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Q & A: The Speed of Light

November 24, 2008 on 3:25 pm | In Physics, Q & A, relativity |

It’s 103 years after Einstein first formulated his Theory of Special Relativity, which explains what happens to objects near the speed of light. But SWAB reader Jacinth wants to do one better, and asks:

What will happen if we can actually travel at the speed of light?

It’s a great question, and provides a lot of learning opportunities. First off, let’s take a look at what happens to regular matter when we bring it close to the speed of light. There are three major things:

1. Lengths contract. This works for everyone. If I move close to the speed of light, then anyone who sees me sees that my length is smaller. But from my point of view, everything that I see is moving towards my rear close to the speed of light, and also looks like it has a smaller length.

2. Time slows down. We call this time dilation, and again, it works for everyone. It means that if I’m moving close to the speed of light, everyone who sees me sees that time is traveling more slowly for me: my clocks run slower, I age slower, my heart beats slower, etc. But I see the same thing: everyone else looks like their clocks are running slower, they’re aging slower, etc. But if I go away close to the speed of light and then come back to Earth at Earth’s speed, we find out that on my journey, although I’ve aged normally, much more time has passed on Earth. (Incidentally, this is what Paris Hilton was worried about.)

3. It takes more energy to accelerate your speed. Some of you who know a little physics know that the rest energy of a particle is E=mc2. Some of you also know that Kinetic Energy = 1/2 mv2. But when you get close to the speed of light, it takes more and more energy to move quickly. In the graph above, the purple line is the old formula for kinetic energy, but the red line is the real (relativistic) energy. Notice that you never quite get up to the speed of light, but that the energy it takes approaches infinity.

So that’s what happens when something made of normal matter approaches the speed of light: it sees lengths contract, times slow down, and it requires more energy to change its speed. Alternatively, things that have no mass (like photons, or perhaps gravitons), have to move at the speed of light.

But let’s say you had a spaceship, and decided to actually go at the speed of light, somehow. What would happen?

Well, if you used all the energy in the Universe for your spaceship, you could probably get up to speeds incredibly close to the speed of light. How close? The speed of light is exactly 299,792,458 meters/second. And you could get to within about 1 x 10-30 meters/second of that value — pretty good. If you got that fast, though, what would happen? First, the entire Universe would contract to appear to only be a few billion kilometers across — less than one light year! Second, time would slow down so much, that as you would only age a few seconds, the Universe would age literally trillions of years. Galaxies would merge, stars would be born and explode in the blink of an eye. And finally, you may get to see the fate of the Universe firsthand; if the Universe has an end, you would slow down time for yourself so much that you might not only see it, you might do it in just a few seconds.

So, in conclusion, not only can’t you move at the speed of light, there’s good reason not to!


17 Comments »

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  1. I just got done reading Tau Zero, which is basically the story of what you described in the last paragraph there.

    A one-way trip, for sure!

    Sean

    Comment by Sean Welton — November 24, 2008 #

  2. I suppose were we to extend this to “something” traveling AT the speed of light (as you say, photons and other massless particles DO, after all), we could easily say how those particles appear to us. (Please correct me if I’m wrong anywhere.)

    1. The object would have zero length dimension. This is actually the one I’m least sure of, but it seems to be what the formulas dictate. I’m pretty sure it’s never been measured, and I don’t know how it’d play off of quantum mechanics’ rules about that sort of thing.
    2. The object’s clock is stopped. The object would not appear to change in any way as it traveled; it’d be frozen in time. I know scientists are pretty sure of this, as they’ve given the fact that neutrinos DO change (oscillation) as evidence that they travel slower than light (and therefore have mass).
    3. Were you to slow down a massive object moving at the speed of light, even a tiny bit, you’d release an infinite amount of energy. Probably not a good idea outside of comic books (I’m thinking the end of Secret Wars II here…)

    It’s a bit harder to say what a (presumably massless) conscious entity traveling at the speed of light would experience, but one can imagine, and it’d be a bit weird. (Again, correct me if I’m wrong.) The universe would contract to have zero length in your direction of travel, and the entire universe’s clock would stop. By the same token as other’s seeing your clock as stopped, you’d cross the entire universe in what appeared to be an instant to you. So navigation would be…difficult.

