velocity of the train and my clocks would match your stationary clocks. The speed of light would remain constant. Relativity now would not equal reality and time and space now becomes absolute.

I see what you are implying but there are implications built-in to that point of view.

Like the whole last century of physics. I've put a lot of thought into this so need we go further?