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Is the present just a sharp line between the past and the future with no time at all, or is the present a short frozen unit of time?

Could time be quantized into a fundamental units? Like Planck time or some other briefest unit of time? Does then time itself jump from one time unit to the next time unit, because there is nothing between? Could everything at the smallest timescale be a frozen 3D-picture, similar to the 2D-pictures in a motion picture? Could this reality be something like a 3D-motion picture with pictures shown with a time frequency?


I guess we will never know if time is quantized if we don't measure that it is quantized. Like if we find something with a high frequency that are affected by the frequency of the fundamental time units. There is one such observation of the redshifted light from galaxies which seem to cluster to specific bands in the energy spectrum:

"The redshifted light we observe is consists of photons, discrete 'particles' of light energy. The energy of a photon is the product of a physical constant (Planck's constant) times the frequency of the light. Frequency is defined as the reciprocal of time, so if only certain redshifts are possible, then only certain energies are present, and hence only certain frequencies (or, equivalently, time intervals) are allowed. To the extent that redshifts of galaxies relate to the structure of time, then, it suggests an underlying quantization.

"In our newest theoretical models we have learned to predict the energies involved. We find that the times involved are always certain special multiples of the 'Planck time,' the shortest time interval consistent with modern physical theories."

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marked as duplicate by Ben Crowell, Brandon Enright, Waffle's Crazy Peanut, twistor59, Qmechanic Jun 13 '13 at 18:01

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You are actually asking if time is quantized. This is different than talking of units in planck time, as they can be as continuous as one wants. There are theories where space is considered quantized, but are not mainstream. At the Planck scale general relativity reigns and there is a problem with the definition of time. It is not a simple problem. – anna v Jun 13 '13 at 10:44
Stuff like this can't be proved, really. Whether time is quantized, or is a continuous flow, I doubt anyone will ever be able to confirm. What we can always do is make an assumption, and choose the assumption which answers most questions appropriately, and fitting in with other data/laws/information too. – mikhailcazi Jun 13 '13 at 10:50
Mikhail: that's simply not true. The assumption of a discrete time in this sense is a very bold conjecture that has many consequences - independently of other aspects of the theories with which it may co-exist - and one may easily empirically demonstrate that it's wrong. – Luboš Motl Jun 13 '13 at 11:06
Lubos: that's not true. Your proof that there is no discrete time makes assumptions about physics that we currently have no way to tell whether they are true or not. – Peter Shor Jun 13 '13 at 13:39
@Dilaton: I didn't say that the lattice in lattice QCD actually exists. But the fact that lattice QCD works shows that you can put dynamics that act just like quantum field theories onto a system with quantized time and space. How can we know that nature isn't doing the same thing with a completely different quantization of time and space? We can't, unless we understand dynamics at the Planck scale. – Peter Shor Jun 13 '13 at 19:13

1 Answer 1

To answer this question, it is easiest to do a thought experiment. Let us assume there is a smallest unit of time and that things cannot change until said smallest unit elapses. It would not be out of line, then, to postulate that every measurable amount of time must be an integer multiple of this smallest unit (call it t). If our thought experiment doesn't offer any logical contradictions, then we should be able to say it is separated into smallest units.

Now, let's say I've invented a new type of propulsion that is capable of accelerating so fast (note: I've got inertial dampeners) that I can reach 0.5c after one t. I put one of these drives at the back of a spaceship and one at the side; at a right angle (not really necessary but I chose to do it anyway). Now you and me agree to a little experiment. We both have computers capable of performing one process per t. You are going to set up your computer so that every t a light will turn on or turn off. I am going to jump in my spaceship, hit the accelerator, stay at max speed for one t then stop. The distance I travel should be something almost unnoticeable, so I don't have to worry about coming back. A third computer will be hooked up to a camera that takes a photo every t (just so that we can actually see what happens).

Here's what we might find. Starting at the same time, your light flashes on and I hit the gas. In your frame, one t later the light flashes off and then on again after another t, and finally off a third t after that. The experiment is over for you. In my frame, one t after I hit the gas, I'm accelerated to ${1\over\sqrt2}c$, I travel at that speed for another t, at which point I hit the brake and after a third t, I find myself at rest again with the experiment over. See the problem?

Let's watch the tape. Time=0: I hit gas and your light turns on. Time=t: your light turns off and I reach ${1\over\sqrt2}c$ (I didn't change in the intervening time so no time dilation affected me then). Time=2t: your light turns on. Time=$(1+\sqrt2)t$: I hit the brakes. Time=3t: your light turns off. Time=$(1+2\sqrt2)t$: I come to a complete stop.

Of course, what the camera will record is only what happens every t. Nevertheless, at 3t, I'm still moving but my brakes are already hit. At 4t, I would already be at rest. Herein lies the problem, Now that we're in the same reference frame, when can I change? would any motion for me take place at the same times as any motion for you? If so, what about my first motion after the experiment? It clearly could not be a multiple of t separated from my previous one. If not, then are we forever separated in actions by a fraction of t? Would that not seem to contradict the idea that everything must be separated by integer multiples of t?

Any way you look at it, there must be a smaller unit of time than t. In my frame I experienced 3t, in your frame you experienced 3t. But when I rejoined your frame, I am a non-integer multiple of t out of sync. A smaller unit is required to allow for this.

I realized that this is not a fact-based answer. Nor does it present anything more than a conceptual experiment. I also realize that GR is prevalent in that time scale and that I used only SR. However, you can scale up all times in this experiment to SR timescales and find that the time difference between us is still a non-integer multiple.

Hopefully, while not directly answering your question, this helps to allow you to come to a conclusion of your own.

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This is really an answer to a different question,… , and I don't think it's a correct answer. – Ben Crowell Jun 13 '13 at 16:52
@Ben fair enough. I had a feeling the ideal point was good but my argument is terrible. Would you say I could make it correct by your standards? Or is it a write off? Can you point out, perhaps, the most incorrect thing about it? – Jim Jun 13 '13 at 16:56
Here's a thought. If time and space are both quantized, then we might say that the speed of light is such that each t the wave propogates 1 unit of space. But how to explain things moving less than the speed of light? Something travelling at 1/10th of the speed of light would only propogate 1 unit every 10t. How does it "know" when 10t are up and it is time to move? – Michael Jun 13 '13 at 17:05
These arguments are assuming classical mechanics. The universe is quantum. – Peter Shor Jun 13 '13 at 19:16
@Jim Nice spaceship! Thank you for not answering my question and thereby helping me to come to a conclusion of my own:-) The frequency of EM-radiation could be affected by the frequency of the fundamental time unit as the updated question shows. I don't see why time and space can't both be a computer they are. – Enos Oye Jun 14 '13 at 9:26

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