    To put it another way, they wouldn’t experience anything at all. From their perspective, the INSTANT they reach the speed of light, they’d get where they were going (because the universe would have zero length). And where they were going is whatever they happen to run into first.

    Comment by benhead — November 25, 2008 #

  3. Ben,

    You’re right about most of this. Yes, photons have zero length, and no time appears to pass for them. However, when they pass through an expanding Universe, their wavelength expands, which is interesting and is also an indication that this is something we don’t understand about Energy (and its conservation).

    Number three is true, but if you had a massive object moving at the speed of light, it would already have an infinite amount of energy, which is bad for things like gravity. (Even in Newton’s estimation, Gm(infinity)/r^2 is a pretty unbearable force.)

    The massless example can easily be slowed down — just move it through a medium instead of a vacuum. But what would a massless object moving at c see? Nothing. Everything would be instantaneous from the POV of the massless object.

    And nobody remembers the Beyonder… or do they?

    Comment by ethan — November 25, 2008 #

  4. Ha, the Beyonder and Secret Wars II made a brief appearance in the recent absurdist 4-issue miniseries “Marvel Apes”, in the section at the end of each issue where they descibe the history of that universe. It was pretty riotously funny. :D

    Comment by benhead — November 27, 2008 #

  5. Einstein and Christ (Furthering Sean’s thoughts above)

    As a fallout of E=mc^2, if time slows to zero at the speed of light, then aging and decay also stop.

    As a consequence of his Jewish ethnicity (Jews historically were driven by their faith to discover the source and aspects of light), Einstein was consumed with the full knowledge of light.

    I find it most remarkable that in 1 John 1:5, the apostle John writes “This is the message we have heard from him and declare to you: God is light; in him there is no darkness at all.”

    If God is light (God = Light), then at the speed of light we will actually travel at the speed of God.

    John also wrote Revelation, which tells us that in verse 21:4 that in Heaven, “He (God) will wipe every tear from their eyes. There will be no more death or mourning or crying or pain, for the old order of things has passed away.”

    In summary, in the presence of God, light in its purest form, death ceases to exist.

    I do not think this coincidence. Would love to entertain your comments…

    Revelation 21
    The New Jerusalem
    1Then I saw a new heaven and a new earth, for the first heaven and the first earth had passed away, and there was no longer any sea. 2I saw the Holy City, the new Jerusalem, coming down out of heaven from God, prepared as a bride beautifully dressed for her husband. 3And I heard a loud voice from the throne saying, “Now the dwelling of God is with men, and he will live with them. They will be his people, and God himself will be with them and be their God. 4He will wipe every tear from their eyes. There will be no more death or mourning or crying or pain, for the old order of things has passed away.”

    5He who was seated on the throne said, “I am making everything new!” Then he said, “Write this down, for these words are trustworthy and true.”

    6He said to me: “It is done. I am the Alpha and the Omega, the Beginning and the End. To him who is thirsty I will give to drink without cost from the spring of the water of life. 7He who overcomes will inherit all this, and I will be his God and he will be my son. 8But the cowardly, the unbelieving, the vile, the murderers, the sexually immoral, those who practice magic arts, the idolaters and all liars—their place will be in the fiery lake of burning sulfur. This is the second death.”

    Comment by Tom Murphy — November 28, 2008 #

  6. Tom,
    You have some interesting ideas and have made some conclusions that are a bit uncommon. Time does slow to zero at the speed of light. Aging and decay stop, true, but so does living.

    As a Jew, though, I think you’re wrong on your second point that Einstein did anything that he did on account of his Jewish ethnicity, and I have a different (i.e., non-scientific) interpretation of the gospels in the Bible than you do.

    But when you’ve written your sentences above that start with 4He 5He 6He and 7He I thought you were talking about Helium isotopes and Big Bang Nucleosynthesis. Such is the mind of a scientist.

