# Would time freeze if you can travel at the speed of light?

I read with interest about Einstein's Theory of Relativity and his proposition about the speed of light being the speed limit for anything with mass. So, if I were to travel in a spacecraft at the speed of light, would I freeze and stop moving? Would the universe around me freeze and stop moving? Who would the time stop for?

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Since you can't move at the speed of light, you should phrase this question about travelling at less than the speed of light. –  Ron Maimon May 28 '12 at 7:23
even so time would not change for you individually only if you returned to the place that you started would you realize that you have had a different experiance of time without returning to compare your time/ageing with the origin of your travels you would not experiance for instance slow motion or any such observable discrepency –  Argus May 28 '12 at 18:07
Does the "place" actually have anything to do with it. I've seen this in documentaries, well the "3" I've watched, and they use this idea but isn't the idea to do with relative velocity? i.e. if you went out into space for 1 light year and then returned all at the speed of light, and I stayed in earth orbit going round and round at the speed of light for 2 years there wouldn't be any relative difference between you or I would there? Clearly u would have had the better time but age wise = same? –  rism Aug 5 '12 at 4:21
–  Ben Crowell May 18 '13 at 18:55

Yes, I agree with David. If somehow, you were able to travel at the speed of light, it would seem that 'your time' would not have progressed in comparison to your reference time once you returned to 'normal' speeds. This can be modeled by the Lorentz time dilation equation:

$$T=\frac{T_0}{\sqrt{1 - (v^2 / c^2)}}$$

When traveling at the speed of light ($v=c$), left under the radical you would have 0. This answer would be undefined or infinity if you will (let's go with infinity). The reference time ($T_0$) divided by infinity would be 0; therefore, you could infer that time is 'frozen' to an object traveling at the speed of light.

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It's not an image. –  Ignacio Vazquez-Abrams May 28 '12 at 19:43
I'm kind of wary about using the phrase "if you were able to travel at the speed of light," because you can't, and in my experience when you say anything less than "this is unequivocally not possible" people start to get ideas that they really shouldn't. Although this does get the point across. –  David Z May 29 '12 at 17:49
@user37390 No. One can get arbitrarily close, which is a different thing. This is similar to saying that you can count as high as you like, but you will never get to infinity. –  dmckee Mar 17 at 18:12

You can't travel at the speed of light. So it's a meaningless question.

The reason some people will say that time freezes at the speed of light is that it's possible to take two points on any path going through spacetime at less than the speed of light and calculate the amount of time that a particle would experience as it travels between those points along that path. The calculation is

$$\Delta\tau^2 = \Delta t^2 - \frac{1}{c^2}(\Delta x^2 + \Delta y^2 + \Delta z^2)$$

where $\Delta\tau$ is the amount of time experienced by the traveling particle, and the other $\Delta$'s are the differences in space and time coordinates between the two points as measured by an external observer. If you take this same calculation and blindly apply it to a path which is at the speed of light, you get $\Delta\tau = 0$.

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nice answer, but probably not at the level of the op –  Larry Harson May 28 '12 at 16:41
Hey, nothing wrong with exposing people to a little math ;-) –  David Z May 28 '12 at 17:00

This kind of question has a long and honorable history. As a young student, Einstein tried to imagine what an electromagnetic wave would look like from the point of view of a motorcyclist riding alongside it. But we now know, thanks to Einstein himself, that it really doesn't make sense to talk about such observers.

The most straightforward argument is based on the positivist idea that concepts only mean something if you can define how to measure them operationally. If we accept this philosophical stance (which is by no means compatible with every concept we ever discuss in physics), then we need to be able to physically realize this frame in terms of an observer and measuring devices. But we can't. It would take an infinite amount of energy to accelerate Einstein and his motorcycle to the speed of light.

Since arguments from positivism can often kill off perfectly interesting and reasonable concepts, we might ask whether there are other reasons not to allow such frames. There are. One of the most basic geometrical ideas is intersection. In relativity, we expect that even if different observers disagree about many things, they agree about intersections of world-lines. Either the particles collided or they didn't. The arrow either hit the bull's-eye or it didn't. So although general relativity is far more permissive than Newtonian mechanics about changes of coordinates, there is a restriction that they should be smooth, one-to-one functions. If there was something like a Lorentz transformation for v=c, it wouldn't be one-to-one, so it wouldn't be mathematically compatible with the structure of relativity. (An easy way to see that it can't be one-to-one is that the length contraction would reduce a finite distance to a point.)

What if a system of interacting, massless particles was conscious, and could make observations? The argument given in the preceding paragraph proves that this isn't possible, but let's be more explicit. There are two possibilities. The velocity V of the system's center of mass either moves at c, or it doesn't. If V=c, then all the particles are moving along parallel lines, and therefore they aren't interacting, can't perform computations, and can't be conscious. (This is also consistent with the fact that the proper time s of a particle moving at c is constant, ds=0.) If V is less than c, then the observer's frame of reference isn't moving at c. Either way, we don't get an observer moving at c.

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Velocity is relative, so it doesn't matter if you're "travelling" at some speed relative to something, or something is travelling at some velocity relative to you - the effects are the same. Right now you have objects in the universe travelling at a wide range of velocities relative to you. If you decided to change your speed to close to the speed of light compared to what it is now, you will find that there is still the same range of velocities of objects relative to you. That's because objects that were travelling close to c in the direction of your increase will have slowed down, and objects that were travelling in the opposite direction will have increased their velocity.

However, you will also find that as objects increase their speed relative to you, the sequence of events there slow down, and that includes the running of their clocks from your view point, which approaches zero as their speed approaches the speed of light.

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The time wouldn't freeze. Instead, all events in the world will happen at the same time and place (from the viewpoint of the observer travelling at the light speed).

It would be better to say that the world (i.e. space & time) would collapse into single point.

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I'm a total novice but i watched NOVA's "Brian Greene's Fabric of the Cosmos" on YouTube and as i understand it, "your" space and time share a finite amount of energy at any given moment called Space-Time.

So the finite amount energy available at any given moment can be consumed "either" by motion through space or ticks of some clock.

But the more you use that energy for one aspect of SpaceTime i.e. motion or ticks, the less there is for the other... kinda like the way your computer seems to run slower the more programs you run at once i.e. a finite amount of processing power is available at any given moment to be distributed among applications.

The upper limit of motion being the speed of light.

So the closer you travel to the speed of light the more energy for a given moment is assigned/consumed by motion, leaving less and less energy for time to tick (relative to someone else). Therefore the slower time goes (relatively speaking).

So the faster you go, the slower time "appears" to go relative to a slower observer because most of your space time energy is being consumed by motion whereas more of theirs is being used for time to tick.

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You seem to have gotten a garbled message here. It is true that all inertial observed can agree on the "interval" between to points in space-time and that the interval is calculated by using space and time components with opposite signs, but the rest is a bit of a mess... –  dmckee Aug 5 '12 at 5:23

## protected by Qmechanic♦May 4 '13 at 12:58

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