# Would time freeze if you could 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 universal speed limit.

1. So, if I were to travel in a spacecraft at (practically) the speed of light, would I freeze and stop moving?

2. Would the universe around me freeze and stop moving?

3. Who would the time stop for?

• – 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 zero would be infinity; therefore, you could infer that time is 'frozen' to an object traveling at the speed of light.

• 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
• @DavidZ, you're not going to prevent thought experiments with semantics! Further, all that needs to change for the question to be entirely rational is to decouple "you" from a physical entity with mass to a consciousness that exists in one or more photons. All that's relevant here is awareness. So, if a photon were to be able to "witness" things, what would it experience relative to the things it was traveling past at the speed of light? :) – Genia S. Feb 29 '16 at 2:15
• Instead of calculating T at v=c, you should calculate the lim v->c for T. That will be infinity. But if you don't use the limit, division by zero is undefined. – Oskar Skog Jul 23 '17 at 4:29
• I had a friend follow through on this reasoning. If from light's point of view time is frozen (I agree) then the light passes each point in the universe at the exact same time. In essence, there is only one "Light" and we are all in the exact same location relative to it. When we measure the speed of light we actually measure the speed of the propagation of light, the light never moves and has no speed. You also can't move AT ALL relative to light. No matter how fast you go, you are still in the same location with the rest of us. – Bill K Aug 7 '17 at 22:27
• But, wouldn't that contradict the fact that light always travels at the speed of light wrt to any inertial observer ? When you travel at $c$, the light still has to travel at $c$ wrt to you, but if the time is not going forward, there is no motion! – onurcanbektas Mar 29 at 9:05

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.

• "can't be conscious" - this is a pretty bold leap given the fact that no one has any idea what consciousness is, how it arises, and what in the universe experiences it. Now - if you say - our paltry minds simply can't visualize the paradox because we were not designed to do so - that's fine, but to decree that consciousness can't arise in a photon is pretty much the dictionary definition of begging the question. – Genia S. Dec 3 '18 at 21:51

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 $\Delta\tau = 0$.

• "You" does not have to mean a person. You in this case could be a photon. So, does time freeze for a photon? Are the photons we see from billions of years ago literally the same as they were back then and hence the movement across space was, from their perspective, instantaneous? Yes, of course we are 'anthropomorphizing' a bundle of energy but I find the question interesting and perhaps it could spark another deeper question or a different way of thinking about the universe for someone else. Calling someone's question meaningless is harsh and not becoming of a good scientist. – CramerTV Oct 24 '16 at 19:43
• @CramerTV No, "you" cannot be a photon, for basically the reasons people explain in the answers here - photons don't have a reference frame. – David Z Oct 24 '16 at 20:10
• You can't multiply a number by itself and get a negative result. Are imaginary numbers meaningless? – Marc.2377 Oct 12 '17 at 7:06
• There is a related answer at How can photons interact with anything? – Marc.2377 Oct 12 '17 at 7:25
• @Marc.2377 "Are imaginary numbers meaningless?" Why yes, they are - at least physically! They have a well-defined mathematical meaning, sure, but you can't ever meaningfully assign a complex number to a physical quantity. There's just no experiment you could make that would give you that number as a result. – Casimir Oct 12 '17 at 12:42

As pointed out you can't travel at the speed of light but you can look at the limits we are tending towards as we approach it.

So, if I were to travel in a spacecraft at the speed of light, would I freeze and stop moving?

From the perspective of a stationary observer if your spacecraft was traveling at close to the speed of light, time on the spacecraft would have slowed down (would be approaching zero or frozen). What does this mean? Everything in the spacecraft would be moving really slowly, e.g. the person moving, electrical signals, everything is slowed down by the same amount (as seen by the stationary observer).

From the perspective of a person on the spacecraft time appears to travel at it's normal rate (because if time slows down you don't notice it as everything slows down at the same rate, including your thinking process). So nothing inside the spaceship seems strange. However if you observe the stars moving past you will observe some strange effects due to aberration and the doppler shift.

See this link for what a spacecraft would see travelling at relativistic speeds.

Would the universe around me freeze and stop moving?

No, the universe keeps on working as it usually does. Essentially in the spacecraft time is moving slower than outside in the rest of the universe. So inside you're aging slower than someone outside. However you don't notice this (time appears to be running normally from your perspective) and you'll just see the stars outside become blue shifted (due to doppler effect of high speed and shifted towards a point around your direction of travel (due to aberration)). See the link above for more detail on this.

Who would the time stop for?

Nobody notices time slowing from their perspective. Instead its only the stationary observer who notes that time is slowing down for the person in the spacecraft.

• But wouldn't you immediately arrive at your ultimate destination? Meaning assuming you're going to collide with a boulder that's a billion light years away - won't you hit that boulder the instant you reach the speed of light? – Genia S. Dec 3 '18 at 21:59

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.

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.

• dont know y down voted but this really explains the true reason for the happening. +1 – Display name Nov 25 '15 at 8:37
• +1. I think that the real paradox is that those of us who live in space time can measure photons whizzing about at the speed of light. A photon isn't a single continuous thing that appears in every point along its tragectory (right?) So it's natural to ask how a photon, from its own perspective, exists along all its paths at once isn't witnessed that way by those looking at it. – Genia S. Dec 4 '18 at 0:19

When traveling with the speed of light time does not "exist". Well sort of. If a body is traveling with the speed of light its origin and destination are one and the same. The question has no point because traveling with the speed of light means you have always been and always will be traveling with the speed of light. Of course from the viewpoint of an observer the speed of light is a defined number, but for a photon time is not a "thing". So overall it wouldn't freeze so much as stop existing.

1. would your time freeze to an external observer
2. would time freeze for you, or what would you experience

The answer to #1 is yes, it would. Them mathematical description is in other answers correctly, so I am not going to repeat it. But to understand it, imagine you have small photon clocks inside your body. (to the best knowledge today, we imagine most of our mass/energy due to massless gluons traveling/oscillating at speed c in some kind of confinement, and quarks, but nobody knows what the structure of a quark would be, we think of it as pointlike). So we will take the small photon clocks as analogy to the gluons. The photon clock has mirrors, and the mirrors reflect the photon, that is a tick. As your body speeds up, the photons would have to catch up to the mirrors, but at speed c, the mirrors would move at speed c too, so the photons would never reach the mirror, no ticks. Your time froze to an external observer.

To point out, this would also mean that the internal structure of your body would freeze to an external observer, since no information could be sent any more about it, since its pieces would be moving at speed c, and the interactions inside your body, and the photon clocks, would seem frozen.

Now also to point out, according to SR length contraction, your body's size would also be pointlike to an observer.

Now to answer #2 is not so simple. You would still see your own photon clocks tick normal. And your body would therefore act normally. But you would see the whole 4th dim. at a glance. You would see the whole timeline all along its path, the beginning of the universe and the end and all of it inbetween as snapshots. And of course as a 3D viewer can see every bit of a 2D plane at once (without obstacle), you, now a 4D viewer would see every bit of the 3D world without obstacle, folded out, every 3D structure would be folded out so that without obstacle you could see every bit of it.

• #2: When time has frozen, you will perceive the time you spend travelling at c is zero. Travelling at light speed is instant teleportation, you experience nothing of the ride. – Oskar Skog Jul 23 '17 at 4:40
• Great answer and as a layperson, I think this explanation is precisely what I expect to hear. I understand that it involves a multitude of things that are contradictory and make no sense in reality but it's frustrating to keep reading answers that basically say "this is not possible, stop asking questions". – Genia S. Dec 4 '18 at 0:16

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