    Comment by ethan — November 28, 2008 #

  7. Which leads me to wonder what would happen if we were traveling at the speed of light and entered a black hole?

    Comment by EZSmirkzz — December 2, 2008 #

  8. I stubled on to this site because I was trying to figure out some of the issues that have already been addressed here. But if you dont mind let me ask this in very layman terms and maye someone might be able to give a very layman explanation:

    Hypothetically speaking, my driveway is 3.00×10^8 meters in length. “Joe” watches me as I run down the driveway at the speed of light and I run back to Joe at the speed of light as well. The trip has taken me 2 seconds. Why, if this is the case, would our ages now be different? I can understand that from my viewpoint anything that Joe is doings is slowed down, effectively time is standing still for Joe as I view him - but only on the trip down. On my trip back down the driveway returning to Joe would it not appear to me that time is speeding up and therefore time would “average out”? Thanks.

    Comment by bmack — December 9, 2008 #

  9. EZsmirkzz,

    You still get killed by the black hole (destroyed by tidal forces, most probably), and once you go in past the event horizon, you never come out. If you moved at the speed of light, it would feel like instant death.

    bmack,

    Joe would age two seconds and you wouldn’t age at all. Why? Because as you move at your very high velocity (super close to the speed of light), the driveway doesn’t appear to be 3×10^8 meters anymore. To you, it looks negligibly small (like, less than 1 meter), and yet it appears to be moving, relative to you, at practically the speed of light. So you can traverse it nearly instantaneously according to your clock. Same deal with the trip back. That’s why Joe times you, and you take two seconds, but you time yourself, and practically no time has passed at all.

    Comment by ethan — December 9, 2008 #

  10. Hi Ethan,

    I am in the process of writing about light and-l came across this page on what would happen if we were moving at the speed of light (http://startswithabang.com/?p=1176)

    The comment that photons do move at the speed of light is key, of course. Photons seem to do this by being pure energy. They are, I guess, everywhere in the universe at once and thus exhibit non-locality.

    I have heard that Einstein asked himself the question about moving at the speed of light. Do you know where I can find info about his thinking on this question?

    I would be happy to discuss this further with you since I am writing an ezine on vibrations that will focus on light and non-locality.

    Marty

    Comment by Marty Rosenblatt — December 29, 2008 #

  11. it’s all bs
    you can have all the formulas you want but…………..
    i leave my brother in california traveling in a car doing 3000 mps i get to ny in 3 seconds.
    be assured that for us living beings the same 3 seconds have passed for both of us..

    time is relative to distance only.
    time you get from point A to point B depending how fast you are traveling.
    but for both of you time ticks away at the same rate.

    larry

    Comment by larry zingales — September 9, 2009 #

  12. time is relative.. that is the point, you need to understand - #1 everything is moving - you - everything around you - everything around earth - everything in our solar system - everything in our milky way - then our systems within systems… e=mc2 can only understood within a zone. how do you know you are not already traveling at the speed of light? what if the idea of light is relative to what we see? if you step out of a plane how would you measure distance? — biblically, interesting, maybe we have already been here… no idea is without thought -matt

    Comment by Matt — September 19, 2009 #

  13. So this is all based of the assumption that time has a speed, and that is can be effected by gravity. Am i understanding or am i way off?

    Comment by JasonP — December 13, 2009 #

  14. Why does everyone say we can’t travel at the speed of light? Aren’t we already (relative to a photon)? Don’t they mean we can’t accelerate to the speed of light? Now that’s quite a different story I’ve been told.

    Comment by RicoPan — December 27, 2009 #

  15. One thing I find somewhat confusing in all this is the mass becoming infinite thing.
    That would seem to point to black holes having infinite mass yet their original mass is retained even though their escape velocity is in excess of light speed. In fact from the evidence their mass does not even appear to slightly increase from the original mass.

    Comment by Ken T — December 29, 2009 #

  16. wow this is soooooo gay

    Comment by fag — March 4, 2010 #

  17. So all that has been said and done! A spaceship traveling at the speed of light can actually time travel into the future but cannot reverse it by traveling at the speed of light into the past! Time travel is theoretically possible into the future but not into the past?!

    Comment by Gabriel — April 25, 2010 #

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