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I know there are several theories as to how the universe might end, if it does. Is it possible for it to end by time stopping? A friend of mine told me about this theory, but her explanation that it would be caused by heat death doesn't have me convinced.

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  • $\begingroup$ What about it doesn't convince you? $\endgroup$ – HDE 226868 Mar 18 '15 at 0:25
  • $\begingroup$ To be fair, if you were to describe a state in which all processes are no longer possible as time stopping, heat death would be time stopping. $\endgroup$ – Mitch Goshorn Mar 18 '15 at 1:18
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    $\begingroup$ What does time have to do with the energy of the Universe being evenly distributed? Is this considered a possibility because time is used by us to order and measure events, so if there aren't any more events to be measured then time wouldn't exist? $\endgroup$ – matryoshka Mar 18 '15 at 1:36
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There are several theories on how the universe might end by time stopping. The problem with cosmology and some other parts of theoretical physics is that it cannot be proven, nor reproduced or tested. This makes it often more a faith/religion than a science. So, if you notice some irony in my answer, please, it's because of this.

There are two types of theories which fantasize about the end of the universe by end of times. I freely call those type the formula type and transcendental type theories.

The first theory I will only briefly describe, because they end up transcendental anyway. There are several models on the universe that will describe what the universe (or universes) looks like and how they will evolve in time. The problem with these models is the variable time. If you have an endless time or an endless amount of universes, you end up with an endless amount of possibilities, which will result in all things will eventually happen. So, somewhere in time or a universe we will all become filthy rich and marry a gorgeous, intelligent, funny, friendly, etc., woman/man that never says no (to you). Because of this anomaly scientists have started to theorize that time must end at some point. If you believe these models to be correct, the scientists might be right. The problem in this lies that you first must believe the model is right.

The transcendental theories are a bit more difficult to explain and I will briefly leap out of astronomy into philosophy. In the 18th century a great philosopher wrote a book on the critique of pure reason (Kritik der reinen Vernunft). In this book he was looking for a transcendental doctrine of method and elements. The transcendental part of his doctrine was that it had to be build up on a priori knowledge that was not based on experience. This was his pure reason, because the elements and the methods are not tainted by (personal) experience from an observer. They are true in itself.

Why is this interesting? Because Kant (that great philosopher) said that there were two transcendental elements, space and time. I will skip space, but must say something on time, because someone thinks it might end. Kant states that time is an a priori element of knowledge in pure form. Kant uses five reasons, why time is universal and not empirical. They all can be brought back to the fact that we cannot see things/phenomena to coexist together or successively when there is no concept of time. Therefore, time is an a priori element of pure form.

Now, what has this to do with the ending of the universe in respect to time? The theory you mentioned as heat death is such a transcendental theory. The theory states that the universe expands until the universe is too big to be heated by the energy provided by the matter in the universe. This theory models that the universe follow the same rules as any thermo dynamic system and therefore at a certain point in time all energy, matter and temperature are evenly distributed in this huge universe. Because all is evenly distributed no stars will be created and all processes come to a grinding halt. Since the state before, now and after are the same, the scientists now determine this as the end of time. The formula theories also end up making some theory that time will end.

The problem with these theories is that time will never end. According to Kant time is an a priori element of pure reason and will be there despite of what we observe. Because the state of the universe doesn't change, doesn't mean that there will be no time. Time has just stopped. Theories that state that time will end, do not comply with Kant's critique of pure reason, which states that time is the formal condition of all phenomena whatsoever.

If it didn't entirely answered your question, I hope it was entertaining and educational.

Kind regards, MacUserT

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For a more analytical and much much less philosophical version of an answer than MacUserT's, here it is.

According to MacUserT,

Now, what has this to do with the ending of the universe in respect to time? The theory you mentioned as heat death is such a transcendental theory. The theory states that the universe expands until the universe is too big to be heated by the energy provided by the matter in the universe. This theory models that the universe follow the same rules as any thermo dynamic system and therefore at a certain point in time all energy, matter and temperature are evenly distributed in this huge universe. Because all is evenly distributed no stars will be created and all processes come to a grinding halt. Since the state before, now and after are the same, the scientists now determine this as the end of time. The formula theories also end up making some theory that time will end.

My issue with this statement, lies in the facts that the eventual heat death of the universe is not so much a transcendental theory so much as it is a thermodynamic law. The heat death of the universe is more closely attached to the lifetime of stars in the universe than the cooling of an evenly distributed temperature throughout space. As galaxies age, they contain less and less star forming regions, thereby creating less and less stars.

Less stars means less heat, and when the final stars and white dwarfs die and cool off respectively the entirety of the universe will finally be able to reach 0K. This is no insignificant timescale, keep in mind that WDs take about $10^{13}$ years just to cool from their initial states down to a temperature where they will no longer emit visible light, which means they could take another $10^{20}$ years to reach anything close to zero kelvin.

Regarding the even distribution of temperature. Space already has a fairly homogeneous distribution of heat ~2.7K it's called the CMB, and it has been cooling since the big bang, and there is no source of heat that will allow for an increase of this temperature on a whole, or in one word... entropy. Space is far too vast and heat sources are far too ... far ... apart to ever affect anything other than extremely local conditions.

Now for the end of time issue. The idea of time involves the transmission of information. For example, if you send a radio transmission to the moon and back, you will state that some time has passed from the sending to the receiving of the transmission. This process is possible because there is a temperature above 0K, for the electromagnetic waves to propagate. Meaning that when the temperature of all space reaches 0K, there will be no energy available for electromagnetic waves to propagate. Thus no information can be transmitted, and time ... is at a standstill.

Therefore, the universe would not end by time stopping, because time stopping is a by product of the "universe ending" because its heat death.

For a fun version of this question being answered, check out Issac Asimov's short story The Last Question Click here to go to Princeton's pdf version of it.

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